As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement?

Correct Option (C)

The problem states that 18 instalments account for 60 percent of the total loan refunded. To determine the total number of instalments for 100 percent of the loan, a direct proportionality can be applied.

• If 60% of the loan corresponds to 18 instalments.
• Then, 1% of the loan corresponds to $\frac{18}{60}$ instalments.
• Therefore, 100% of the loan corresponds to $\frac{18}{60}\times 100$ instalments.
• Calculating this value: $\frac{18}{60}\times 100=\frac{3}{10}\times 100=3\times 10=30$ instalments.

Thus, there were 30 instalments in the agreement.

Incorrect Options:

Options A (22), B (24), and D (33) are incorrect as they do not satisfy the given condition that 18 instalments represent 60 percent of the loan. If any of these options were the total number of instalments, the percentage of the loan refunded after 18 instalments would be different:

• For 22 total instalments: $\frac{18}{22}\times 100\mathrm{\%}\approx 81.8\mathrm{\%}$
• For 24 total instalments: $\frac{18}{24}\times 100\mathrm{\%}=75\mathrm{\%}$
• For 33 total instalments: $\frac{18}{33}\times 100\mathrm{\%}\approx 54.5\mathrm{\%}$

None of these percentages match the given 60 percent, confirming that 30 is the only correct total number of instalments.