After two successive increments, Gopal’s salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first incre ment, then the percentage of salary increase in the first increment was:

The correct option is 25.

Let the initial salary of Gopal be represented by S.
After two successive increments, his salary became 187.5% of his initial salary. Therefore, the final salary is:

$$\text{Final Salary}=1.875\times S$$

Let the percentage increase in the first increment be x%.
According to the problem, the percentage increase in the second increment was twice that of the first increment, which is 2x%.

We can write the equation for the successive percentage increases as:

$$S\times (1+\frac{x}{100})\times (1+\frac{2x}{100})=1.875\times S$$

Dividing both sides by S, we get:

$$(1+\frac{x}{100})(1+\frac{2x}{100})=1.875$$

Let us test the correct option, x = 25, to verify:

First factor:
$$1+\frac{25}{100}=1+0.25=1.25$$

Second factor:
$$1+\frac{2\times 25}{100}=1+\frac{50}{100}=1+0.5=1.5$$

Now, multiplying the two factors:

$$1.25\times 1.5=1.875$$

Since the left-hand side matches the right-hand side, the percentage of salary increase in the first increment was indeed 25%.