Multiple choice

A sum of Rs. $18750$ is left by will by a father to be divided between two sons, $12$ and $14$ years of age, so that when they attain maturity at $18$, the amount received by each of them at $5$ per cent simple interest will be the same. Find the sum allotted at present to each son?

  1. Rs. $9500$, Rs. $9250$
  2. Rs. $8000$, Rs. $1750$
  3. Rs. $9000$, Rs. $9750$
  4. Rs. $10000$, Rs. $8750$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sums be x and y. x+y = 18750. Time for first son = 18-12 = 6 years. Time for second son = 18-14 = 4 years. Amount = P(1 + rt/100). x(1 + 0.05*6) = y(1 + 0.05*4). 1.3x = 1.2y. y = 1.3/1.2 x = 13/12 x. x + 13/12 x = 18750. 25/12 x = 18750. x = 18750 * 12 / 25 = 9000. y = 18750 - 9000 = 9750.

AI explanation

Let the present shares of the 12-year-old and 14-year-old sons be x and (18750 - x) respectively. Using the simple interest formula, their amounts at age 18 will be x + (x * 6 * 5 / 100) and (18750 - x) + ((18750 - x) * 4 * 5 / 100). Setting them equal gives 1.3x = 1.2(18750 - x), which simplifies to 2.5x = 22500. Solving this yields x = 9000, making the other share 9750.

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