CAT 2023 Slot 1 QA Question 12

Multiple choice (+3 / −1) · Arithmetic · Profit & Loss · Try it, then check the answer and solution below.

Gita sells two objects

A

and

B

at the same price such that she makes a profit of $20 \%

on object

and

loss of &#36;10 \%

on object

B

. If she increases the selling price such that objects

A

and

B

are still sold at an equal price and a profit of $10 \%

is made on object

B , then the profit made on object A will be nearest to

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: C

Answer and solution

Answer: C) $47\%$

📌 Core Concept

The problem involves calculating profit percentages based on cost prices and selling prices. The key formulas used are:

Selling Price (SP) = Cost Price (CP) × (1 + Profit Percentage)

Selling Price (SP) = Cost Price (CP) × (1 - Loss Percentage)

🔢 Step-by-Step Solution

Initial Selling Prices:

For object A:

SP = 1.2 \times C_A

For object B:

SP = 0.9 \times C_B

Since both SPs are equal:

&#36;1.2 \times C_A = 0.9 \times C_B \implies \frac{C_A}{C_B} = \frac{0.9}{1.2} = \frac{3}{4}

Thus,

C_B = \frac{4}{3} C_A

New Selling Price for B:

New SP' for B with 10% profit:

SP' = 1.1 \times C_B

Express SP' in terms of

C_A

SP' = 1.1 \times \frac{4}{3} C_A = \frac{4.4}{3} C_A \approx 1.4667 C_A

Calculate Profit Percentage on A:

\text{Profit} = SP' - C_A = 1.4667 C_A - C_A = 0.4667 C_A

\text{Profit Percentage} = 0.4667 \times 100 \approx 46.67\%

The closest option is 47%.

⚡ 30-Second Shortcut

Recognize that the ratio of cost prices

C_A : C_B = 3 : 4

After adjusting SP for B to a 10% profit, calculate the new SP in terms of

C_A

The new SP leads to a profit of approximately 46.67%, which rounds to 47%.

🎯 Final Answer

Correct Answer: C

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