Samacheer Kalvi Class 6 Maths Solutions Term 2 Chapter 3 Bill, Profit and Loss Exercise 3.2

Miscellaneous Practice Problems

Question 1. A Shopkeeper buys three articles for Rs 325, Rs 450, and Rs 510. He is able to sell them for Rs 350, Rs 425, and Rs 525 respectively. Find the gain or loss to the shopkeeper on the whole.
Answer:
Cost Price (C.P) of the three articles \( = Rs \text{ } 325 + Rs \text{ } 450 + Rs \text{ } 510 = Rs \text{ } 1285 \)
Selling Price (S.P) of the three articles \( = Rs \text{ } 350 + Rs \text{ } 425 + Rs \text{ } 525 = Rs \text{ } 1300 \)
Here, S.P \( (Rs \text{ } 1300) \) is greater than C.P \( (Rs \text{ } 1285) \). This means the shopkeeper made a profit.
Profit \( = S.P - C.P \)
\( = Rs \text{ } 1300 - Rs \text{ } 1285 \)
\( = Rs \text{ } 15 \)
The shopkeeper gained Rs 15 on the whole transaction. Knowing the profit helps a shopkeeper manage their business better.
In simple words: The shopkeeper spent Rs 1285 to buy three items and sold them for Rs 1300. Since he sold them for more, he made a profit of Rs 15.

🎯 Exam Tip: To find overall gain or loss, first calculate the total cost price (C.P) and total selling price (S.P), then compare them to see if it's a profit or a loss.

Question 2. A stationery shop owner bought a scientific calculator for Rs 750. He had put a battery worth Rs 100 in it. He had spent Rs 50 for its outer pouch. He was able to sell it at Rs 850. Find his profit or loss.
Answer:
Cost of the scientific calculator \( = Rs \text{ } 750 \)
Cost of its battery \( = Rs \text{ } 100 \)
Cost of outer pouch \( = Rs \text{ } 50 \)
Total Cost Price (C.P) of the calculator \( = Rs \text{ } 750 + Rs \text{ } 100 + Rs \text{ } 50 = Rs \text{ } 900 \)
Selling Price (S.P) of the calculator \( = Rs \text{ } 850 \)
Here, S.P \( (Rs \text{ } 850) \) is less than C.P \( (Rs \text{ } 900) \). This means the shop owner faced a loss.
Loss \( = C.P - S.P \)
\( = Rs \text{ } 900 - Rs \text{ } 850 \)
\( = Rs \text{ } 50 \)
The shop owner incurred a loss of Rs 50. Understanding all costs helps calculate true profit or loss.
In simple words: The shop owner spent a total of Rs 900 on the calculator. He sold it for Rs 850, so he lost Rs 50.

🎯 Exam Tip: Remember to include all additional expenses like batteries, pouches, or repair costs when calculating the total cost price of an item.

Question 3. Nathan paid Rs 800 and bought 10 bottles of honey from a village vendor. He sold them in a gain for Rs 100 per bottle. Find his profit or loss.
Answer:
Cost Price (C.P) of 10 bottles of honey \( = Rs \text{ } 800 \)
C.P of 1 bottle of honey \( = Rs \text{ } \frac{800}{10} = Rs \text{ } 80 \)
Selling Price (S.P) of a bottle of honey \( = Rs \text{ } 100 \)
Here, S.P \( (Rs \text{ } 100) \) is greater than C.P \( (Rs \text{ } 80) \). This means Nathan made a profit.
Profit per bottle \( = S.P - C.P \)
\( = Rs \text{ } 100 - Rs \text{ } 80 \)
\( = Rs \text{ } 20 \)
Total profit for 10 bottles \( = Rs \text{ } 20 \times 10 = Rs \text{ } 200 \)
Nathan made a profit of Rs 200. Calculating profit per unit can be useful for pricing.
In simple words: Nathan bought 10 honey bottles for Rs 800, which is Rs 80 per bottle. He sold each bottle for Rs 100. This gave him a total profit of Rs 200.

🎯 Exam Tip: Be careful to distinguish between "profit per unit" and "selling price per unit" when reading the question text.

Question 4. A man bought 400 metres of cloth for Rs 60,000 and sold it at the rate of Rs 400 per metre. Find his profit or loss.
Answer:
Cost Price (C.P) of 400 metres of cloth \( = Rs \text{ } 60,000 \)
Selling Price (S.P) per metre \( = Rs \text{ } 400 \)
Total S.P of 400 metres of cloth \( = 400 \times Rs \text{ } 400 = Rs \text{ } 1,60,000 \)
Here, S.P \( (Rs \text{ } 1,60,000) \) is greater than C.P \( (Rs \text{ } 60,000) \). This means the man made a profit.
Profit \( = S.P - C.P \)
\( = Rs \text{ } 1,60,000 - Rs \text{ } 60,000 \)
\( = Rs \text{ } 1,00,000 \)
The man earned a profit of Rs 1,00,000. It's smart to calculate total selling price before deciding profit or loss.
In simple words: The man bought cloth for Rs 60,000 and sold it all for Rs 1,60,000. He made a profit of Rs 1,00,000.

