Three numbers are in the ratio 7 : 9 : 12. If the difference between the…
2026
Three numbers are in the ratio 7 : 9 : 12. If the difference between the smallest and the largest numbers is 10, what is the sum of the numbers?
Answer: A. 56 — ConceptWhen quantities are in the ratio a : b : c, they can be written as ak, bk and ck for one common scale factor k. The difference of two quantities equals…
- A.
56
- B.
72
- C.
61
- D.
42
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Correct answer: A
Concept
When quantities are in the ratio a : b : c, they can be written as ak, bk and ck for one common scale factor k.
The difference of two quantities equals the difference of their ratio terms multiplied by k, while the total equals the sum of the ratio terms multiplied by k.
Application
Let the three numbers be 7k, 9k and 12k.
The largest-minus-smallest difference is 12k - 7k = 5k. Since this difference is 10, 5k = 10, so k = 2.
Therefore, the numbers are 14, 18 and 24.
Their sum is (7 + 9 + 12) × 2 = 28 × 2 = 56.
Cross-check
The difference 24 - 14 is 10, and 14 : 18 : 24 reduces to 7 : 9 : 12. Also, 14 + 18 + 24 = 56.