Explanation:

- The shopkeeper marks up the LED price by 60% above the cost price, i.e., if the cost price is \( C \), then the marked price becomes \( 1.6C \).

- He provides three successive discounts: 12.5%, \( d\% \), and 25%.

- After applying these discounts, the final selling price can be calculated as:

$$

\text{Selling Price} = 1.6C \times \left(1 - \frac{12.5}{100}\right) \times \left(1 - \frac{d}{100}\right) \times \left(1 - \frac{25}{100}\right)

$$

- The shopkeeper's final loss is 16%, so the selling price is 84% of the cost price:

$$

1.6C \times 0.875 \times \left(1 - \frac{d}{100}\right) \times 0.75 = 0.84C

$$

- Solving for \( d \):

$$

1.6 \times 0.875 \times 0.75 \times \left(1 - \frac{d}{100}\right) = 0.84

$$

$$

\left(1 - \frac{d}{100}\right) = \frac{0.84}{1.6 \times 0.875 \times 0.75}

$$

$$

\left(1 - \frac{d}{100}\right) = \frac{0.84}{1.05}

$$

$$

\left(1 - \frac{d}{100}\right) = 0.8

$$

$$

\frac{d}{100} = 0.2

$$

$$

d = 20\%

$$

- Correct Answer: Option 2, 20%

.