CAT 2025 Slot1 Quant: A shopkeeper offers a discount of 22% on the marked price
February 20, 2026 2026-02-20 22:58CAT 2025 Slot1 Quant: A shopkeeper offers a discount of 22% on the marked price
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Total CP for 13 chairs = $13 \times 100 = 1300$.
Total SP (with 26% profit) = $1.26 \times 1300 = 1638$.
This SP is the discounted price of 12 chairs: $12 \times (0.78 \times MP) = 1638$.
$MP = \frac{1638}{12 \times 0.78} = \mathbf{175}$.
Detailed Step-by-Step Solution
Step 1: Calculate Total Cost Price (CP)
The shopkeeper gives 13 chairs. Each chair costs Rs 100.
Total $CP = 13 \times 100 = \text{Rs } 1,300$.
Step 2: Calculate Total Selling Price (SP)
The shopkeeper earns a 26% profit on the transaction.
Total $SP = CP + 26\% \text{ of } CP$
Total $SP = 1300 \times 1.26 = \text{Rs } 1,638$.
Step 3: Relate SP to Marked Price (MP)
The customer pays for 12 chairs at a 22% discounted price.
Discounted Price of 1 chair = $MP \times (1 - 0.22) = 0.78 \times MP$.
Total $SP$ (from 12 chairs) $= 12 \times (0.78 \times MP)$.
Step 4: Solve for MP
$12 \times 0.78 \times MP = 1,638$
$9.36 \times MP = 1,638$
$MP = \frac{1,638}{9.36} = \mathbf{175}$.