Question 31

Two numbers are such that their difference,their sum and their product are in the ratio of 1 : 7 : 24. The product of the numbers is

Solution

let the numbers be x and y

x - y = a .............(1)

x + y = 7a ...............(2)

xy = 24a.................(3)

solving (1) and (2)

we get x = 4a

substituting x = 4a in equation (2) we get y = 3a

$$ x \times y = 4a \times 3a = 12a^2 $$

from (3) $$ 12a^2 = 24a $$

solving a = 2

product of the numbers = xy = 24a =$$ 24 \times 2 = 48 $$

Create a FREE account and get: