Given condition, \[2x2\text{ }\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }x\text{ }=\text{ }0\] \[4x2\text{ }\text{ }x\text{ }=\text{ }0\] \[x\left( 4x\text{ }\text{ }1 \right)\text{ }=\text{...

### For each graph given alongside, write an inequation taking x as the variable:

(i) (ii) Solution:- (i) \[x\text{ }\le \text{ }1,\text{ }x\in R\] (ii) \[x\text{ }\ge \text{ }2,\text{ }x\in R\]

### Represent the following inequalities on real number line: -5 < x ≤ -1

\[-\text{ }5\text{ }<\text{ }x\text{ }\le \text{ }-\text{ }1\] Arrangement on the number line is as beneath

### Represent the following inequalities on real number line: (i) -2 ≤ x -3

(i) \[-\text{ }2\text{ }\le \text{ }x\text{ }<\text{ }5\] Arrangement on the number line is as beneath (ii) \[8\text{ }\ge \text{ }x\text{ }>\text{ }-\text{ }3\] Arrangement on the...

### Solve equation using factorization method: x2 – 16 = 0

Given condition, \[x2\text{ }\text{ }16\text{ }=\text{ }0\] \[x2\text{ }+\text{ }4x\text{ }\text{ }4x\text{ }+\text{ }16\text{ }=\text{ }0\] \[x\left( x\text{ }+\text{ }4 \right)\text{ }-\text{...

### Represent the following inequalities on real number line: (i) 2(2x – 3) ≤ 6 (ii) -4 < x < 4

(i) \[2\left( 2x\text{ }\text{ }3 \right)\text{ }\le \text{ }6\] \[\begin{array}{*{35}{l}} 4x\text{ }\text{ }6\text{ }\le \text{ }6 \\ 4x\text{ }\le \text{ }12 \\ x\text{ }\le \text{ }3 \\...

### Represent the following inequalities on real number line: (i) 2x – 1 < 5 (ii) 3x + 1 ≥ -5

(I) \[2x\text{ }\text{ }1\text{ }<\text{ }5\] \[\begin{array}{*{35}{l}} 2x\text{ }<\text{ }6 \\ x\text{ }<\text{ }3 \\ \end{array}\] Arrangement on the number line is as beneath ...

### Solve equation using factorization method: x2 – 10x – 24 = 0

Given condition, \[x2\text{ }\text{ }10x\text{ }\text{ }24\text{ }=\text{ }0\] \[x2\text{ }\text{ }12x\text{ }+\text{ }2x\text{ }\text{ }24\text{ }=\text{ }0\] \[x\left( x\text{ }\text{ }12...

### If 25 – 4x ≤ 16, find: (i) the smallest value of x, when x is a real number, (ii) the smallest value of x, when x is an integer.

\[\begin{array}{*{35}{l}} 25\text{ }\text{ }4x\text{ }\le \text{ }16 \\ -\text{ }4x\text{ }\le \text{ }16\text{ }\text{ }25 \\ -\text{ }4x\text{ }\le \text{ }-\text{ }9 \\ x\text{ }\ge \text{...

### Solve the inequation: 3 – 2x ≥ x – 12 given that x ∈ N.

\[\begin{array}{*{35}{l}} 3\text{ }\text{ }2x\text{ }\ge \text{ }x\text{ }\text{ }12 \\ -\text{ }2x\text{ }\text{ }x\text{ }\ge \text{ }-\text{ }12\text{ }\text{ }3 \\ \end{array}\]...

### If the replacement set is the set of whole numbers, solve: (i)x – 3/2 < 3/2 – x (ii) 18 ≤ 3x – 2

(i) \[x\text{ }\text{ }3/2\text{ }<\text{ }3/2\text{ }\text{ }x\] \[\begin{array}{*{35}{l}} x\text{ }+\text{ }x\text{ }<\text{ }3/2\text{ }+\text{ }3/2 \\ 2x\text{ }<\text{ }3 \\ x\text{...

### If the replacement set is the set of whole numbers, solve: (i) 8 – x > 5 (ii) 7 – 3x ≥ -1/2

(i) \[8\text{ }\text{ }x\text{ }>\text{ }5\] \[\begin{array}{*{35}{l}} \text{ }x\text{ }>\text{ }5\text{ }\text{ }8 \\ \text{ }x\text{ }>\text{ }-\text{ }3 \\ x\text{ }<\text{ }3 \\...

