By selling 22 items, Rohit gains the selling price of 6 items. His gain per cent is:

Correct option is A

Given Data:
· Number of items sold = 22
· Gain = Selling price of 6 items
Formulas Used:
· Let the cost price of one item = CP
· Selling price of one item = SP
· Total cost price = 22×CP
· Total selling price = 22×SP
· Gain = Total selling price - Total cost price
· Gain percentage = ($$\frac{Gain }{Total \ Cost \ Price}$$​ )×100
Solution:
Calculate total selling price and gain:
Gain =6×SP
Using the relationship:
Total Selling Price =22×SP
Express total cost price:
Total Cost Price =22×CP
Set up the gain equation:
6×SP=22×SP-22×CP
Rearranging gives:
22×CP=22×SP-6×SP
22×CP=16×SP
​$$CP=\frac{16}{22}SP = \frac{8}{11}SP$$​​
Calculate gain per item:
Gain per item = SP-CP= $$SP- \frac{8}{11} SP= \frac{3}{11} SP$$​​
Gain percentage:
Gain Percentage = $$\frac{(\frac{3}{11} SP)}{(\frac{8}{11} SP)}×100=\frac{3}{8}×100=37.5 \%$$​​
Answer: (a) 37 $$\frac{1}{2}$$​%