Question

A man sells a TV set for ₹. $ 6900 $ and makes a profit of $ 15\% $ . He sells a second T.V. set a loss of $ 10\% $ . If on the whole, he neither gains nor loses, find the cost price of the second T.V. set.
(A) ₹. $ 9000 $
(B) ₹. $ 10000 $
(C) ₹. $ 11000 $
(D) ₹. $ 12000 $

Answer 1

Hint: In this problem we first calculate the Cost price of the first T.V. set using selling price and profit percentage by using formula and then for second T.V. set finding selling price in term of cost price. Finally equating both cost price and selling price as it is given there is no profit no loss.

Complete step-by-step answer:
Let the cost of the first T.V. set is ‘x’.
Selling price of first T.V. set is ₹. $ 6900 $
Profit on first T.V. set is $ 15\% $
We know that formula to find C.P. when S.P. and profit is given is given as:
On substituting values in above formula we have
 $
  x = 6900\left\{ {\dfrac{{100}}{{100 + 15}}} \right\} \\
   \Rightarrow x = 6900 \times \dfrac{{100}}{{115}} \\
   \Rightarrow x = \dfrac{{690000}}{{115}} \\
   \Rightarrow x = 6000 \\
  $
Therefore the cost price of the first T.V. The set is ₹. $ 6000 $
Now, let CP be the second T.V. the set is ‘y’.
Loss on second T.V. set $ 10\% $ .
Then selling the price of the second T.V. set is given
 $
  S.P. = C.P.\left\{ {\dfrac{{100 - L\% }}{{100}}} \right\} \\
  S.P. = y\left\{ {\dfrac{{100 - 10}}{{100}}} \right\} \\
  S.P. = y\left\{ {\dfrac{{90}}{{100}}} \right\} \\
  S.P. = \dfrac{9}{{10}}y \\
  $
As it is given there is no loss and no profit.

Hence, sum of Cost price of both T.V. set is equal to sum of selling price of both T.V. set.
 $ \Rightarrow 6000 + y = 6900 + \dfrac{9}{{10}}y $
Shifting ‘y’ term on one side and other term on other side.
 $
  y - \dfrac{9}{{10}}y = 6900 - 6000 \\
   \Rightarrow \dfrac{{10y - y}}{{10}} = 900 \\
  $
 $ \Rightarrow \dfrac{y}{{10}} = 900 $
 $ \Rightarrow y = 9000 $
Therefore, the cost price of the second T.V. set is ₹. $ 9000 $ .
Hence, from the above we see that the correct option is (A).

So, the correct answer is “Option A”.

Note: For profit loss problems we must see what conditions are given in statement and in double problems we first solve first condition and then second. Finally using the condition given to find unknown variables for required solution.