Question

A TV set is being sold for Rs.$x$ in Chandigarh. A dealer went to Delhi and bought the TV at 20% discount (from the price of Chandigarh). He spent Rs.600 on transport. Thus he sold the set in Chandigarh for Rs.\[x\] making $14\dfrac{2}{7}$% profit. Find the value of $x$?
a)Rs.9600
b)Rs.8800
c)Rs.8000
d)Rs.7200

Answer 1

Hint: Use the formula that relates selling price to the cost price of an article (in this case, the TV).
Selling Price $=Cost\text{ }price\times \left( \dfrac{100+Profit\%}{100} \right)$
Discounts are reduction of the cost price, generally expressed as a fraction or percentage of the original cost price (20% discount in this case). Margin of profit reduces on external/additional expenditures (Money spent on transport).

Complete step by step answer:
We are given that a TV set is being sold for Rs.$x$ in Chandigarh.
We are given that a dealer bought the same TV for a discount of 20% from Delhi.
Hence, the cost price of the TV bought from Delhi, $C=x-(20\%\,of\,x)$
But, we are also given that he spent an amount of Rs.600 for transport.
Hence, we can write that
The total cost price $=\left( x-\dfrac{20x}{100} \right)+600$
$=\left( \dfrac{100x-20x}{100} \right)+600$
$=\dfrac{80x}{100}+600$
$=0.8x+600$
$\therefore $ The total cost price$=0.8x+600$
We are given that the dealer sold the TV set in Chandigarh for Rs.$x$ and made a $14\dfrac{2}{7}$% profit.
We know that,
Selling Price $=Cost\text{ }price\times \left( \dfrac{100+Profit\%}{100} \right)$
Hence, the selling price of the TV $=Cost\text{ }price\times \left( \dfrac{100+Profit\%}{100} \right)$
$=(0.8x+600)\times \left( \dfrac{100+14\dfrac{2}{7}}{100} \right)$
But, the price for which the dealer sold the TV set was Rs.$x$. Hence, we can formulate the equation as
$x=(0.8x+600)\times \left( \dfrac{100+14\dfrac{2}{7}}{100} \right)$
Converting the mixed fraction into normal fraction, we have
$x=(0.8x+600)\times \left( \dfrac{100+\dfrac{100}{7}}{100} \right)$
Taking the LCM and simplifying further, we have
\[x=(0.8x+600)\times \left( \dfrac{1+\dfrac{1}{7}}{1} \right)\]
\[x=(0.8x+600)\times \left( \dfrac{7+1}{7} \right)\]
\[7x=(8\times 0.8x)+(8\times 600)\]
\[7x-6.4x=4800\]
\[0.6x=4800\]
\[\therefore x=\dfrac{4800}{0.6}=Rs.8000\]
Hence, the dealer sold the TV set for an amount of Rs.8000 in Chandigarh.

So, the correct answer is “Option C”.

Note: The selling price of an article is the actual price for which the article is sold by the possessor. The cost price is the price for which the buyer bought the article.
The same question could have been asked to find the profit margin, in which case the selling price would be given. The equation for profit is,
$Profit\,\%=\left( \dfrac{Selling\,price\,-\,Cost\,price}{Cost\,price} \right)\times 100$
Likewise,
$Loss\,\%=\left( \dfrac{Cost\,price\,-\,Selling\,price}{Cost\,price} \right)\times 100$
The question can also be solved using the equation, $Profit\,\%=\left( \dfrac{Selling\,price\,-\,Cost\,price}{Cost\,price} \right)\times 100$
by substituting the known values and solving for the selling price ($x$).