Question

A house and a shop were sold for Rs.1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit. The entire transaction resulted in:
A. no loss, no gain
B. loss of \[{\text{Rs}}{\text{.}}\dfrac{1}{{12}}{\text{ lakh}}\]
C. loss of \[{\text{Rs}}{\text{.}}\dfrac{1}{{18}}{\text{ lakh}}\]
D. gain of \[{\text{Rs}}{\text{.}}\dfrac{1}{{24}}{\text{ lakh}}\]

Answer 1

Hint: The cost price can be calculated by the formula \[{\text{CP}} = \dfrac{{{\text{SP}} \times 100}}{{100 + {\text{Profit% }}}}\] for profit or gain and \[{\text{CP}} = \dfrac{{{\text{SP}} \times 100}}{{100 - {\text{Loss% }}}}\] for loss. So, use this concept to reach the solution of the problem.

Complete step-by-step answer:
Given, total selling price of house and shop = 1 lakh + 1 lakh = 2 lakhs
Given, Selling price of House = Rs.1 lakh
The house sale resulted in 20% loss.
We know that \[{\text{CP}} = \dfrac{{{\text{SP}} \times 100}}{{100 - {\text{Loss % }}}}\]
Cost price of house \[ = \dfrac{{1{\text{ lakh}} \times 100}}{{100 - 20}}\]
 \[
   = 1{\text{ lakh }} \times \dfrac{{100}}{{80}} \\
   = \dfrac{5}{4}{\text{ lakh}} \\
\]
Given, Selling price of shop = Rs.1 lakh
The shop sale resulted in 20% gain.
We know that \[{\text{CP}} = \dfrac{{{\text{SP}} \times 100}}{{100 + {\text{Profit% }}}}\]
Cost price of shop \[ = \dfrac{{1{\text{ lakh}} \times 100}}{{100 + 20}}\]
\[
   = 1{\text{ lakh }} \times \dfrac{{100}}{{120}} \\
   = \dfrac{5}{6}{\text{ lakh}} \\
\]
So, total cost price (C.P) of house and shop = cost price of house + cost price of shop
\[
   = \left( {\dfrac{5}{4} + \dfrac{5}{6}} \right){\text{ lakh}} \\
  {\text{ = }}\dfrac{{25}}{{12}}{\text{ lakh}} \\
\]
Since the total cost price is more than the total selling price, there is loss in the entire transaction.
We know that loss = total cost price – total selling price
 \[
   = \left( {\dfrac{{25}}{{12}} - 2} \right){\text{ lakh}} \\
  {\text{ = }}\dfrac{{25 - 24}}{{12}}{\text{ }}{\text{lakh}} \\
  {\text{ = }}\dfrac{1}{{12}}{\text{ lakh}} \\
\]

Therefore, the loss in the entire transaction is \[\dfrac{1}{{12}}{\text{ lakh}}\].
Thus, the correct option is B. loss of \[{\text{Rs}}{\text{.}}\dfrac{1}{{12}}{\text{ lakh}}\]

Note: Loss occurs whenever the total cost price is more than the total selling price. And Profit or Gain occurs whenever the total selling price is more than the total cost price. Profit and Gain are the same.