🎯 Exam Tip: Always ensure you are comparing the total Cost Price with the total Selling Price, especially when rates are given per unit.

Challenge Problems

Question 5. A fruit seller bought 2 dozen bananas at Rs 20 a dozen and sold them at Rs 3 per banana. Find his gain or loss.
Answer:
Cost of one dozen bananas \( = Rs \text{ } 20 \)
Cost of 2 dozen bananas \( = Rs \text{ } 20 \times 2 = Rs \text{ } 40 \)
Total Cost Price (C.P) \( = Rs \text{ } 40 \)
We know that 1 dozen \( = 12 \) bananas.
\( \implies \) 2 dozen \( = 2 \times 12 = 24 \) bananas.
Selling Price (S.P) per banana \( = Rs \text{ } 3 \)
Total S.P for 2 dozen bananas \( = Rs \text{ } 3 \times 24 = Rs \text{ } 72 \)
Here, S.P \( (Rs \text{ } 72) \) is greater than C.P \( (Rs \text{ } 40) \). This means the fruit seller made a profit.
Profit \( = S.P - C.P \)
\( = Rs \text{ } 72 - Rs \text{ } 40 \)
\( = Rs \text{ } 32 \)
The fruit seller gained Rs 32. Knowing how many items are in a dozen is important for calculations.
In simple words: The seller bought 24 bananas for Rs 40. He sold each banana for Rs 3, making a total of Rs 72. He made a profit of Rs 32.

🎯 Exam Tip: When dealing with items sold by the dozen, convert everything to the total number of individual items to avoid calculation errors.

Question 6. A store purchased pens at Rs 216 per dozen. He paid Rs 58 for conveyance and sold the pens at the discount of Rs 2 per pen and made an overall profit of Rs 50. Find the M.P of each pen.
Answer:
Cost of a dozen pens \( = Rs \text{ } 216 \)
Paid for conveyance \( = Rs \text{ } 58 \)
Total Cost Price (C.P) of 12 pens \( = Rs \text{ } 216 + Rs \text{ } 58 = Rs \text{ } 274 \) (Since 1 dozen = 12 pens)
Overall Profit of 12 pens \( = Rs \text{ } 50 \)
We know that Profit \( = S.P - C.P \)
\( \implies Rs \text{ } 50 = S.P - Rs \text{ } 274 \)
\( \implies S.P = Rs \text{ } 50 + Rs \text{ } 274 = Rs \text{ } 324 \)
Discount allowed per pen \( = Rs \text{ } 2 \)
Total discount for 12 pens \( = Rs \text{ } 2 \times 12 = Rs \text{ } 24 \)
We know that S.P \( = M.P - \) Discount
\( \implies Rs \text{ } 324 = M.P - Rs \text{ } 24 \)
\( \implies M.P = Rs \text{ } 324 + Rs \text{ } 24 = Rs \text{ } 348 \)
Marked Price (M.P) for 12 pens \( = Rs \text{ } 348 \)
M.P of a single pen \( = Rs \text{ } \frac{348}{12} = Rs \text{ } 29 \)
The Marked Price of each pen is Rs 29. Understanding all costs and discounts helps set the right price.
In simple words: The store spent Rs 274 on 12 pens. With a Rs 50 profit, they sold them for Rs 324. Since they gave a Rs 2 discount per pen (Rs 24 total), the original marked price for each pen was Rs 29.

🎯 Exam Tip: Always account for all extra costs to find the true Cost Price, and remember the relationship between Selling Price, Marked Price, and Discount.

