CAT 2019Slot 2QAQuestion & 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
1
1.2
0.50
0.7
Solution
1. Concept Used
- Topic: Profit and Loss — Successive Percentage Changes
- Formula: $$\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{profit%}}{100}\right) \quad \text{or} \quad \text{Cost Price} \times \left(1 - \frac{\text{loss%}}{100}\right)$$
2. Calculation
Each table has an original cost price of $$p$$.
The shopkeeper sells to Amal at a 20% profit, so Amal pays: $$1.2p$$
The shopkeeper sells to Asim at a 20% loss, so Asim pays: $$0.8p$$
Now, Amal sells his table to Bimal at a 30% profit on his own cost price of $$1.2p$$: $$x = 1.2p \times 1.3 = 1.56p$$
Asim sells his table to Barun at a 30% loss on his own cost price of $$0.8p$$: $$y = 0.8p \times 0.7 = 0.56p$$
Notice something elegant here — both $$x$$ and $$y$$ end up as products of symmetric multipliers: $$(1.2 \times 1.3)$$ and $$(0.8 \times 0.7)$$. The first pair multiplies numbers above 1 and below 1 in opposite directions, but their difference locks in perfectly: $$x - y = 1.56p - 0.56p = 1.00p$$
Therefore: $$\frac{x - y}{p} = \frac{1.00p}{p} = 1$$
3. Solution
Answer = Option 1 ✅
The final calculated value is 1. Remarkably, the difference between what Bimal and Barun pay is exactly equal to the original cost price $$p$$ of each table.