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?
Answers
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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