Question

Keerthi’s father gave him some money to buy books. He spent half of the money equally to buy books and entertaining his friends. Whatever amount left with him, he deposited half in his savings account and gave Rs. 5 to a poor person as charity. Finally, Keerthi was left with Rs. 20 which he returned to his father. What amount did his father give him initially?

• A. Rs. 160
• B. Rs. 100
• C. Rs. 200
• D. Rs. 120

Hint:

Translate step-by-step spending into equations — reverse calculation from the final amount is often the fastest method in such word problems.

Answer 1

The Correct Option is B

Let the initial amount be \( x \) rupees.
He spent half of it, i.e., \( \frac{x}{2} \), equally on books and entertainment, meaning \( \frac{x}{4} \) on each.
Thus, the remaining after spending half is \( x - \frac{x}{2} = \frac{x}{2} \).
He deposited half of the remaining amount, i.e., \( \frac{1}{2} \times \frac{x}{2} = \frac{x}{4} \) in his savings account.
He then gave Rs. 5 as charity, leaving \( \frac{x}{4} - 5 \) rupees in hand.
Finally, this remaining money was Rs. 20, which he returned to his father.
Therefore: \( \frac{x}{4} - 5 = 20 \).
\( \frac{x}{4} = 25 \).
\( x = 100 \).
Hence, Keerthi’s father initially gave him Rs. 100.