Multiple choice

A man wants to divide a sum of Rs $37500$ among his son and daughter aged $12$ years and $14$ years respectively in such a way that on attaining the age of $18$ years each gets the same amount at $5\%$ p.a. simple interest. The son's share is

  1. Rs. $19500$
  2. Rs. $18000$
  3. Rs. $15000$
  4. Rs. $20000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let shares be S and D. S(1 + 0.05*6) = D(1 + 0.05*4) => 1.3S = 1.2D => D = 13/12 S. S + 13/12 S = 37500 => 25/12 S = 37500 => S = 18000.

AI explanation

The son needs 6 years to turn 18, while the daughter needs 4 years. If the son's share is x, then the daughter's share is (37500 - x). Using the amount formula for simple interest, x + (x * 5 * 6)/100 = (37500 - x) + ((37500 - x) * 5 * 4)/100. This simplifies to 1.3x = 1.2(37500 - x), meaning 2.5x = 45000, so x = 18000. The son's share is Rs 18000.

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