CAT 2019 Slot 2 QA Question & Solution
Question
A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x − y) / p equals
Options
Solution
Let the cost price of each table $= p$.
It is given that the shopkeeper sold the tables to Amal at a profit of 20% and to Asim at a loss of 20%.
Hence, the selling prices of the tables are:
- To Amal: $1.2p$
- To Asim: $0.8p$
Amal sells his table to Bimal at a profit of 30%:
$$
\text{Cost price for Bimal } (x) = 1.2p \times 1.3 = 1.56p
$$
Asim sells his table to Barun at a loss of 30%:
$$
\text{Cost price for Barun } (y) = 0.8p \times 0.7 = 0.56p
$$
The difference in cost prices relative to $p$ is:
$$
\frac{x - y}{p} = \frac{1.56p - 0.56p}{p} = \frac{1p}{p} = 1
$$
Hence, the difference between the cost prices of the tables for Bimal and Barun is equal to the original cost price $p$.