Question

In a winter sale offer a shopkeeper allows a discount of 15% even after giving the discount he makes a profit of 6.25%. Raghav bought a sweater which was marked at Rs 5000. Find the cost price of this sweater for the shopkeeper.
A. Rs 5000
B. Rs 4000
C. Rs 4250
D. Rs 5250

Answer 1

Hint: The concept of percentages and profit-loss will be applied in this problem. To find the cost price of the sweater, first we will find the discounted amount of the sweater with the 15% discount. After that, we will apply the condition that the discounted price itself is 6.25% greater than the actual cost price. This will give us the final answer.

Complete step-by-step answer:

We have been given that Raghav buys a sweater which is marked at Rs 5000. This means that the actual MRP of the sweater is Rs 5000. The selling price of this sweater is 15% less than the actual price, which can be calculated as-
$5000 - 15\% \;of\;5000 = SP$
$SP = 5000 - \dfrac{{15}}{{100}} \times 5000 = 5000\left( {1 - \dfrac{{15}}{{100}}} \right) = 5000\left( {\dfrac{{85}}{{100}}} \right) = Rs\;4250$
Now, we have also been given that the shopkeeper earns a 6.25% profit on the discounted selling price. So we can imply here that the selling price(SP) is 6.25% greater than the cost price(CP), which is-
$CP + 6.25\% \;of\;CP = SP$
$CP + \dfrac{{6.25}}{{100}} \times CP = 4250$
$CP\left( {1 + \dfrac{{6.25}}{{100}}} \right) = 4250$
$CP\left( {\dfrac{{106.25}}{{100}}} \right) = 4250$
$CP = 4250 \times \dfrac{{100}}{{106.25}} = Rs\;4000$
This is the required cost price of the sweater, the correct option is B.

Note: A common mistake here is that students in a hurry often mark the selling price as the answer, which is Rs 4250. Such options are always mentioned in the questions to confuse the students, so we should always read and interpret the question carefully. Also, some students might think that Rs 5000 is the discounted price of 15%, but it is written that the sweater is marked at Rs 5000, and the marked price is always the MRP.