Question 7. A Vegetable vendor buys 10 kg of tomatoes per day at Rs 10 per kg, for the first three days of a week. 1 kg of tomatoes got smashed every day for those 3 days. For the remaining 4 days of the week, he buys 15 kg of tomatoes daily at Rs 8 per kg. If for the entire week he sells tomatoes at Rs 20 per kg, then find his profit or loss for the week.
Answer:
**For the first 3 days:**
Total tomatoes bought \( = 3 \text{ days} \times 10 \text{ kg/day} = 30 \text{ kg} \)
Cost of 1 kg \( = Rs \text{ } 10 \)
Cost of 30 kg tomatoes \( = 30 \times Rs \text{ } 10 = Rs \text{ } 300 \)
Tomatoes smashed \( = 1 \text{ kg/day} \times 3 \text{ days} = 3 \text{ kg} \)
**For the remaining 4 days:**
Total tomatoes bought \( = 4 \text{ days} \times 15 \text{ kg/day} = 60 \text{ kg} \)
Cost of 1 kg \( = Rs \text{ } 8 \)
Cost of 60 kg tomatoes \( = 60 \times Rs \text{ } 8 = Rs \text{ } 480 \)
**Total for the week:**
Total tomatoes bought in the week \( = 30 \text{ kg} + 60 \text{ kg} = 90 \text{ kg} \)
Total Cost Price (C.P) for the week \( = Rs \text{ } 300 + Rs \text{ } 480 = Rs \text{ } 780 \)
Total kg of tomatoes available for sale \( = 90 \text{ kg} - 3 \text{ kg (smashed)} = 87 \text{ kg} \)
Selling Price (S.P) of 1 kg tomatoes \( = Rs \text{ } 20 \)
Total S.P of 87 kg tomatoes \( = 87 \times Rs \text{ } 20 = Rs \text{ } 1740 \)
Here, S.P \( (Rs \text{ } 1740) \) is greater than C.P \( (Rs \text{ } 780) \). This means the vendor made a profit.
Profit \( = S.P - C.P \)
\( = Rs \text{ } 1740 - Rs \text{ } 780 \)
\( = Rs \text{ } 960 \)
The vegetable vendor made a profit of Rs 960 for the week. Tracking waste helps improve business profits.
In simple words: The vendor spent Rs 780 on tomatoes for the week. After 3 kg were smashed, he sold 87 kg for Rs 1740. His total profit for the week was Rs 960.

🎯 Exam Tip: Break down complex problems into smaller, manageable parts (like different days of the week) and remember to subtract any damaged goods before calculating the total selling price.

Question 8. An electrician buys a used T.V for Rs 12,000 and a used Fridge for Rs 11,000. After spending Rs 1000 on repairing the T.V and Rs 1500 on painting the Fridge, he fixes up the M.P of T.V as Rs 15,000 and that of the Fridge as Rs 15,500. If he gives each Rs 1000 discount on each find his profit or loss.
Answer:
**(i) For the T.V:**
Cost of a T.V \( = Rs \text{ } 12,000 \)
Paid for repair \( = Rs \text{ } 1,000 \)
Total Cost Price (C.P) of the T.V \( = Rs \text{ } 12,000 + Rs \text{ } 1,000 = Rs \text{ } 13,000 \)
Marked Price (M.P) of the T.V \( = Rs \text{ } 15,000 \)
Discount on T.V \( = Rs \text{ } 1,000 \)
Selling Price (S.P) of the T.V \( = M.P - \) Discount \( = Rs \text{ } 15,000 - Rs \text{ } 1,000 = Rs \text{ } 14,000 \)
Here, S.P \( (Rs \text{ } 14,000) \) is greater than C.P \( (Rs \text{ } 13,000) \).
Profit on the T.V \( = S.P - C.P = Rs \text{ } 14,000 - Rs \text{ } 13,000 = Rs \text{ } 1,000 \)
** (ii) For the Fridge:**
Cost of the Fridge \( = Rs \text{ } 11,000 \)
Painting charge \( = Rs \text{ } 1,500 \)
Total Cost Price (C.P) of the Fridge \( = Rs \text{ } 11,000 + Rs \text{ } 1,500 = Rs \text{ } 12,500 \)
Marked Price (M.P) of the Fridge \( = Rs \text{ } 15,500 \)
Discount allowed \( = Rs \text{ } 1,000 \)
Selling Price (S.P) of the Fridge \( = M.P - \) Discount \( = Rs \text{ } 15,500 - Rs \text{ } 1,000 = Rs \text{ } 14,500 \)
Here, S.P \( (Rs \text{ } 14,500) \) is greater than C.P \( (Rs \text{ } 12,500) \).
Profit on the Fridge \( = S.P - C.P = Rs \text{ } 14,500 - Rs \text{ } 12,500 = Rs \text{ } 2,000 \)
**Total Profit:**
Total profit \( = \) Profit on T.V \( + \) Profit on Fridge \( = Rs \text{ } 1,000 + Rs \text{ } 2,000 = Rs \text{ } 3,000 \)
The electrician's total profit is Rs 3,000. Breaking down costs and profits for each item helps in overall business assessment.
In simple words: The electrician spent Rs 13,000 on the TV (including repair) and sold it for Rs 14,000, making Rs 1,000 profit. He spent Rs 12,500 on the fridge (including painting) and sold it for Rs 14,500, making Rs 2,000 profit. His total profit from both items was Rs 3,000.

🎯 Exam Tip: When dealing with multiple items, calculate the cost price, selling price, and profit/loss for each item separately before finding the overall profit or loss.