CAT 2025 Slot1 Quant: A shopkeeper offers a discount of 22% on the marked price

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
$12 \times 0.78 \times MP = 1,638$
$9.36 \times MP = 1,638$
$MP = \frac{1,638}{9.36} = \mathbf{175}$.