Question

A certain number is added to each of a pair of numbers which are in the ratio 4:7.The sum of the resulting numbers is 75 and their ratio is 8:17. What is the number added?

Answer 1

Given :- A certain number is added to each of a pair of numbers which are in the ratio 4:7. The sum of the resulting numbers is 75 and their ratio is 8:17.

To Find :- What is the number added ?

Answer :-

Let the original numbers were 4x and 7x . number added is y .

so,

→ (4x + y) / (7x + y) = 8/17

→ 68x + 17y = 56x + 8y

→ 68x - 56x = 8y - 17y

→ 12x = (-9y)

→ 4x = (-3y)

→ x = (-3y/4)

also,

→ 4x + y + 7x + y = 75

→ 11x + 2y = 75

putting value of x,

→ 11(-3y/4) + 2y = 75

→ (-33y + 8y) / 4 = 75

→ (-25y) = 75 * 4

→ (-25y) = 300

→ y = (-12) (Ans.)

Hence, the number added is (-12) .

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