Q.A man left ₹18,750 for his two sons aged 12 and 14, in such a way that when they each turn 18, they will receive the same amount including simple interest at 5%. How much money did he leave for each son?

Let the man leave ₹\(x\) for his younger son and ₹\((18750 - x)\) for his elder son. Therefore, the amount the younger son will receive at age 18 (including simple interest): \[ = x + \frac{x \times (18 - 12) \times 5}{100} = x + \frac{3x}{10} = \frac{13x}{10} \] And the amount the elder son will receive at age 18: \[ = (18750 - x) + \frac{(18750 - x) \times (18 - 14) \times 5}{100} = (18750 - x) + \frac{2(18750 - x)}{10} = \frac{12(18750 - x)}{10} \] According to the question: \[ \frac{13x}{10} = \frac{12(18750 - x)}{10} \] Multiplying both sides by 10: \[ 13x = 12(18750 - x) \Rightarrow 13x = 225000 - 12x \Rightarrow 25x = 225000 \Rightarrow x = \frac{225000}{25} = 9000 \] ∴ He left ₹9000 for the younger son and ₹\(18750 - 9000 = 9750\) for the elder son.
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