Question

A trader marked a watch 40 % above the cost price and then gave a discount of 10 %. He made a net profit of Rs. 468 after paying a tax of 10 % on the gross profit. What is the cost price of the watch?
(a) Rs. 1200
(b) Rs. 1800
(c) Rs. 2000
(d) Rs. 2340

Answer 1

Hint: In order to find the solution to this question, we will consider a variable x as the cost price, and then we will find the other values like marked price, selling price, gross profit, etc. in terms, and then we will simplify it to find x.

Complete Step-by-Step solution:
In this question, we are asked to find the cost price of the watch with a few given conditions. For that, we will consider the cost price of the watch as Rs. x. So, we can write it as,
The cost price of the watch = x…..(i)
Now, in the question, it is given that the trader marked the price of watch 40 % above the cost price. So, we can write it as,
Marked price = x + 40 % of x
Marked Price = \[x+\dfrac{40}{100}\left( x \right)\]
Now, we will simplify it further, we will get,
Marked price = \[x+\dfrac{2}{5}x\]
Now, we will take the LCM. So, we will get,
Marked price \[=\dfrac{5x+2x}{5}\]
Or we can write it as,
Marked price \[=\dfrac{7x}{5}....\left( ii \right)\]
Now, it is given that the trader gave a discount of 10 % on the marked price. So, we can write the selling price as
Selling Price \[=\left[ \dfrac{7x}{5} \right]-\]10 % of \[\left[ \dfrac{7x}{5} \right]\]
Now, we will simplify it further, so we will get,
Selling price \[=\dfrac{7x}{5}-\dfrac{10}{100}\times \dfrac{7x}{5}\]
Selling price \[=\dfrac{7x}{5}-\dfrac{1}{10}\times \dfrac{7x}{5}\]
Now, we will take the LCM. So, we will get,
Selling price \[=\dfrac{70x-7x}{50}\]
Selling price \[=\dfrac{63x}{50}....\left( iii \right)\]
Now, we know that the gross profit is the profit made by the trader after deducting the cost price of the watch from selling the price of the watch. Therefore, we can write it as,
Gross Profit = Selling Price – Cost Price
From equation (i) and (iii), we will put the value of cost price and selling price to get the value of gross profit. So, we get,
Gross profit = \[\dfrac{63x}{50}-x\]
Now, we will take LCM, so we will get,
Gross Profit \[=\dfrac{63x-50x}{50}\]
Gross Profit \[=\dfrac{13x}{50}....\left( iv \right)\]
Now, it is given that after paying a tax of 10 % on gross profit, the trader made a net profit of Rs. 468. So, we can write,
\[468=\dfrac{13x}{50}-\] 10 % \[\left[ \dfrac{13x}{50} \right]\]
\[468=\dfrac{13x}{50}-\dfrac{10}{100}\times \dfrac{13x}{50}\]
Now, we will simplify it further, so we will get,
\[468=\dfrac{13x}{50}-\dfrac{13x}{500}\]
Now, we will take LCM. So, we will get,
\[468=\dfrac{130x-13x}{500}\]
\[468\times 500=117x\]
\[\dfrac{468\times 500}{117}=x\]
\[4\times 500=x\]
\[x=2000\]
Here, we have found the value of x, that is the cost price.
Therefore, the cost price of the watch is Rs. 2000.
Hence, the option (c) is the correct answer.

Note: In this question, mistakes are possible at the steps where we added a percentage of something like the step where we have marked price, selling price, etc. Also, we have to be very careful while solving the question because there are high possibilities of calculation mistakes. We must read the question carefully and formulate the right equations to get the value of x.