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

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 $\dfrac{{Gain}}{{CP}} \times 100\%$, equate the list price and find the value of the list price.

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:
$SP = x - 10\% ofx$
Simplifying, we get:
$SP = x - \dfrac{{10}}{{100}}x$
$SP = x - 0.1x$
$SP = 0.9x...........(1)$
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:
$Gain\% = \dfrac{{Gain}}{{CP}} \times 100\%$
It is given that the gain percent is 10 %. Hence, using equation (2), we get:
$10\% = \dfrac{{0.9x - 450}}{{450}} \times 100\%$
Simplifying, we have:
$10 = \dfrac{{0.9x - 450}}{9} \times 2$
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:
$x = \dfrac{{990}}{{1.8}}$
$x = Rs.500$
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.