Question

A trader marked the price of a T.V 30% above the cost price of the T.V. and gave the purchaser 10% discount on the marked price, thereby gaining Rs 340. Find the cost price of the T.V.?

Answer 1

Hint: First, we will assume some variable for the value of the cost price of the T.V. Then, we will find the marked price of the T.V., which is 30% above the cost price of the T.V. After that, we will find the discounted price which is 10% less than the marked price. Thus, the difference between this discounted price and the cost price is Rs 340. With this information, we can find the cost price of the T.V.

Complete step by step answer:
Let the cost price of the T.V. be x.
It is given that the marked price is 30% above the cost price.
30% of the cost price is given as $\dfrac{30}{100}\times x$ = 0.3x.
Marked price = (cost price + 30% of cost price)
$\Rightarrow $ Marked price = x + 0.3x = 1.3x
It is also given that the trader gives a discount of 10% on the marked price.
10% of marked price is given as
$\Rightarrow \dfrac{10}{100}\times 1.3x$
$\Rightarrow $ 0.1 (1.3x)
$\Rightarrow $ 0.13x
Therefore, the discount is 0.03x and the discounted price will be equal to difference of marked price and discount.
$\Rightarrow $ Discounted price = marked price – discount
$\Rightarrow $ Discounted price = 1.3x – 0.13x = 1.17x
We know that after giving this discount, the trader earns Rs 340. This means the difference between the discounted price and cost price is 340.
$\Rightarrow $ 1.17x – x = 340
$\Rightarrow $ 0.17x = 340
$\Rightarrow $ x = 2000
Therefore, the cost price of the T.V is Rs 2000.

Note: Step-by-step is the only approach to this question, when options are not given. Students are advised to have a good hold on the concepts of percentage to be quicker in solving profit-loss questions.