Discussion
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:
Answer: C
The ratio is 21 : 22. Let the numbers be \(10k\) and \(13k\). \[ \frac{10k-90}{13k-90} = \frac{7}{10} \] \[ 100k - 900 = 91k - 630 \] \[ 9k = 270,\quad k = 30 \] So A = 300 and B = 390. Adding 57 to A and subtracting 16 from B: \[ A = 357,\quad B = 374 \] \[ 357 : 374 = 21 : 22 \] since both are divisible by 17. The ratios 19 : 20, 20 : 21 and 22 : 23 do not match 357 : 374. Check: with \(k = 30\) the numbers are 300 and 390, and after subtracting 90 they become 210 and 300, which is 7 : 10 as the question says.
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