Question

A bank customer had Rs. 100 in his account. He then made 6 withdrawals, totaling Rs. 100. He kept a record of these withdrawals, and the balance remaining in the account, as follows:

Withdrawals	Balance left
Rs. 50	Rs. 50
Rs. 25	Rs. 25
Rs. 10	Rs. 15
Rs. 8	Rs. 7
Rs. 5	Rs. 2
Rs. 2	Rs. 0
Rs. 100	Rs. 99

So, why are the totals not exactly right?

• A. There is a mistake in the total of withdrawals.
• B. There is a mistake in the total of the balance.
• C. The two totals need not be equal.
• D. The bank has cheated the customer.

Hint:

Check whether the "balance left" column is even supposed to add up to anything meaningful in the first place, since each balance already includes every earlier withdrawal.

Answer 1

The Correct Option is C

Step 1: Try a simple made-up example to expose the trick.
Suppose someone starts with Rs. 100 and withdraws Rs. 1 at a time, one hundred times. The withdrawals column would then add up to exactly $100 \times 1 = 100$, matching the starting balance.

Step 2: Add up the balance column for that same example.
The balance after each withdrawal runs $99, 98, 97, \ldots, 1, 0$. Adding all of these gives $99 + 98 + \cdots + 1 + 0 = \frac{99 \times 100}{2} = 4950$.

Step 3: Compare the two totals.
The withdrawals add to 100, while the balances add to 4950, a huge gap. Nobody would call this a mistake or an act of cheating; it simply shows that these two columns were never meant to add up to the same number.

Step 4: Apply the same idea back to the original problem.
In the original table, the withdrawals genuinely sum to Rs. 100. The balance column sums to Rs. 99, which is close only because there happen to be just six withdrawals of these particular sizes, not because of any accounting error.

Final Answer:
Since a running balance and a set of withdrawals are fundamentally different kinds of numbers, there is no requirement that their totals match, so the two totals need not be equal. \[ \boxed{\text{The two totals need not be equal.}} \]