### If the replacement set is the set of whole numbers, solve: (i) x + 7 ≤ 11 (ii) 3x – 1 > 8

(I) \[x\text{ }+\text{ }7\text{ }\le \text{ }11\] \[\begin{array}{*{35}{l}} x\text{ }\le \text{ }11\text{ }\text{ }7 \\ x\text{ }\le \text{ }4 \\ \end{array}\] As the substitution set = \[W\](set...

### If x ∈ N, find the solution set of inequations. (i) 5x + 3 ≤ 2x + 18 (ii) 3x – 2 < 19 – 4x

(I) \[5x\text{ }+\text{ }3\text{ }\le \text{ }2x\text{ }+\text{ }18\] \[\begin{array}{*{35}{l}} 5x\text{ }\text{ }2x\text{ }\le \text{ }18\text{ }\text{ }3 \\ 3x\text{ }\le \text{ }15 \\ x\text{...

### State whether the following statements are true or false. (i)If a – c > b – d, then a + d > b + c (ii) If a ** 0, then a – c > b – c Where a, b, c and d are real numbers and c ≠ 0.**

(i) Given proclamation is valid. As \[a\text{ }\text{ }c\text{ }>\text{ }b\text{ }\text{ }d\Rightarrow a\text{ }+\text{ }d\text{ }>\text{ }b\text{ }+\text{ }c\] (ii) Given proclamation is...

### State whether the following statements are true or false. (i) If a

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### State whether the following statements are true or false. (i) If a ** bc (ii) If a > b, then a/c < b/c Where a, b, c and d are real numbers and c ≠ 0.**

(i) Given articulation is bogus. (As per rule\[3\]) (ii) Given articulation is bogus. (As per rule\[3\])

### State whether the following statements are true or false. (i) a < b, then a – c

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### State whether the following statements are true or false. (i) a < b, then a – c ** b, then a + c > b + c Where a, b, c and d are real numbers and c ≠ 0.**

(I) Given articulation is valid. (Taking away equivalents on the two sides won't change the disparity) (ii) Given articulation is valid. (Including approaches the two sides won't change the...

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### State, true or false: (i)2x ≤ -7 ⇒ 2x/-4 ≥ -7/-4 (ii) 7 > 4 ⇒ 1/7 < 1/5

(i) Given proclamation is valid. (as per Rule\[4\]) (ii) Given proclamation is valid. (as indicated by Rule\[6\])

### State, true or false: (i) x y (ii) -5x ≥ 15 ⇒ x ≥ -3

(I) Given articulation is valid. (as indicated by Rule\[5\]) (ii) Given proclamation is bogus. (as indicated by Rule\[4\])

### Find the value of ‘p’, if the following quadratic equations has equal roots: (i) 4×2 – (p – 2)x + 1 = 0 (ii) x2 + (p – 3)x + p = 0

(i) \[4x2\text{ }\text{ }\left( p\text{ }\text{ }2 \right)x\text{ }+\text{ }1\text{ }=\text{ }0\] Here, \[a\text{ }=\text{ }4,\text{ }b\text{ }=\text{ }-\text{ }\left( p\text{ }\text{ }2...

### Without solving, comment upon the nature of roots of each of the following equations:(v) x2 – ax – b2 = 0 (vi) 2×2 + 8x + 9 = 0

(v) Given quadratic condition, \[x2\text{ }\text{ }ax\text{ }\text{ }b2\text{ }=\text{ }0\] Here, \[a\text{ }=\text{ }1,\text{ }b\text{ }=\text{ }-\text{ }an\text{ }and\text{ }c\text{ }=\text{...

### Without solving, comment upon the nature of roots of each of the following equations:(iii) 25×2 – 10x + 1= 0 (iv) x2 + 2√3x – 9 = 0

(iii) Given quadratic condition, \[25x2\text{ }\text{ }10x\text{ }+\text{ }1\text{ }=\text{ }0\] Here, \[a\text{ }=\text{ }25\] , \[b\text{ }=\text{ }-\text{ }10\] and \[c\text{ }=\text{ }1\] Along...

### Without solving, comment upon the nature of roots of each of the following equations: (i) 7×2 – 9x +2 = 0 (ii) 6×2 – 13x +4 = 0

(i) Given quadratic condition, \[7x2\text{ }\text{ }9x\text{ }+\text{ }2\text{ }=\text{ }0\] Here, \[a\text{ }=\text{ }7\] , \[b\text{ }=\text{ }-\text{ }9\] and \[c\text{ }=\text{ }2\] Along these...

