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Gita sells two objects AA and BB at the same price such that she makes a profit of 20%20 \% on object AA and aa loss of 10%10 \% on object BB. If she increases the selling price such that objects AA and BB are still sold at an equal price and a profit of 10%10 \% is made on object BB, then the profit made on object A will be nearest to

Solution

✅ Correct Option: 3

Gita has two objects A and B that she sells at equal prices in two different scenarios. We need to find how the profit on object A changes when she adjusts her selling strategy.

Key insight: When objects are sold at equal prices, we can set up equations using their cost prices and profit/loss percentages.


Let's define:

Cost Price of object A = aa

Cost Price of object B = bb


Object A: 20% profit means Selling Price = Cost Price + 20% of Cost Price

SP of A = a+0.2a=1.2aa + 0.2a = 1.2a

Object B: 10% loss means Selling Price = Cost Price - 10% of Cost Price

SP of B = b−0.1b=0.9bb - 0.1b = 0.9b

Since both objects are sold at the same price:

1.2a=0.9b1.2a = 0.9b

This equation tells us how the cost prices of A and B are related.


Now Gita increases the selling price so that:

Object B makes 10% profit: SP of B = 1.1b1.1b

Objects A and B are still sold at equal prices

The ratio between the cost prices aa and bb remains the same, but the selling prices increase proportionally.


From the first scenario: 0.9b=1.2a0.9b = 1.2a

In the second scenario: SP of B = 1.1b1.1b

Using proportions: If 0.9b0.9b corresponds to 1.2a1.2a, then 1.1b1.1b corresponds to:

1.1b=1.10.9×1.2a1.1b = \tfrac{1.1}{0.9} \times 1.2a

1.1b=1.466a1.1b = 1.466a (approximately)

We're scaling up both selling prices by the same factor (1.10.9)\left(\tfrac{1.1}{0.9}\right).


New SP of A = 1.466a1.466a

Cost Price of A = aa

Profit on A = SP - CP = 1.466a−a=0.466a1.466a - a = 0.466a

Profit percentage = ProfitCost Price×100\tfrac{\text{Profit}}{\text{Cost Price}} \times 100

Profit% = 0.466aa×100=46.6%\tfrac{0.466a}{a} \times 100 = 46.6\%

Therefore, the profit on object A is approximately 47%.


Answer: 47%

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