Two numbers, A and B, are in the ratio of 10 : 13. If 90 is subtracted from…
2023
Two numbers, A and B, are in the ratio of 10 : 13. If 90 is subtracted from each of them, the resulting numbers are in the ratio of 7 : 10. If 57 is added to A and 16 is subtracted from B, then the ratio of the resulting numbers will be —
- A.
19 : 20
- B.
20 : 21
- C.
21 : 22
- D.
22 : 23
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Correct answer: C
Solution outline: Use algebra to find the numbers, then compute the required ratio.
Let A = 10k and B = 13k.
After subtracting 90: (10k - 90)/(13k - 90) = 7/10. Cross-multiply: 10(10k - 90) = 7(13k - 90).
Compute: 100k - 900 = 91k - 630 ⇒ 9k = 270 ⇒ k = 30. Thus A = 300 and B = 390.
Add 57 to A and subtract 16 from B: new A = 300 + 57 = 357, new B = 390 - 16 = 374.
Simplify the ratio 357 : 374. Their difference is 17, and 357 = 17 × 21, 374 = 17 × 22, so the ratio reduces to 21 : 22.
Answer: 21 : 22