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.

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:
\[SP = x - 10\% ofx\]
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.