Question

Two whole numbers are such that the square of first number exceeds the second by 112 and the ratio of the numbers is 4:3. What is the value of smaller number?

Answer 1

Hey Dear,

◆ Answer -

Bigger number = 4x = 4×4 = 16

Smaller number = 3x = 3×4 = 12

● Explaination -

Given that the numbers are in ratio 4:3. Taking x as common multiple,

Bigger number = 4x

Smaller number = 3x

Also, difference between squares is 112.

(4x)^2 - (3x)^2 = 112

16x^2 - 9x^2 = 112

7x^2 = 112

x^2 = 112/7

x^2 = 16

x = √16

x = 4

Now,

Bigger number = 4x = 4×4 = 16

Smaller number = 3x = 3×4 = 12

Therefore, value of smaller number is 12.

Thanks dear..