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

Let the total number of equal installments in the original agreement be $N$.
According to the question, $18$ installments account for exactly $60\%$ of the total loan repayment. Because all installments are equal and interest-free, we can establish the linear percentage equality:

$$18=60\%\text{ of }N$$

$$18=\frac{60}{100}\times N$$

$$18=\frac{3}{5}N$$

Solving directly for $N$:

$$N=18\times \frac{5}{3}$$

$$N=6\times 5=30$$

Therefore, there were $30$ total installments in the agreement.