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Home » 15. A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
15. A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
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15. A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.

Solution:-

Let us assume the two numbers be, P and Q,

Then, P = 10P … [because it comes in tens digit]

As per the condition given in the question,

PQ = 8 … [equation (i)]

10P + Q - 18 = 10Q + P

10P - P + Q - 10Q - 18 = 0

9P - 9Q - 18 = 0

Divide by 2 for both side of each term we get,

9P/9 - 9Q/9 - 18/9 = 0/9

P - Q - 2 = 0 … [equation (ii)]

Consider the equation (i),PQ = 8

P = 8/Q

Now, substitute the value of P in equation (ii) we get,

8/Q - Q - 2 = 0

By simplification,

    \[8-{{Q}^{2}}-2Q\text{ }=\text{ }0\]

    \[{{Q}^{2}}~+\text{ }2Q-8\text{ }=\text{ }0\]

    \[{{Q}^{2}}~+\text{ }4Q-2Q-8\text{ }=\text{ }0\]

Take out common in each terms,

Q(Q + 4) - 2(Q + 4) = 0

(Q + 4) (Q - 2)

Equate both to zero,

Q + 4 = 0

Q - 2= 0

Q = - 4

Q = 2

So, Q = 2

From equation (i),PQ = 8

2P = 8

P = 8/2

P = 4

Therefore, the number is 42.

i

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