Multiple choice

A father left a will that his capital of Rs. 18,750 be divided between his two sons, aged 12 and 14 years, such that when they attain the age of 18 years, the amounts received by each at 5% simple interest are the same. Find the sum allotted to the elder son.

  1. Rs. 9750

  2. Rs. 9450

  3. Rs. 9000

  4. Rs. 8700
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the amount for the elder son (14 years old) and (18750-x) for the younger (12 years old). Elder son's money grows for 4 years, younger for 6 years. x(1 + 0.05*4) = (18750-x)(1 + 0.05*6). x(1.2) = (18750-x)(1.3). 1.2x = 24375 - 1.3x. 2.5x = 24375 => x = 9750.

AI explanation

Let the sum allotted to the elder son be x, making the younger son's share (18750 - x). The elder son is 14 years old, so his investment period is 4 years, while the younger son is 12 years old, giving his investment period is 6 years. Since their final amounts at 5% simple interest are equal, x + (x*5*4)/100 = (18750 - x) + ((18750 - x)5*6)/100, which simplifies to 1.2x = 1.3(18750 - x). Solving this equation gives 2.5x = 24375, so x = Rs. 9750.

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