Question

Find a single discount equivalent to two successive discounts of 15% and 20%.

Answer 1

Hint: Let the initial price of the article be Rs. 100. Then, find the price of the article left after two successive discounts of 15% and 20%. Then , find the discounted amount by subtracting the discounted price from the initial price. Then, calculate the net discount by using the formula, ${\displaystyle \frac{\text{Discount}}{\text{Initial Price}}}\times 100$.

Complete step-by-step answer:
We have to give a single discount when two successive discounts of 15% and 20% are on a product.
Let the price of the article be Rs. 100.
If first discount is 15% on Rs. 100, then the discount on the price will be ${\displaystyle \frac{15}{100}}\times 100=15$
The effective price will be calculated by subtracting 15 from Rs. 100.
$100-15=85$
Next, 20% discount is given on Rs. 85
${\displaystyle \frac{20}{100}}\times 85=17$
Then, the net price will be $85-17=68$
We will calculate the discounted amount by subtracting 68 from 100.
$100-68=32$
The net discount percent is ${\displaystyle \frac{\text{Discount}}{\text{Initial Price}}}\times 100$
Hence, ${\displaystyle \frac{32}{100}}\times 100=32\mathrm{\%}$
Thus, the net discount is 32%.

Note: We have assumed Rs. 100 as the initial price. But, we can also do this question by letting the initial price as $x$ and then solving in the similar manner. Discount is always calculated on marked price. Many students make mistakes by just adding the given discounts which is incorrect. The given discounts are successive discounts. This implies, first the discount of 15% is applied and then on the left amount discount of 20% is applied.