A retailer allows a 22% discount on the marked price. What should be the marked price (in ₹) of an item whose cost price is ₹780, in order to make a profit of 26%?

Correct option is C

​Given:
Cost Price (C.P.) = ₹780
Desired Profit = 26%
Discount = 22%
Formula Used:
​$$\frac{C.P.}{M.P.} = \frac{100 - \text{discount percentage}}{100 + \text{gain percentage}}$$​​

Solution:
​$$\frac{780}{M.P.} = \frac{100 - 22}{100 + 26}\\\ \\\frac{780}{M.P.} = \frac{78}{126}\\\ \\M.P. = \frac{780 \times 126}{78}\\\ \\M.P. = \frac{98280}{78}\\\ \\M.P. = ₹1260\\$$​​
Alternate Method 1:
Let C.P. = 50 unit
So, S.P. = 50 + 26% of 50 = 63
So, 63 =  M.P. -  22% of M.P
M.P. = 80.769
50 unit = Rs. 780 
80.769 unit  = Rs. 1260 
Alternate Method 2:
Profit = 26% of ₹780 = 0.26 × ₹780 = ₹202.8
Selling Price = Cost Price + Profit = ₹780 + ₹202.8 = ₹982.8
Selling Price = Marked Price × (1 - 0.22)
₹982.8 = Marked Price × 0.78
Marked Price = $$\frac {₹982.8}{ 0.78}$$​ = ₹1260
The marked price should be ₹1260.