### Is x = -3 a solution of the quadratic equation 2×2 – 7x + 9 = 0?

Given quadratic condition, \[2x2\text{ }\text{ }7x\text{ }+\text{ }9\text{ }=\text{ }0\] We realize that, for \[x\text{ }=\text{ }-\text{ }3\] to be arrangement of the given quadratic condition it...

### Is x = 5 a solution of the quadratic equation x2 – 2x – 15 = 0?

Given quadratic condition, \[x2\text{ }\text{ }2x\text{ }\text{ }15\text{ }=\text{ }0\] We realize that, for \[x\text{ }=\text{ }5\] to be an answer of the given quadratic condition it ought to...

### Find which of the following equations are quadratic (v) 7×3 – 2×2 + 10 = (2x – 5)2 (vi) (x – 1)2 + (x + 2)2 + 3(x + 1) = 0

\[\left( v \right)\text{ }7x3\text{ }\text{ }2x2\text{ }+\text{ }10\text{ }=\text{ }\left( 2x\text{ }\text{ }5 \right)2\] ⇒ \[7x3\text{ }\text{ }2x2\text{ }+\text{ }10\text{ }=\text{ }4x2\text{...

### Find which of the following equations are quadratic (iii) (x -4) (3x + 1) = (3x – 1) (x + 2) (iv) x2 + 5x – 5 = (x – 3)2

(iii) \[\left( x\text{ }\text{ }4 \right)\text{ }\left( 3x\text{ }+\text{ }1 \right)\text{ }=\text{ }\left( 3x\text{ }\text{ }1 \right)\text{ }\left( x\text{ }+2 \right)\] ⇒ \[3x2\text{ }+\text{...

### Find which of the following equations are quadratic: (i) (3x – 1)2 = 5(x + 8) (ii) 5×2 – 8x = -3(7 – 2x)

(i) \[\left( 3x\text{ }\text{ }1 \right)2\text{ }=\text{ }5\left( x\text{ }+\text{ }8 \right)\] ⇒ \[(9x2\text{ }\text{ }6x+\text{ }1)\text{ }=\text{ }5x\text{ }+\text{ }40\] ⇒\[9x2\text{ }\text{...

### A man invests Rs 3,072 in a company paying 5% per annum, when its Rs 10 share can be bought for Rs 16 each. Find: (i) his annual income (ii) his percentage income on his investment.

Given, Market worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }16\] Nominal worth of \[1\text{ }share=\text{ }Rs\text{ }10\] Also, the cash contributed \[=\text{ }Rs3,072\] Thus, the quantity of...

### Find the annual income derived from 125, Rs.120 shares paying 5% dividend.

Given, The Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }120\] In this way, the ostensible worth of \[125\text{ }offers\text{ }=\text{ }125\text{ }x\text{ }Rs\text{ }120\text{ }=\text{...

### A man invests Rs800 in buying Rs5 shares and when they are selling at a premium of Rs1.15, he sells all the shares. Find his profit and profit percent.

Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }5\] Market esteem \[1\text{ }offer\text{ }=\text{ }Rs\text{ }5\text{ }+\text{ }Rs\text{ }1.15\text{ }=\text{ }Rs6.15\] All out cash...

### Find the cost of 85 shares of Rs 60 each when quoted at Rs 63.25.

Given, Market worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }63.25\] In this way, the market worth of \[85\text{ }shares\] \[=\text{ }Rs\text{ }63.25~x~85\] \[=\text{ }Rs\text{...

### A person buys 120 shares at a nominal value of Rs 40 each, which he sells at Rs 42.50 each. Find his profit and profit percent.

Given, The nominal worth of each offer is \[Rs\text{ }40\] In this way, the ostensible worth of \[120\text{ }offers\text{ }=\text{ }Rs\text{ }40\text{ }x\text{ }120\text{ }=\text{ }Rs\text{ }4,800\]...

### How much money will be required to buy 250, Rs.15 shares at a discount of Rs.1.50?

The quantity of offers to be purchased is \[250.\] Furthermore, \[Rs\text{ }15\]offers at a markdown of \[Rs\text{ }1.50\]means Nominal worth of the offer is \[Rs\text{ }15\]and Its reasonable worth...

