Question

A dealer bought a refrigerator for Rs. 11515. After allowing a discount of 16% on its marked price, he gains 20%. Find the marked price of a refrigerator.

Answer 1

Hint: In this question it is given that a dealer bought a refrigerator for Rs. $11515$. After allowing a discount of 16% on its marked price, he gains $20\%$. We have to find the marked price of a refrigerator. So to find the solution we need to know that the discount always applies on its marked price (M.P) and gain and loss applies on its cost price (C.P).

Complete step-by-step solution:
Here it is given that a dealer bought a refrigerator for Rs. $11515$.
Therefore the cost price, C.P = Rs. $11515$
Let us consider the marked price(M.P) = Rs. $x$
16% discount on M.P, i.e, the discount = 16% of x = $$\dfrac{16x}{100}$$
Therefore, the selling price (S.P) = M.P - discount
i.e, S.P = $$x-\dfrac{16}{100} \times x$$
                        = $$x-\dfrac{16x}{100}$$
                        = $$\dfrac{100x-16x}{100}$$
                        = $$\dfrac{84x}{100}$$..........(1)
Also by selling that refrigerator, he gained 20%, i.e, he gets the profit of 20%.
Therefore, profit = 20% of C.P
                          = $$\dfrac{20}{100} \times 11515$$
                          = $$\dfrac{1}{5} \times 11515$$
                          = $$2303$$
Therefore, S.P = C.P + profit
                        = $$11515+2303$$
                        = $13818$……….(2)
Now from (1) and (2) we can write,
  $$\dfrac{84x}{100} =13818$$
$$\Rightarrow 84x=13818\times 100$$
$$\Rightarrow 84x=1381800$$
$$\Rightarrow 84x=1381800$$
$$\Rightarrow x=16450$$
Therefore the marked price of the refrigerator is Rs. $16450$.

Note: While solving this type of question you need to know that discount is always applied on marked price (M.P) and the selling price (S.P) = M.P - Discount
Also while calculating ($r \%$ of A) can be written as,
r % of A = $$\dfrac{r}{100} \times A$$
Where, we have transformed the statement into mathematical expression, we replaced $‘\%’$ by $$\dfrac{1}{100}$$ and ‘of’ by $$\times$$.