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A shopkeeper bought six identical mobile phones for ₹ 30000, and sold two of them for ₹ 28000. Find his gain percentage.
178%
181%
180%
183%
180%
Given: Cost Price (CP) of 6 mobile phones = ₹ 30,000; Selling Price (SP) of 2 mobile phones = ₹ 28,000
Cost Price (CP) of 6 mobile phones = ₹ 30,000; Selling Price (SP) of 2 mobile phones = ₹ 28,000
Gain %=(CPSP−CP)×100
Find CP and SP per unit: CP of 1 phone = 30000/6 = ₹ 5000. SP of 1 phone = 28000/2 = ₹ 14000. Ratio CP : SP = 5000 : 14000 = 5 : 14. Profit units = 14 - 5 = 9. Gain % = (9/5) × 100 = 180%.
Students often calculate profit based on the total CP of 6 phones (₹ 30,000) against the SP of only 2 phones (₹ 28,000), incorrectly concluding a loss instead of comparing identical quantities.
Calculate Cost Price (CP) per mobile phone
The shopkeeper bought 6 identical mobile phones for ₹ 30,000. Calculate the cost price of one mobile phone.
CP of 1 phone=630000=₹5000
Calculate Selling Price (SP) per mobile phone
He sold 2 of those mobile phones for ₹ 28,000. Calculate the selling price of one mobile phone.
SP of 1 phone=228000=₹14000
Determine Profit per mobile phone
Subtract the cost price of one phone from its selling price to find the profit per phone.
Profit=SP−CP=14000−5000=₹9000
Calculate Gain Percentage
Apply the profit percentage formula using CP of 1 phone as base.
Gain %=(CPProfit)×100=(50009000)×100=180%
Option C is correct because calculating the CP per phone (₹ 5,000) and SP per phone (₹ 14,000) gives a gain of ₹ 9,000 per phone, which equals an 180% profit margin.
Always convert total quantities to unit rates (per item) in profit-loss questions whenever the number of items bought and sold differ.