### How much money will be required to buy 400, Rs.12.50 shares at a premium of Rs.1?

Given, The quantity of offers needed to be purchased \[=\text{ }400\] What's more, \[Rs\text{ }12.50\]offers at a higher cost than normal of \[Rs\text{ }1\]method; Ostensible worth of the offer is...

### A company, with 10,000 shares of Rs 100 each, declares an annual dividend of 5%. If he received only 4% of his investment, find the price he paid for each share.

Given, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs100\] Then, at that point, nominal worth of \[10,000\text{ }offers\text{ }=10,000\text{ }x\text{ }Rs\text{ }100=\text{ }Rs\text{...

### A company, with 10,000 shares of Rs 100 each, declares an annual dividend of 5%. (i) What is the total amount of dividend paid by the company? (ii) What should be the annual income of a man who has 72 shares in the company?

Given, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs100\] Then, at that point, nominal worth of \[10,000\text{ }offers\text{ }=10,000\text{ }x\text{ }Rs\text{ }100=\text{ }Rs\text{...

### A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% on his money. Calculate: (i) the amount invested by him. (ii) the rate of dividend paid by the company.

The nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }20\] Market worth of \[1\text{ }offer\text{ }=\text{ }Rs20\text{ }\text{ }\left( 20percent\text{ }of\text{ }Rs\text{ }20 \right)\]...

### A man buys 400, twenty-rupee shares at a premium of Rs 4 each and receives a dividend of 12%. Find: percentage return on his money.

Given, The nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }20\] Market worth of $1$ \[~offer\text{ }=\text{ }Rs\text{ }20\text{ }+\text{ }Rs\text{ }4\text{ }=\text{ }Rs\text{ }24\] No....

### A man buys 400, twenty-rupee shares at a premium of Rs 4 each and receives a dividend of 12%. Find: (i) the amount invested by him. (ii) his total income from the shares.

Given, The nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }20\] Market worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }20\text{ }+\text{ }Rs\text{ }4\text{ }=\text{ }Rs\text{ }24\]...

### A company declares a dividend of 11.2% to all its share-holders. If its Rs 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company, in order to have an annual income of Rs 1,680?

Given, Nominal value of \[1\text{ }share\text{ }=\text{ }Rs60\] Market value of 1 share \[~=\text{ }Rs\text{ }60\text{ }+\text{ }25percent\text{ }of\text{ }Rs\text{ }60\] \[=\text{ }Rs\text{...

### How much should a man invest in Rs 100 shares selling at Rs 110 to obtain an annual income of Rs 1,680, if the dividend declared is 12%?

From the inquiry, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs100\] Also, the market worth of \[1\text{ }offer\text{ }=\text{ }Rs110\] Let the quantity of offers bought \[=\text{ }n\] Then,...

### A company declares 8 percent dividend to the shareholders. If a man receives Rs 2,840 as his dividend, find the nominal value of his shares.

Given, \[Profit\text{ }percent\text{ }=\text{ }8\text{ }percent\] Also, the profit is \[Rs\text{ }2,840\] Leave the Nominal worth of offers alone \[Rs\text{ }y\] Then, at that point,...

### Rs 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 percent.

Given, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }50\] Markdown on each offer \[=\text{ }10\text{ }percent\] Thus, the market worth of \[1\text{ }offer\text{ }=\text{ }Rs50\text{...

### Hundred rupee shares of a company are available in the market at a premium of Rs 20. Find the rate of dividend given by the company, when a man’s return on his investment is 15%.

Given, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }100\] Furthermore, the market worth of \[=\text{ }Rs100\text{ }+\text{ }Rs\text{ }20\text{ }=\text{ }Rs120\] (as the premium is Rs...

### By purchasing Rs 25 gas shares for Rs 40 each, a man gets 4 percent profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?

Given, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs25\] Market worth of \[1\text{ }offer\text{ }=\text{ }Rs40\] Also, the profit% on speculation \[=\text{ }4percent\] Then, at that point,...

### A man buys 75, Rs 100 shares paying 9 percent dividend. He buys shares at such a price that he gets 12 percent of his money. At what price did he buy the shares?

Given, Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs100\] In this way, the nominal worth of \[75\text{ }shares\text{ }=\text{ }100\text{ }x\text{ }75\text{ }=\text{ }Rs\text{ }7,500\]...

### A man invested Rs45,000 in 15% Rs100shares quoted at Rs125. When the market value of these shares rose to Rs140, he sold some shares, just enough to raise Rs8,400. Calculate: (i)the number of shares he still holds; (ii)the dividend due to him on these remaining shares.

