A discount series of 15%, 20% and 25% is equal to the single discount of ?

15%, 20% और 25% की छूटश्रृंखला कितने % की एकल छूट के बराबर है ?

Options

A. `48%`
B. `49%`
C. `50%`
D. `51%`

Explanation

To find the equivalent single discount for a series of discounts of 15%, 20%, and 25%, we can use the formula for calculating the equivalent discount for two successive discounts, which is:

\[ D = A + B - \frac{A \times B}{100} \]

Where \(D\) is the equivalent discount, and \(A\) and \(B\) are the two successive discounts.

### Step 1: Calculate the equivalent discount for the first two discounts (15% and 20%).

Let \(A = 15\%\) and \(B = 20\%\).

Using the formula:

\[ D_1 = 15 + 20 - \frac{15 \times 20}{100} \]

Calculating the product:

\[ 15 \times 20 = 300 \]

Now, substituting back into the equation:

\[ D_1 = 15 + 20 - \frac{300}{100} \]
\[ D_1 = 15 + 20 - 3 = 32\% \]

### Step 2: Now calculate the equivalent discount using the result from Step 1 (32%) and the third discount (25%).

Let \(A = 32\%\) and \(B = 25\%\).

Using the formula again:

\[ D_2 = 32 + 25 - \frac{32 \times 25}{100} \]

Calculating the product:

\[ 32 \times 25 = 800 \]

Now, substituting back into the equation:

\[ D_2 = 32 + 25 - \frac{800}{100} \]
\[ D_2 = 32 + 25 - 8 = 49\% \]

### Final Answer:
The equivalent single discount for the series of discounts of 15%, 20%, and 25% is **49%**.

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