Question

An almirah of market price Rs.4,000 is sold for Rs. 3,700 after allowing a certain discount. Find the rate of discount.

Answer 1

Hint: First of all use the formula for discount = market price – selling price, by putting market price = Rs.4000 and selling price = Rs. 3700. Now use the formula to calculate the rate of discount that is $\dfrac{Discount}{Market\ price}\times 100$.

Complete step-by-step answer:
Here we are given an almirah whose market price is Rs. 4000. This almirah is sold for Rs. 3700 after allowing a certain discount. We have to find the rate of this discount.
Before proceeding with the question, we must know the meaning of market price, selling price, discount etc.
Market price is the economic price for which a good or service is offered in the marketplace. This price is the original value of the item without any concession etc.
Now, selling price is the price at which a good or service is actually sold to the consumer. It includes concession etc. in the market price of the item.
Now, discount is the deduction in an amount from its usual price. In other words, we can also say that discount is the difference between the market price and selling price. We can write as,
Discount = Market Price – Selling Price.
As we know that discount is given in market price. Therefore, the discount rate is always calculated with respect to the market price. So, we get,
Rate of Discount $=\dfrac{Discount}{Market\ price}\times 100$
Here Discount = Market Price – Selling Price.
Now, we are given an almirah whose market price = Rs. 4000. We are also given that this almirah is sold at Rs. 3700. Therefore, we get the selling price of almirah = Rs. 3700.
We know that Discount = Market Price – Selling Price. By putting the value of market price and selling price of almirah, we get the discount on almirah as,
Discount = Rs. 4000 – Rs. 3700
Discount = Rs. 300
Therefore, we have got the discount on almirah as Rs. 300. Now, we know that the discount $=\dfrac{Discount}{Market\ price}\times 100$. So, to get the rate of discount on almirah, we put the value of discount and market price in the above formula, we get,
Rate of discount $=\dfrac{Rs.300}{Rs.4000}\times 100$
By simplifying it we get,
Rate of discount $=\dfrac{30}{4}\%=7.5\%$
Therefore, almirah is sold at Rs. 3700 after the discount of $7.5\%$ on market price that is Rs. 4000.

Note: Students must note that the rate of anything is always in percentage $(\%)$. Also, students can cross-check their answer as follows,
Suppose our market price is m.p. and selling price s.p., as we know the selling price is price after the discount of say x% in market price, therefore, we get,
$(M.P.) – x\% of (M.P.) = S.P.$
By putting the value of M.P. = Rs. 4000 and discount = $7.5\%$ we get;
$S.P. = (4000) - (7.5\% \text{of} 4000)$
By simplifying the above equation, we get $S.P. = (4000) – (300)$.
Therefore, we get S.P. = Rs. 3700 which is equal to our given selling price.
Therefore, our answer is correct.