Multiple choice

A man gave $50\%$ of his savings of $84100$ to his wife and divided the remaining sum among his two sons $A$ and $B$ of $15$ and $13$ years of age respectively. He divided it in such a way that each of his sons, when they attain the age of $20$ years would receive the same amount at $5\%$ compound interest per annum, the share of $B$ was -

  1. $20000$
  2. $20500$
  3. $22000$
  4. $22500$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Savings = 84100. 50% = 42050. Let A's share be x and B's be y. x + y = 42050. x(1.05)^5 = y(1.05)^7. x = y(1.05)^2 = y(1.1025). y(1.1025 + 1) = 42050. y = 42050 / 2.1025 = 20000.

AI explanation

The remaining sum of 42050 is divided such that both sons receive the same amount at age 20, meaning their shares compound at 5% for 5 and 7 years respectively. Equating their final amounts gives share of A multiplied by 1.05 to the power of 5 equals share of B multiplied by 1.05 to the power of 7, which simplifies to share of A equals share of B multiplied by 1.1025. Solving the system where A plus B equals 42050 and A equals 1.1025 times B yields the share of B as 20000.

Keep practicing — related questions