(I) Total speculation \[=\text{ }Rs\text{ }45,000\] Furthermore, the market worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }125\] Hence, the quantity of offers bought \[=\text{ }45000/125\text{...

### Ashok invested Rs.26,400 in 12%, Rs.25 shares of a company. If he receives a dividend of Rs.2,475, find the: (i) number of shares he bought. (ii) market value of each share.

(I) Given, absolute profit \[=\text{ }Rs\text{ }2,475\] Along these lines, the profit on each offer \[=\text{ }12%\text{ }of\text{ }Rs\text{ }25\text{ }=\text{ }12/100\text{ }x\text{ }Rs\text{...

### Mr. Gupta has a choice to invest in ten-rupee shares of two firms at Rs13 or at Rs16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find: (i) which firm is paying better. (ii) if Mr. Gupta invests equally in both the firms and the difference between the returns from them is Rs 30, find how much, in all, does he invest.

(I) The primary firm: \[\begin{array}{*{35}{l}} Nominal\text{ }worth\text{ }of\text{ }1\text{ }offer\text{ }=\text{ }Rs\text{ }10 \\ Market\text{ }worth\text{ }of\text{ }1\text{ }offer\text{...

### A man invests a certain sum of money in 6% hundred-rupee shares at Rs.12 premium. When the shares fell to Rs.96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs.8. If the change in his income is Rs.540, Find the sum invested originally

How about we expect the first total contributed to be \[Rs\text{ }x\] Then, at that point, the quantity of \[Rs\text{ }100\]offers bought at premium of \[Rs\text{ }12\]will be \[=\text{ }x/\left(...

### Gopal has some Rs.100 shares of company A, paying 10% dividend. He sells a certain number of these shares at a discount of 20% and invests the proceeds in Rs.100 shares at Rs.60 of company B paying 20% dividend. If his income, from the shares sold, increases by Rs.18,000, find the number of shares sold by Gopal.

Given, The nominal worth of each offer \[=\text{ }Rs\text{ }100\] Pace of profit \[=\text{ }10%\] Profit on each offer \[=\text{ }10%\text{ }of\text{ }Rs\text{ }100\text{ }=\text{ }Rs\text{ }10\]...

### Ashwarya bought 496, Rs.100 shares at Rs.132 each, find: How much extra must Ashwarya invest in order to increase her income by Rs.7,200

Given, The nominal worth of each offer \[=\text{ }Rs\text{ }100\] Market cost of each offer \[=\text{ }Rs\text{ }132\] Number of offers purchased \[=\text{ }496\] Assuming she needs to build her pay...

### Ashwarya bought 496, Rs.100 shares at Rs.132 each, find: (i) Investment made by her (ii) Income of Ashwarya from these shares, if the rate of dividend is 7.5%.

Given, (I) The nominal worth of each offer \[=\text{ }Rs\text{ }100\] Market cost of each offer \[=\text{ }Rs\text{ }132\] Number of offers purchased \[=\text{ }496\] In this way, the speculation...

### Gagan invested 80% of his savings in 10% Rs.100 shares at 20% premium and the rest of his savings in 20% Rs.50 shares at Rs.20% discount. If his incomes from these shares is Rs.5,600 calculate: Percentage return, on the shares bought on the whole.

\[\begin{array}{*{35}{l}} The\text{ }complete\text{ }profit\text{ }or\text{ }the\text{ }return\text{ }=\text{ }0.8x/12\text{ }+\text{ }0.2x/4 \\ =\text{ }0.8\left( 48,000 \right)/12\text{ }+\text{...

### Gagan invested 80% of his savings in 10% Rs.100 shares at 20% premium and the rest of his savings in 20% Rs.50 shares at Rs.20% discount. If his incomes from these shares is Rs.5,600 calculate: (i) His investment in shares on the whole (ii) The number of shares of first kind that he bought

(I) Let's expect the complete reserve funds be \[Rs\text{ }x\](which is the venture) For the first part \[\text{ }80%\]of his investment funds Nominal worth of each offer \[=\text{ }Rs\text{ }100\]...

### A man invests a certain sum on buying 15% Rs.100 shares at 20% premium. Find : Sum invested

Considering that the man purchased portions of \[Rs\text{ }100\text{ }at\text{ }20%\]exceptional, the market worth of one offer \[\begin{array}{*{35}{l}} =\text{ }Rs\text{ }\left( 1\text{ }+\text{...

