A vegetable vendor bought 100 kg of potatoes at the rate of ₹19 per kg and spent ₹100 as cartage. He sold 60 kg of potatoes with a 50% profit and half of the remaining stock with a 40% profit. He sold half of the still remaining potatoes with a 25% profit. What profit percentage should he aim for when selling the ultimate remaining potatoes to achieve an overall profit of 42%?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 0.15.
Let's break down the problem step by step:
Total Cost Price (CP):
⇒ Cost of potatoes = 100 kg × ₹19/kg = ₹1900
⇒ Cartage cost = ₹100
⇒ Total CP = ₹1900 + ₹100 = ₹2000
Sales and Profits:
⇒ First Sale: 60 kg at 50% profit
⇒ CP of 60 kg = 60 × ₹20/kg = ₹1200
⇒ SP of 60 kg = 1.5 × ₹1200 = ₹1800
Second Sale: 20 kg (half of remaining 40 kg) at 40% profit
⇒ CP of 20 kg = 20 × ₹20/kg = ₹400
⇒ SP of 20 kg = 1.4 × ₹400 = ₹560
Third Sale: 10 kg (half of remaining 20 kg) at 25% profit
⇒ CP of 10 kg = 10 × ₹20/kg = ₹200
⇒ SP of 10 kg = 1.25 × ₹200 = ₹250
Remaining Stock and Desired Overall Profit:
Remaining stock = 10 kg
Desired overall profit = 42%
⇒ Total desired SP = 1.42 × ₹2000 = ₹2840
Calculating Required Profit on Remaining Stock:
⇒ Total SP from previous sales = ₹1800 + ₹560 + ₹250 = ₹2610
⇒ Required SP from remaining 10 kg = ₹2840 - ₹2610 = ₹230
⇒ CP of remaining 10 kg = ₹200
Calculating Required Profit Percentage on Remaining Stock:
⇒ Profit required = ₹230 - ₹200 = ₹30
⇒ Profit percentage = (Profit/CP) × 100 = (30/200) × 100 = 15%