Question

A horse and a carriage together cost Rs. 8000. If by selling the horse at a profit of 10% and the carriage at a loss of 10% a total profit of 2.5 is made, then what is the cost price of the horse?
A. Rs.3000
B. Rs.6000
C. Rs.2000
D. Rs.5000

Answer 1

Hint: As we know that cost price (C.P.) means the amount which is pound by the seller to acquire that product and selling price (S.P.) is the money that is finally received by the seller after selling that same product to any customers.
If the S.P. is more than C.P then there will be profit and if C.P. is more then there will be loss for the seller.
Hence profit% is the percent of profit gained by the seller and loss% is percent of loss suffered by the seller.
Profit and loss for any product is given by
Profit \[ = S.P. - C.P\]
Loss \[ = C.P. - S.P\]
Now, profit and loss percentage can be calculated by
\[\begin{gathered}
  Profit\% = \dfrac{{Profit}}{{C.P}} \times 100 \\
  Loss\% = \dfrac{{Loss}}{{C.P}} \times 100 \\
\end{gathered} \]

Complete step by step solution:
Let C.P. of horse \[ = Rs\,x\]
C.P. of carriage \[ = Rs\,(8000 - x)\]
Profit at horse \[ = 10\% \,of\,x\]
Loss at carriage \[ = 10\% \,of\,(8000 - x)\]
Total profit\[ = 2.5\% \,of\,8000\]
According to question
Total profit= profit at horse- loss at carriage
\[
   = 2.5\% \,of\,8000 = 10\% \,of\,x - 10\% \,of\,(8000 - x) \\
\dfrac{{2.5}}{{100}} \times 8000 = \dfrac{{10}}{{100}} \times x - \dfrac{{10}}{{100}} \times (8000 - x) \\
\]
\[
\dfrac{{25}}{{1000}} \times 8000 = \dfrac{{10}}{{100}}\left[ {x - 8000 + x} \right] \\
  25 \times 8 = \dfrac{1}{{10}}\left[ {2x - 8000} \right] \\
  200 \times 10 = 2x - 8000 \\
\]
\[
  2000 = 2x - 8000 \\
  2x = 200 + 8000 \\
  2x = 10000 \\
  x = \dfrac{{10000}}{2} \\
  x = 5000 \\
\]
Hence, C.P. of horse i.e. \[x = 5000\]

Note: Cost price can also be calculated by simply using the formula given below
\[C.P = \dfrac{{100}}{{100 + P\% }} \times S.P\]