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Q.

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


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a

54%

b

64%

c

74%

d

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 a100×b.
So, the new price will be 50100×x=0.5x.
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 90100×0.5x=0.45x.
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 80100×0.45x=0.36x.
We know that the percent change in the price will be the final equivalent discount provided.
So, we have final equivalent discount = initial price - final priceinitial price × 100.
⇒ Final equivalent discount = x-0.36xx×100.
⇒ Final equivalent discount = 0.64xx×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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