The sum of three numbers is 124. If the ratio between the first and the second…
2023
The sum of three numbers is 124. If the ratio between the first and the second is 2 : 3 and between the second and the third is 7 : 9, then the third number is:
Answer: B. 54 — ConceptWhen two ratios share a quantity, first rewrite them so that the shared quantity has the same number of parts. The resulting combined ratio gives one…
- A.
48
- B.
54
- C.
64
- D.
66
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Correct answer: B
Concept
When two ratios share a quantity, first rewrite them so that the shared quantity has the same number of parts. The resulting combined ratio gives one common part scale for all quantities.
Application
Let the three numbers be x, y, and z. From x : y = 2 : 3 and y : z = 7 : 9, make the shared y-term equal in both ratios. Since LCM(3, 7) = 21, multiply 2 : 3 by 7 and 7 : 9 by 3.
This gives x : y = 14 : 21 and y : z = 21 : 27, so x : y : z = 14 : 21 : 27.
The total number of ratio parts is 14 + 21 + 27 = 62. Since their sum is 124, one part equals 124 ÷ 62 = 2.
The third number is z = 27 × 2 = 54.
Cross-check
The numbers are 28, 42, and 54. Their sum is 124, while 28 : 42 = 2 : 3 and 42 : 54 = 7 : 9.
Therefore, the third number is 54.