### A man invests a certain sum on buying 15% Rs.100 shares at 20% premium. Find : (i) His income from one share (ii) The number of shares bought to have an income, from the dividend, Rs.6480

(I) \[\begin{array}{*{35}{l}} Dividend\text{ }on\text{ }one\text{ }offer\text{ }=\text{ }15%\text{ }of\text{ }Rs\text{ }100 \\ =\text{ }Rs\text{ }\left( 15/100\text{ }x\text{ }100 \right)\text{...

### Mrs. Kulkarni invests Rs.1, 31,040 in buying Rs.100 shares at a discount of 9%. She sells shares worth Rs.72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole.

Given, Speculation \[=\text{ }Rs\text{ }1,31,040\] Nominal worth of \[1\text{ }offer\text{ }=\text{ }Rs\text{ }100\] Rebate \[=\text{ }9%\text{ }of\text{ }Rs\text{ }100\text{ }=\text{ }Rs\text{ }9\]...

### By investing Rs.45,000 in 10% Rs.100 shares, Sharad gets Rs.3,000 as dividend. Find the market value of each share.

We realize that, Yearly pay from \[1\text{ }offer\text{ }=\text{ }10%\text{ }of\text{ }Rs\text{ }100\text{ }=\text{ }Rs\text{ }10\] Given, the absolute pay\[~=\text{ }Rs\text{ }3000\text{ }\left(...

### Mr. Richard has a recurring deposit account in a post office for 3 years at 7.5 % p.a. simple interest. If he gets Rs. 8,325 as interest at the time of maturity, find: (i) the monthly instalment (ii) the amount of maturity

How about we expect the regularly scheduled payment be \[Rs\text{ }P\] Interest over the period \[=\text{ }Rs.\text{ }8,325\] \[Pace\text{ }of\text{ }revenue\text{ }=\text{ }7.5percent\]...

### Mr. Bajaj needs Rs 30,000 after 2 years. What least money (in multiple of Rs 5) must he deposit every month in a recurring deposit account to get required money after 2 years, the rate of interest being 8% p.a.?

How about we accept the portion each month to be \[Rs\text{ }P\] Number of months \[\left( n \right)\text{ }=\text{ }24\] \[Pace\text{ }of\text{ }revenue\text{ }=\text{ }8percent\text{ }p.a.\] In...

### The maturity value of a R.D. Account is Rs 16,176. If the monthly installment is Rs 400 and the rate of interest is 8%; find the time (period) of this R.D Account.

Given, Installment per month \[\left( P \right)\text{ }=\text{ }Rs\text{ }400\] Let the time, number of months \[\left( n \right)\text{ }=\text{ }n\] Rate of interest \[\left( r \right)\text{...

### Ritu has a Recurring Deposit Account in a bank and deposits Rs 80 per month for 18 months. Find the rate of interest paid by the bank if the maturity value of account is Rs 1,554.

Given, Portion each month \[\left( P \right)\text{ }=\text{ }Rs\text{ }80\] Number of months \[\left( n \right)\text{ }=\text{ }18\] Let pace of revenue \[\left( r \right)\text{ }=\text{ }r\text{...

### Pramod deposits Rs 600 per month in a Recurring Deposit Account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account.

Given, Portion each month \[\left( P \right)\text{ }=\text{ }Rs\text{ }600\] Number of months \[\left( n \right)\text{ }=\text{ }48\] Pace of revenue \[\left( r \right)\text{ }=\text{ }8percent...

### A man has a Recurring Deposit Account in a bank for 3½ years. If the rate of interest is 12% per annum and the man gets Rs 10,206 on maturity, find the value of monthly installments.

How about we expect that the portion each month \[\left( P \right)\text{ }=\text{ }Rs\text{ }y\] Number of months \[\left( n \right)\text{ }=\text{ }42\] Pace of revenue $$\[\left( r \right)\text{...

### Ashish deposits a certain sum of money every month is a Recurring Deposit Account for a period of 12 months. If the bank pays interest at the rate of 11% p.a. and Ashish gets Rs 12,715 as the maturity value of this account, what sum of money did he pay every month?

Allow us to expect the portion each month \[\left( P \right)\text{ }as\text{ }Rs\text{ }y\] Number of months \[\left( n \right)\text{ }=\text{ }12\] Pace of revenue \[\left( r \right)\text{ }=\text{...

