Question

A mirror is listed at Rs. 1,000. A retailer buys it with two discounts of 20% and 10% each. The retailer incurs an additional cost of 10% of the cost of the mirror on woodwork for making a dressing table. At what price should he sell the dressing table to make a profit of 15%?
(a) Rs 900
(b) Rs 910.80
(c) Rs 800
(d) Rs 840

Answer 1

Hint: It is given that the retailer gets 2 discounts in the order of 20% and 10%. Thus, we will first deduct 20% of the price of the mirror and then deduct 10% of the reduced price from the reduced price. It is also given that he incurs a cost of 10% of the final reduced price for woodwork. Thus, the cost price will be the sum of the reduced price and 10% of the reduced price. Then we will find the sum of the cost price and 15% of the cost price to find the selling price so that he can make a profit of 15%. To find the p percent of the amount x, we will use the relation $x\times \dfrac{p}{100}$.

Complete step-by-step solution:
It is given to us that the initial cost of the mirror is Rs 1000 and he gets 2 discounts of 20% and 10% each.
So, 20% of the cost of mirror, i.e. Rs 1000 is $1000\times \dfrac{20}{100}$ = 200.
So, the first reduced price will be the difference between the initial cost and 20% of the initial cost.
Thus, the first reduced price is 1000 – 200 = Rs 800
Now, the retailer got another discount of 10%.
10% of the first reduced cost will be $800\times \dfrac{10}{100}$ = 80.
So, the final discounted price will be the difference between the first reduced cost and 10% of the first reduced cost.
Thus, the final discounted price is 800 – 80 = Rs 720
Now, it is given that he incurs a cost of 10% of the final discounted cost for woodwork.
So, 10% of the final discounted is $720\times \dfrac{10}{100}$ = 72
The cost price of the mirror is the sum of the discounted price and woodwork cost.
Therefore, the cost price of the mirror is 720 + 72 = Rs 792
Now, he wants to earn a profit of 15%.
So, the selling price of the mirror will be the sum of the cost price and 15% of the cost price.
15% of cost price is $792\times \dfrac{15}{100}$ = 118.80
Therefore, the selling price for 15% profit should be 792 + 118.80 = Rs 910.80
Hence, option (c) is the correct option.

Note: It is to be noted that two discounts of 20% and 10% will give different values than a complete discount of 30%. Students are advised to be careful in such scenarios. Some students add both discounts and then go to the final answer which is wrong as here we are given the discount successively.