Find a single discount equivalent to following successive discounts of 50%, 10% and 20% in percent?

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54%

64%

74%

84%

answer is B.

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Detailed Solution

According to the problem, we are asked to find the single discount equivalent to successive discounts of 50%, 10% and 20%.
Let us assume the price for which we apply the successive discounts is ‘x’.
Let us apply 50% to this price. So, the new price will be (100−50)% = 50% of ‘x’.
We know that a% of b is defined as

\frac{a}{100} \times b .

So, the new price will be

\frac{50}{100} \times x = 0.5 x .

Now, let us apply a 10% discount to this new price. So, the updated price will be (100−10)% = 90% of 0.5x.
So, the updated price will be

\frac{90}{100} \times 0.5 x = 0.45 x .

Now, let us apply a 20% discount to this updated price. So, the final price will be (100−20)% = 80% of 0.45x.
So, the final price will be

\frac{80}{100} \times 0.45 x = 0.36 x .

We know that the percent change in the price will be the final equivalent discount provided.
So, we have final equivalent discount =

\frac{initial price - final price}{initial price} \times 100 .

⇒ Final equivalent discount

= \frac{x - 0.36 x}{x} \times 100 .

⇒ Final equivalent discount =

\frac{0.64 x}{x} \times 100 .

⇒ Final equivalent discount = 64%.
So, we have found the single equivalent discount of the successive discounts 50%, 10% and 20% as 64%.
So, the correct answer is “Option 2”.

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