Question : A sum of Rs. 15525 is divided among Sunil, Anil, and Jamil such that if Rs. 22, Rs. 35, and Rs. 48 are diminished from their shares, respectively, their remaining sums shall be in the ratio 7 : 10 : 13. What would have been the ratio of their sums if Rs. 16, Rs. 77, and Rs. 37, respectively, were added to their original shares?
Option 1: 9 : 13 : 17
Option 2: 18 : 26 : 35
Option 3: 36 : 52 : 67
Option 4: None of these
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Correct Answer: 36 : 52 : 67
Solution : Total sum = Rs.15525 Distributed sum = 15525 – 22 – 35 – 48 = Rs.15420 The ratio of remaining share = 7 : 10 : 13 New share of Sunil = ($\frac{7}{7+10+13}$ × 15420) + 22 + 16 = ($\frac{7}{30}$ × 15420) + 22 + 16 = Rs. 3636 New share of Anil = ($\frac{10}{7+10+13}$ × 15420) + 35 + 77 = ($\frac{10}{30}$ × 15420) + 35 + 77 = Rs. 5252 New share of Jamil = ($\frac{13}{7+10+13}$ × 15420) + 48 + 37 = ($\frac{13}{30}$ × 15420) + 48 + 37 = Rs. 6767 So, the new ratio = 3636 : 5252 : 6767 = 36 : 52 : 67 Hence, the correct answer is 36 : 52 : 67.
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