Question

Ranjan purchased 120 tables at a price of Rs.110 per table. He sold 30 tables at a profit of Rs.12 per table and 75 tables at a profit of Rs.14 per table. The remaining tables were sold at a loss of Rs.7 per table. What is the average profit per table?

Answer 1

Hint: In this question a person purchased 120 tables and has sold a different number of tables at different profits or some tables even in loss as well. Average profit can easily be calculated using the concept of total profit divided by the total number of tables sold. Remember that the tables gone in loss means negative profit to them.

Complete step-by-step answer:
Cost price of one table = 110 Rs.
Total number of tables = 120
So the total cost price $ = \left( {110 \times 120 = 13200} \right)$Rs.
Now Ranjan sold 30 tables at the profit of Rs. 12 per table.
So the total profit he earns by selling 30 tables $ = \left( {30 \times 12 = 360} \right)$ Rs.
Now Ranjan sold 75 tables at the profit of Rs. 14 per table.
So the total profit he earns by selling 75 tables $ = \left( {75 \times 14 = 1050} \right)$ Rs.
So the remaining tables are = (120 – 30 - 75) = 15
Now Ranjan sold the remaining tables at the loss of Rs. 7 per table.
So the total loss he bears by selling 15 tables $ = \left( {15 \times 7 = 105} \right)$ Rs.
So the total profit he earns by selling 120 tables $ = \left( {360 + 1050 - 105} \right) = 1305$ Rs.
So the average profit (PA) per table is the ratio of total profit to total tables.
$ \Rightarrow {P_A} = \dfrac{{{\text{total profit}}}}{{{\text{total tables}}}} = \dfrac{{1305}}{{120}} = 10.875$ Rs.
So this is the total profit he earns.
Hence option (B) is correct.

Note: Whenever we face such types of problems the key concept is simply to use the information provided in the question to formulate the total profit thus obtained after reducing the loss amount for the tables being sold. This concept will help to get on the right track to reach the solution.