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 \(\frac{(x −y) }{ p}\) equals

• A. 0.7
• B. 1
• C. 1.2
• D. 0.50

Answer 1

The Correct Option is B

Let the shopkeeper purchase the table at price \( p \).

Transaction with Amal:

• The shopkeeper sells the table to Amal at a profit of 20%.
• So, Amal buys it at: \[ \text{Cost Price for Amal} = 1.2p \]
• Amal sells the table at a profit of 30%: \[ \text{Selling Price by Amal} = 1.3 \times 1.2p = 1.56p \]
• Let this price be \( x \), so: \[ x = 1.56p \]

Transaction with Asim:

• The shopkeeper sells the table to Asim at a loss of 20%.
• So, Asim buys it at: \[ \text{Cost Price for Asim} = 0.8p \]
• Asim sells the table at a loss of 30%: \[ \text{Selling Price by Asim} = 0.7 \times 0.8p = 0.56p \]
• Let this price be \( y \), so: \[ y = 0.56p \]

Difference between Amal's and Asim's Selling Prices:

To find the difference in their selling prices relative to the shopkeeper's cost price: \[ \frac{x - y}{p} = \frac{1.56p - 0.56p}{p} = \frac{1.0p}{p} = 1 \]

Conclusion: The difference between the selling prices of Amal and Asim is exactly equal to the shopkeeper's cost price, that is, \( \boxed{p} \).