A man left ₹28,000 for his 13-year-old son and 15-year-old daughter with the instruction that, at the age of 18, the amount each receives — including simple interest at an annual rate of 10% — should be equal. Determine the amount allocated to each child.

Q.A man left ₹28,000 for his 13-year-old son and 15-year-old daughter with the instruction that, at the age of 18, the amount each receives — including simple interest at an annual rate of 10% — should be equal. Determine the amount allocated to each child.

Let the amount allocated for the son be \(x\) rupees and for the daughter be \((28000 - x)\) rupees.

\(\therefore\) At the age of 18, the total amount the son receives with simple interest: \(= \left(x + \cfrac{x \times (18 - 13) \times 10}{100}\right)\) rupees \(= \left(x + \cfrac{x}{2}\right)\) rupees = \(\cfrac{3x}{2}\) rupees

And at the age of 18, the total amount the daughter receives with simple interest: \(= \left\{(28000 - x) + \cfrac{(28000 - x) \times (18 - 15) \times 10}{100}\right\}\) rupees \(= \left\{(28000 - x) + \cfrac{3(28000 - x)}{10}\right\}\) rupees \(= \cfrac{13(28000 - x)}{10}\) rupees

According to the question, \(\cfrac{3x}{2} = \cfrac{13(28000 - x)}{10}\) Or, \(30x = 26(28000 - x)\) Or, \(30x = 26 \times 28000 - 26x\) Or, \(30x + 26x = 26 \times 28000\) Or, \(56x = 26 \times 28000\) Or, \(x = \cfrac{26 \times 28000}{56}\) Or, \(x = 13000\)

\(\therefore\) He allocated ₹13,000 to his son and ₹(28000 - 13000) = ₹15,000 to his daughter.