Maharashtra Board Class 6 Maths Chapter 13 Profit Loss Set 33 Solutions

Question 1. Maganlal bought trousers for Rs 400 and a shirt for Rs 200 and sold them for Rs 448 and Rs 250 respectively. Which of these transactions was more profitable?
Answer:
Cost price of trousers = Rs 400
Selling price of trousers = Rs 448
Profit = Selling price - Cost price
= 448 - 400 = Rs 48
Let Maganlal make x % profit on selling trousers
\( \frac{x}{100} = \frac{48}{400} \)
\( \frac{x}{100} \times 100 = \frac{48}{400} \times 100 \)
(Multiplying both sides by 100)
\( x = \frac{48 \times 100}{400} \)
\( = \frac{4800}{400} \)
\( = \frac{48}{4} \)
\( \therefore \) x = 12%
Cost price of shirt = Rs 200
Selling price of shirt = Rs 250
\( \therefore \) Profit = Selling price - Cost price
= 250 - 200
= Rs 50
Let Maganlal make y% profit on selling shirt.
\( \frac{y}{100} = \frac{50}{200} \)
\( \frac{y}{100} \times 100 = \frac{50}{200} \times 100 \)
(Multiplying both sides by 100)
\( y = \frac{50 \times 100}{200} \)
\( = \frac{5000}{200} \)
\( = \frac{50}{2} \)
\( \therefore \) y = 25%
\( \therefore \) Transaction involving selling of shirt was more profitable.
In simple words: To find out which transaction was more profitable, we calculate the profit percentage for both the trousers and the shirt. The transaction with the higher profit percentage is the more profitable one. In this case, selling the shirt yielded a higher profit percentage.

🎯 Exam Tip: Always calculate the profit percentage for each item when comparing profitability, not just the absolute profit amount, as the initial cost price can vary significantly.

Question 2. Ramrao bought a cupboard for Rs 4500 and sold it for Rs 4950. Shamrao bought a sewing machine for Rs 3500 and sold it for Rs 3920. Whose transaction was more profitable?
Answer:
Cost price of cupboard = Rs 4500
Selling price of cupboard = Rs 4950
\( \therefore \) Profit = Selling price - Cost price
= 4950 - 4500
= Rs 450
Let Ramrao make x% profit on selling cupboard
\( \frac{x}{100} = \frac{450}{4500} \)
\( \frac{x}{100} \times 100 = \frac{450}{4500} \times 100 \)
(Multiplying both sides by 100)
\( x = \frac{450 \times 100}{4500} \)
\( = \frac{45000}{4500} \)
\( = \frac{450}{45} \)
\( \therefore \) x = 10%
Cost price of sewing machine = Rs 3500
Selling price of sewing machine = Rs 3920
\( \therefore \)Profit = Selling price - Cost price
= 3920 - 3500
= Rs 420
Shamrao make y% profit on selling sewing machine.
\( \frac{y}{100} = \frac{420}{3500} \)
\( \frac{y}{100} \times 100 = \frac{420}{3500} \times 100 \)
(Multiplying both sides by 100)
\( y = \frac{420 \times 100}{3500} \)
\( = \frac{42000}{3500} \)
\( = \frac{420}{35} \)
\( \therefore \) y = 12%
Shamrao's transaction was more profitable.
In simple words: To determine whose transaction was more profitable, we calculate the profit percentage for Ramrao's cupboard and Shamrao's sewing machine. Shamrao's transaction had a higher profit percentage (12%) compared to Ramrao's (10%), making it more profitable.

🎯 Exam Tip: When comparing profitability for different items, always express profit as a percentage of the cost price to get a standardized measure for comparison.

Question 3. Hanif bought one box of 50 apples for Rs 400. He sold all the apples at the rate of Rs 10 each. Was there a profit or loss? What was its percentage?
Answer:
Cost price of 50 apples = Rs 400
Selling price of one apple = Rs 10
\( \therefore \) Selling price of 50 apples = 10 x 50 = Rs 500
Selling price is greater than the total cost price.
\( \therefore \) Hanif made a profit.
\( \therefore \) Profit = Selling price - Cost price
= 500 - 400
= Rs 100
Let Hanif make of x% profit on selling apples.
\( \frac{x}{100} = \frac{100}{400} \)
\( \frac{x}{100} \times 100 = \frac{100}{400} \times 100 \)
(Multiplying both sides by 100)
\( x = \frac{100 \times 100}{400} \)
\( = \frac{10000}{400} \)
\( = \frac{100}{4} \)
\( \therefore \) x = 25%
\( \therefore \) Hanif made a profit of 25%.
In simple words: Hanif bought 50 apples for Rs 400. By selling each apple for Rs 10, his total selling price was Rs 500, which is more than his cost price. This resulted in a profit of Rs 100, which calculates to a 25% profit.

🎯 Exam Tip: For problems involving bulk purchases and individual sales, always calculate the total selling price first to correctly determine if there's a profit or loss before calculating the percentage.