Question

A merchant purchases a wristwatch for Rs. 450 and fixes the list price in such a way after allowing a discount of 10 % he earns a profit of 20 %. What is the list price of the watch?
(a). Rs. 500
(b). Rs. 600
(c). Rs. 700
(d). Rs. 750

Answer 1

Hint: Assume a variable for the list price of the watch and then calculate the price after 10 % discount. Then using the formula for gain percent, which is $${\displaystyle \frac{Gain}{CP}}\times 100\mathrm{\%}$$, equate the list price and find the value of the list price.

Complete step-by-step answer:
The cost price of the watch is Rs. 450.
The list price of the watch is the selling price of the watch and let it be Rs. X.
After a discount of 10 %, the value of the selling price will be reduced by 10 % of the selling price.
Hence, the reduced selling price is given as:
$$SP=x-10\mathrm{\%}ofx$$
Simplifying, we get:
$$SP=x-{\displaystyle \frac{10}{100}}x$$
$$SP=x-0.1x$$
$$SP=0.9x...........(1)$$
The gain is the difference between the selling price and the cost price. The gain by selling the wrist watch at a discount of 10 % is given as follows:
Gain = SP – CP
Gain = $$0.9x-450..........(2)$$
The formula for gain percent is given as follows:
$$Gain\mathrm{\%}={\displaystyle \frac{Gain}{CP}}\times 100\mathrm{\%}$$
It is given that the gain percent is 10 %. Hence, using equation (2), we get:
$$10\mathrm{\%}={\displaystyle \frac{0.9x-450}{450}}\times 100\mathrm{\%}$$
Simplifying, we have:
$$10={\displaystyle \frac{0.9x-450}{9}}\times 2$$
Taking 9 in the denominator to the other side, we have:
$$90=(0.9x-450)\times 2$$
Simplifying, we have:
$$90=1.8x-900$$
Taking 900 to the other side, we have:
$$90+900=1.8x$$
$$990=1.8x$$
Solving for x, we have:
$$x={\displaystyle \frac{990}{1.8}}$$
$$x=Rs.500$$
Hence, the original list price of the wristwatch is Rs. 500.
Hence, the correct answer is option (a).

Note: You can also solve the question backward starting by finding the gain, then the discounted selling price, then the original selling price using the discount percentage.