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

$0.7$

$1$

$0.50$

$1.2$

✅ Correct Option: 2

When we say someone sells at a 20% profit, the selling price becomes 120% of the cost price (original price + 20% extra). Similarly, a 20% loss means the selling price becomes 80% of the cost price (original price - 20% reduction).

Profit of 20% → Selling price = Cost price × 1.2

Loss of 20% → Selling price = Cost price × 0.8

Cost price for shopkeeper: $p$

Selling price to Amal: $p \times 1.2 = 1.2p$

This means Amal pays $1.2p$ for his table.

Cost price for shopkeeper: $p$

Selling price to Asim: $p \times 0.8 = 0.8p$

This means Asim pays $0.8p$ for his table.

Cost price for Amal: $1.2p$ (what he paid)

Selling price to Bimal: $1.2p \times 1.3 = 1.56p$

This means Bimal pays $x = 1.56p$

Note: 30% profit means selling at 130% of cost price.

Cost price for Asim: $0.8p$ (what he paid)

Selling price to Barun: $0.8p \times 0.7 = 0.56p$

This means Barun pays $y = 0.56p$

Note: 30% loss means selling at 70% of cost price.

Now we can find $(x - y)/p$ :

$\tfrac{x - y}{p} = \tfrac{1.56p - 0.56p}{p} = \tfrac{1.00p}{p} = 1$

Answer: $(x - y)/p = 1$

In chain transactions, we can multiply all the percentage factors directly:

For Bimal: $p \times 1.2 \times 1.3 = 1.56p$

For Barun: $p \times 0.8 \times 0.7 = 0.56p$

This saves time and reduces calculation errors!

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