After getting two successive discounts, a shirt with a list price of 150 taka is available at 105 taka. If the second discount is 12.5% find the first discount.

Let's denote the original price of the shirt as "P."

According to the information given, after two successive discounts, the shirt is available for 105 taka, and the second discount is 12.5%.

After the first discount: The shirt's price is reduced by some percentage, which we'll call "x." So, the price after the first discount is (100% - x%) of the original price, or (100% - x%) * P.

After the second discount: The second discount is 12.5%, which means the price is reduced by 12.5%. So, the price after the second discount is (100% - 12.5%) of the price after the first discount, or (100% - 12.5%) * [(100% - x%) * P].

According to the information given, this final price is 105 taka. So, we can write the equation:

(100% - 12.5%) * [(100% - x%) * P] = 105

Now, let's solve for x:

(87.5%) * [(100% - x%) * P] = 105

First, simplify the left side:

(0.875) * [(1 - x/100) * P] = 105

Now, divide both sides by 0.875:

[(1 - x/100) * P] = 105 / 0.875

[(1 - x/100) * P] = 120

Now, isolate the expression (1 - x/100):

1 - x/100 = 120 / P

Now, isolate x:

x/100 = 1 - 120 / P

x = 100 * (1 - 120 / P)

Now, plug in the original price P = 150 taka:

x = 100 * (1 - 120 / 150)

x = 100 * (1 - 0.8)

x = 100 * 0.2

x = 20

So, the first discount is 20%, which is option C.