### Each of A and B both opened recurring deposit accounts in a bank. If A deposited Rs 1,200 per month for 3 years and B deposited Rs 1,500 per month for 2½ years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.

Ascertaining for\[A\]: Portion each month \[\left( P \right)\text{ }=\text{ }Rs\text{ }1,200\] Number of months \[\left( n \right)\text{ }=\text{ }36\] Pace of revenue \[\left( r \right)\text{...

### Mrs. Mathew opened a Recurring Deposit Account in a certain bank and deposited Rs. 640 per month for 41/2 years. Find the maturity value of this account, if the bank pays interest at the rate of 12% per year.

Portion each month \[\left( P \right)\text{ }=\text{ }Rs\text{ }640\] Number of months \[\left( n \right)\text{ }=\text{ }54\] Pace of revenue \[\left( r \right)\text{ }=\text{ }12percent\text{...

### Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits Rs. 600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.

From the question, we have Installment per month \[\left( P \right)\text{ }=\text{ }Rs\text{ }600\] Number of months \[\left( n \right)\text{ }=\text{ }20\] Rate of interest\[\left( r \right)\text{...

### For a trader, marked price of a refrigerator = Rs. 15,680 inclusive of GST at the rate of 12% on the marked price. Gagan, a customer for this refrigerator, asks the trader to reduce the marked price of the refrigerator to such extend that its reduced price plus GST on it is equal to marked price of the refrigerator. Find the required reduction.

Allow us to accept the stamped cost of the fridge be \[Rs.\text{ }x.\] Which is comprehensive of \[GST\text{ }\left( 12percent \right)\] Thus, \[\begin{array}{*{35}{l}} x\text{ }+\text{...

### A is a manufacturer of T.V. sets in Delhi. He manufacturers a particular brand of T.V. set and marks it at Rs. 75,000. He then sells this T.V. set to a wholesaler B in Punjab at a discount of 30%. The wholesaler B raises the marked price of the T.V. set bought by 30% and then sells it to dealer C in Delhi. If the rate of GST = 5% find tax (under GST) paid by wholesaler B to the government.

We realize that, Introductory stamped cost by maker \[A\text{ }is\text{ }Rs.\text{ }75,000\] Then, at that point, \[B\]purchased the T.V. at a rebate of \[30percent.\] In this way, the cost of...

### The marked price of an article is Rs. 6000. A wholesaler sells it to a dealer at 20% discount. The dealer further sells the article to a customer at a discount of 10% on the marked price. If the rate of GST at each stage is 18%, find the amount of tax (under GST) paid by the dealer to the government.

We have, Initial marked price by manufacturer \[A\text{ }is~Rs.\text{ }6000\] Then, \[B\]bought the T.V. at a discount of \[20percent.\] Now, Cost price of \[B\text{ }=\text{ }80percent\text{...

### For a dealer A, the list price of an article is Rs. 9000, which he sells to dealer B at some lower price. Further, dealer B sells the same article to a customer at its list price. If the rate of GST is 18% and dealer B paid a tax, under GST, equal to Rs. 324 to the government, find the amount (inclusive of GST) paid by dealer B.

Let seller \[A\]offer to vendor \[B\text{ }at\text{ }Rs.\text{ }x\]lower cost. Then, at that point, from the inquiry, Net Tax paid by seller B is \[\begin{array}{*{35}{l}} \Rightarrow Output\text{...

### Consultancy services, worth Rs. 50,000, are transferred from Delhi to Calcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at Nainital

Since, the vendor in Nainital doesn't sell the item. Subsequently, the yield GST (charge marked down) \[=\text{ }Rs.\text{ }0\]

### Consultancy services, worth Rs. 50,000, are transferred from Delhi to Calcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at (i) Delhi (ii) Calcutta

(I) Output charge in Delhi (between state): \[\begin{array}{*{35}{l}} IGST\text{ }=\text{ }9percent\text{ }of\text{ }50,000\text{ }=\text{ }Rs.\text{ }4500\\ Accordingly, the yield charge in Delhi...

### A dealer X in Hapur (U.P.) supplies goods/services, worth Rs. 50,000 to some other dealer Y in the same city. Now the dealer Y supplies the same goods/services to dealer Z in Calcutta at a profit of Rs. 20,000. Find: (i) Output and input taxes for the dealer Y (ii) Net GST payable by dealer Y. [The rate of GST at each stage is 28%]

From the inquiry, we have For the vendor \[X\](intra-state exchange) The \[SP\text{ }=\text{ }Rs.\text{ }50,000\] For the vendor \[Y\](intra-state exchange) \[\begin{array}{*{35}{l}} CP\text{...

