Solved UPSC CDS/OTA Question
A solved UPSC CDS/OTA PYQ - decoded step-by-step.
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Four years ago, the ratio of ages of a father and his son was 11:4. Four years hence, the ratio will be 13:6. Find present ages.
Step-by-Step Solution
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Four years ago, their ages were:
Father: F – 4
Son: S – 4 Ratio: (F – 4)/(S – 4) = 11/4 → 4(F – 4) = 11(S – 4) → 4F – 16 = 11S – 44 → 4F – 11S = –28 (Equation 1)
Four years hence, their ages will be:
Father: F + 4
Son: S + 4 Ratio: (F + 4)/(S + 4) = 13/6 → 6(F + 4) = 13(S + 4) → 6F + 24 = 13S + 52 → 6F – 13S = 28 (Equation 2)
From Equation 1: 4F – 11S = –28 From Equation 2: 6F – 13S = 28
Let’s eliminate one variable. Multiply Equation 1 by 3: → 12F – 33S = –84
Multiply Equation 2 by 2: → 12F – 26S = 56
Now subtract: (12F – 33S) – (12F – 26S) = –84 – 56 → –7S = –140 → S = 20
Now plug back to find F: F = (11S – 28)/4 = (220 – 28)/4 = 192/4 = 48