Question

A shopkeeper allows a discount of 10% on a watch whose marked price is Rs. 3400 and in the process makes a gain of Rs. 220. What is the cost price of the watch?
A. Rs.2340
B. Rs.2540
C. Rs.2840
D. Rs.2440

Answer 1

- Hint: Assume the cost price to be $Rs.x$, so on a gain of 220 the selling price should be \[Rs.\left( x+220 \right)\]. Equate this with the selling price given in question i.e. 10% on Rs.3400 to form an equation in x and finally solve the obtained equation to get the value of x.

Complete step-by-step solution -

According to the question, the shopkeeper sells the watch at a discount of 10% on marked price of Rs.3400.
So, selling price = (marked price) – (10% of marked price)
$\begin{align}
  & =Rs.3400-Rs.\left( \dfrac{10}{100}\times 3400 \right) \\
 & =Rs.3400-Rs.340 \\
 & Selling\ price=Rs.3060............\left( 1 \right) \\
\end{align}$
We have to find the cost price of the watch, profit gained by shopkeeper = Rs. 220.
Let us assume the cost price of the watch to be $Rs.x$.
From equation (1), selling price = Rs. 3060. Putting this value of selling price, we will get,
$\begin{align}
  & gain=\left( Rs.3060 \right)-Rs.x \\
 & \Rightarrow gain=Rs.\left( 3060-x \right) \\
\end{align}$
But according to question, gain = Rs. 220.
So, $3060-x=220$
Taking constant term to RHS, we will get,
$\begin{align}
  & -x=220-3060 \\
 & \Rightarrow -x=-2840 \\
\end{align}$
Multiplying both sides of equation by “-1”, we will get,
$\Rightarrow x=2840$
Hence, the required cost price of watch will be Rs. 2840 and option (C) is the correct answer.

Note: Students can make mistakes by taking a 10% discount on cost price. But be careful that the shopkeeper has given discount on marked price, so selling price will be marked price – 10% of marked price.