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

The correct answer is 175.

Let's break down the problem step-by-step to find the marked price of each chair.

First, we establish the cost price (CP) of each chair, which is given in the problem:

$\text{Cost Price of 1 chair}=\text{Rs.}100$

Let the marked price (MP) of each chair be denoted by $x$.

The shopkeeper offers a discount of 22% on the marked price of a chair. This means the discounted selling price (before any quantity deals) is 78% of the marked price:

$\text{Discounted Price of 1 chair}=x-0.22x=0.78x$

Next, we look at the terms of the transaction. The shopkeeper gives 13 chairs to a customer but only charges them for the price of 12 discounted chairs. This means the revenue (Total Selling Price) the shopkeeper actually receives is the cost of 12 chairs at the discounted rate:

$\text{Total Selling Price (SP)}=12\times 0.78x=9.36x$

However, the shopkeeper is giving away 13 chairs in total. The total cost incurred by the shopkeeper must account for all 13 chairs given to the customer:

$\text{Total Cost Price (CP)}=13\times 100=\text{Rs.}1300$

The problem states that on this entire transaction, the shopkeeper earns a profit of 26%. The formula relating Total SP, Total CP, and Profit Percentage is:

$\text{Total SP}=\text{Total CP}\times (1+\frac{\text{Profit \%}}{100})$

We can now substitute the values we have derived into this formula:

$9.36x=1300\times (1+0.26)$

$9.36x=1300\times 1.26$

Multiplying the terms on the right side of the equation:

$9.36x=1638$

Finally, we isolate $x$ to find the marked price of a single chair:

$x=\frac{1638}{9.36}$

$x=175$

Therefore, the marked price of each chair is Rs. 175.