Login/Sign Up
Home » The sum of two numbers is . If the sum of two numbers is four times their difference, find the numbers
The sum of two numbers is 8. If the sum of two numbers is four times their difference, find the numbers
CBSE | Class 10 | Exercise 3.7 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
The sum of two numbers is 8. If the sum of two numbers is four times their difference, find the numbers

Let’s assume the two numbers to be ‘a’ and ‘b’.

Let’s consider that, ‘a’ is greater than or equal to ‘b’.

Now, according to the question

The sum of the two numbers, a+b=8…………. (i)

Also, sum is four times their difference. So, we can write;

a+b=4(a-b)

⇒ a+b=4a-4b

⇒ 4a-4b-a-b=0

⇒ 3b-5b=0………………. (ii)

On solving equations (i) and (ii), we can find the value of a and b.

On multiplying equation (i) by 5 and then add with equation (ii), we get-

5\left( a+b \right)+\left( 3a-5b \right)=5\times 8+0

⇒ 5a+5b+3a-5b=40

⇒ 8a=40

⇒ a=5

Putting the value of a in (i), we het value of b

5+b=8

⇒ b=8-5

⇒ b=3

Therefore, the two numbers are 5 and 3.

i

More Material