Two numbers are in the ratio of 6 : 7. If 12 is added to each of the numbers,…
2022
Two numbers are in the ratio of 6 : 7. If 12 is added to each of the numbers, their ratio becomes 7 : 8. Find the two numbers.
Answer: A. 72, 84 — ConceptWhen two quantities are in the ratio a : b, represent them as ax and bx for a common multiplier x. If the same amount c is added to both, the new ratio…
- A.
72, 84
- B.
84, 96
- C.
84, 98
- D.
96, 84
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Show answer & explanation
Correct answer: A
Concept
When two quantities are in the ratio a : b, represent them as ax and bx for a common multiplier x. If the same amount c is added to both, the new ratio becomes (ax + c) : (bx + c), which gives an equation for x.
Application
Let the numbers be 6x and 7x because their ratio is 6 : 7.
After adding 12 to each, (6x + 12)/(7x + 12) = 7/8.
Cross-multiplying gives 8(6x + 12) = 7(7x + 12), so 48x + 96 = 49x + 84.
Therefore x = 12, and the numbers are 6 × 12 = 72 and 7 × 12 = 84.
Cross-check
For 72 and 84, the original ratio is 72 : 84 = 6 : 7. After adding 12, the ratio is 84 : 96 = 7 : 8, so both conditions are satisfied.
The two numbers are 72 and 84.