Question

Jaideep was given some money by his mother on his birthday. Jaideep spent all of it in five stores. In each store he spent one rupee more than half of what he had when he came in. How much did he get from his mother ?

• A. Rs. 25
• B. Rs. 30
• C. Rs. 46
• D. Rs. 52

Answer 1

The Correct Option is B

To determine the amount of money Jaideep received from his mother, let's analyze the spending pattern as he moves through each store. Assume, he initially has 'x' amount of money.

In the first store, Jaideep spends half of his money plus an additional one rupee: \((\frac{x}{2} + 1)\).

After his first purchase, the remaining money is:

\[ x - \left(\frac{x}{2} + 1\right) = \frac{x}{2} - 1 \]

Continuing this pattern for five stores, after spending in the fifth store, Jaideep will have zero money left. Let's set up the recursive relationship:

Let \(A_5\) be the amount left after the fifth store, \(A_5 = 0\).

For each store, the rule is: \(A_{n} = \frac{A_{n-1}}{2} - 1\).

Start from the fifth store and work backwards:

\(A_5 = 0\)

\(A_4 = 2 \times (A_5 + 1) = 2 \times (0 + 1) = 2\)

\(A_3 = 2 \times (A_4 + 1) = 2 \times (2 + 1) = 6\)

\(A_2 = 2 \times (A_3 + 1) = 2 \times (6 + 1) = 14\)

\(A_1 = 2 \times (A_2 + 1) = 2 \times (14 + 1) = 30\)

Therefore, Jaideep initially had Rs. 30 from his mother.