### A is a dealer in Meerut (U.P.). He supplies goods/services, worth Rs. 15,000 to a dealer B in Ratlam (M.P.). Dealer B, in turn, supplies the same goods/services to dealer C in Jabalpur (M.P.) at a profit of Rs. 3000. If rate of tax (under GST system) is 18%, find : (i) The cost of goods/services to the dealer C in Jabalpur. (ii) Net tax payable by dealer B.

From the inquiry, For \[A\](instance of between state exchange) S.P. in Meerut \[=\text{ }Rs.\text{ }15,000\] For B (instance of between state exchange) C.P. \[=~Rs.\text{ }15,000\] IGST \[=\text{...

### A is a dealer in Banaras (U.P.). he supplies goods/services worth Rs. 8000 to a dealer B in Agra (U.P.). Dealer B, in turn, supplies the same goods/services to dealer C in Patna (Bihar) at a profit of Rs. 1200. Find the input and output taxes for the dealer C under GST system; if the rate of GST is 18% and C does not sell his goods/services further.

From the inquiry, For the seller A (intra-state exchange) \[SP\text{ }=\text{ }Rs.\text{ }8,000\] For the seller B (intra-state exchange) \[\begin{array}{*{35}{l}} CP\text{ }=\text{ }Rs.\text{...

### Goods/services are sold from Kota (Rajasthan) to Mumbai for Rs. 20,000 and then from Mumbai to Pune. If the rate of GST is 12% and the profit made at Mumbai is Rs. 5000; find the net GST paid at Pune, if the dealer at Pune is the end-user.

From the inquiry, we have For the seller in Mumbai (between state exchange) C.P. \[=~Rs.\text{ }20,000\] IGST \[=~12percent\text{ }of~Rs.\text{ }20,000~\] \[=\text{ }12/100\text{ }x\text{...

### Goods/services are sold from Agra (U.P.) to Kanpur (U.P.) for Rs. 20,000 and then from Kanpur to Jaipur (Rajasthan). If the rate of GST is 18% and the profit made at Kanpur is Rs. 5000, find: (i) the net GST payable by the dealer at Kanpur. (ii) the cost of goods/services at Jaipur.

From the inquiry, when the item is sold from Agra to Kanpur (intra-state exchange) For the vendor in Agra: S.P. in Agra \[=~Rs.\text{ }20,000\] CGST \[=\text{ }9percent\text{ }of~Rs.\text{ }20,000\]...

### Fill in the blanks: When the goods/services are sold for Rs. 15,000 under intra-state transaction from station A to station B and the rate of GST is 12%. Now the same goods/services are moved under inter-state transaction from station B to station C and the rate of tax is 12%. (a) GST = ………………… (b) C.P. at station C = …………………

Presently similar merchandise/administrations are moved under between state exchange from station \[B\]to station \[C\]and the pace of duty is \[12%.\] (a) \[GST\text{ }=\text{ }12%\text{ }of\text{...

### Fill in the blanks: When the goods/services are sold for Rs. 15,000 under intra-state transaction from station A to station B and the rate of GST is 12%. As per GST System (a) C.P. at station B = ………………… (b) If profit = Rs. 5000 S.P. at station B = ………………………

At the point when the products/administrations are sold for \[Rs.\text{ }15,000\]under intra-state exchange from station \[A\]to station \[B\]and the pace of GST is \[12percent.\] According to GST...

### Fill in the blanks: When the goods/services are sold for Rs. 15,000 under intra-state transaction from station A to station B and the rate of GST is 12%. As per GST System (a) S.P. at station A = ………………… (b) CGST = 6% of 15,000 = ……………… SGST = 6% of 15,000 = ………………………

At the point when the products/administrations are sold for \[Rs.\text{ }15,000\]under intra-state exchange from station \[A\]to station\[~B\] and the pace of GST is \[12percent.\] According to GST...

### Determine P (E|F) in: A coin is tossed three times, where (i) : head on third toss, : heads on first two tosses (ii) : at least two heads, : at most two heads (iii) : at most two tails, at least one tail

Solution: The sample space of the given experiment will be: S={HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} (i) Given that, E: head-on third toss And F: heads on first two tossesSo writing the sample...