CAT 2025 Slot 1 QA Question 22

Type-in-the-answer (no negative marking) · Arithmetic · Profit & Loss · Try it, then check the answer and solution below.

CAT 2025 Slot 1QAArithmetic • Profit & LossModerate

A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is

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Official Convenor Answer Key: 175

Verified Solution:

### Core Concept The problem involves calculating the marked price of chairs based on the given discounts, cost price, and profit percentage. The key formula used is:

\text{Profit Percentage} = \left( \frac{\text{Total Selling Price} - \text{Total Cost Price}}{\text{Total Cost Price}} \right) \times 100\%

### Step-by-Step Solution

Let the Marked Price (M.P.) of each chair be

M

rupees.

Selling Price (S.P.) after 22\% discount:

\text{S.P. per chair} = M \times (1 - 0.22) = 0.78M

Total Selling Price for 12 chairs:

\text{Total S.P.} = 12 \times 0.78M = 9.36M

Total Cost Price (C.P.) for 13 chairs:

\text{Total C.P.} = 13 \times 100 = 1300 \text{ rupees}

Profit of 26\% on Total C.P.:

\text{Profit} = 0.26 \times 1300 = 338 \text{ rupees}

Equation for Profit:

\text{Total S.P.} - \text{Total C.P.} = \text{Profit} 9.36M - 1300 = 338

Solving for

M

$$ 9.36M = 338 + 130

Answer and solution

Answer: 175

### Core Concept The problem involves calculating the marked price of chairs based on the given discounts, cost price, and profit percentage. The key formula used is:

\text{Profit Percentage} = \left( \frac{\text{Total Selling Price} - \text{Total Cost Price}}{\text{Total Cost Price}} \right) \times 100\%

### Step-by-Step Solution

Let the Marked Price (M.P.) of each chair be

M

rupees.

Selling Price (S.P.) after 22\% discount:

\text{S.P. per chair} = M \times (1 - 0.22) = 0.78M

Total Selling Price for 12 chairs:

\text{Total S.P.} = 12 \times 0.78M = 9.36M

Total Cost Price (C.P.) for 13 chairs:

\text{Total C.P.} = 13 \times 100 = 1300 \text{ rupees}

Profit of 26\% on Total C.P.:

\text{Profit} = 0.26 \times 1300 = 338 \text{ rupees}

Equation for Profit:

\text{Total S.P.} - \text{Total C.P.} = \text{Profit} 9.36M - 1300 = 338

Solving for

M

$$ 9.36M = 338 + 130

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