CBSE Class 8 Mathematics Comparing Quantities Assignment Set 08

Profit and Loss

Question 1. A retailer buys a watch for Rs 335. By paying Rs 15 more, he replaces its strap by a costlier strap. If he sells the watch for Rs 400. Find his gain or loss percent.
Answer: Cost price of the watch = Rs 335
Additional overhead charges (extra strap) = Rs 15
Total Cost Price (C.P.) = \(335 + 15 =\) Rs 350
Selling Price (S.P.) = Rs 400
Since \(\text{S.P.} > \text{C.P.}\), there is a profit.
\(\text{Profit} = \text{S.P.} - \text{C.P.} = 400 - 350 =\) Rs 50
\(\text{Profit percent} = \left( \frac{\text{Profit}}{\text{C.P.}} \right) \times 100 = \frac{50}{350} \times 100 = \frac{1}{7} \times 100 = \frac{100}{7}\% = 14\frac{2}{7}\%\)
In simple words: Add extra expenses to the original cost price to find the total cost, then calculate the profit percentage.

Exam Tip: Always include overhead charges (repairs, transport, or extra parts) in the total cost price before calculating profit or loss.

Question 2. A shopkeeper looses 20% by selling a bicycle for Rs 1536. Find the cost price of the bicycle.
Answer: Selling Price (S.P.) = Rs 1536
Loss percent = \(20\%\)
Let the Cost Price (C.P.) be \(x\).
\(\text{S.P.} = \text{C.P.} \times \left( \frac{100 - \text{Loss}\%}{100} \right)\)
\(1536 = x \times \left( \frac{100 - 20}{100} \right)\)
\(1536 = x \times \frac{80}{100}\)
\(x = \frac{1536 \times 100}{80}\)
\(x = 192 \times 10 =\) Rs 1920
In simple words: When loss is given, subtract it from 100% to find the selling price percentage relative to the cost price.

Exam Tip: Formula to find C.P. when S.P. and loss percent are given: \(\text{C.P.} = \frac{\text{S.P.} \times 100}{100 - \text{Loss}\%}\).

Question 3. Anil purchased an old type-writer for Rs 1200 and spent Rs 200 on repairs. He sold it for Rs 1680. Find his profit and loss, and express it as a %
Answer: Purchase price = Rs 1200
Repair cost = Rs 200
Total Cost Price (C.P.) = \(1200 + 200 =\) Rs 1400
Selling Price (S.P.) = Rs 1680
Since \(\text{S.P.} > \text{C.P.}\), there is a profit.
\(\text{Profit} = \text{S.P.} - \text{C.P.} = 1680 - 1400 =\) Rs 280
\(\text{Profit percent} = \left( \frac{280}{1400} \right) \times 100 = \frac{280}{14} = 20\%\)
In simple words: Add repair costs to the purchase price to get the total cost, then find the profit and convert it into a percentage.

Exam Tip: Repairs and overheads are always added to the initial buying price to establish the true cost price.

Question 4. By selling an article for Rs 630, a person gains 5%. Find the cost price of the article.
Answer: Selling Price (S.P.) = Rs 630
Gain percent = \(5\%\)
Let the Cost Price (C.P.) be \(x\).
\(\text{S.P.} = \text{C.P.} \times \left( \frac{100 + \text{Gain}\%}{100} \right)\)
\(630 = x \times \left( \frac{100 + 5}{100} \right)\)
\(630 = x \times \frac{105}{100}\)
\(x = \frac{630 \times 100}{105}\)
\(x = 6 \times 100 =\) Rs 600
In simple words: Use the selling price and gain percentage formula in reverse to isolate and find the original cost price.

Exam Tip: Formula for C.P. when S.P. and gain percent are given: \(\text{C.P.} = \frac{\text{S.P.} \times 100}{100 + \text{Gain}\%}\).

Question 5. If the C.P. of 15 chairs is equal to the S.P. of 10 chairs, find the gain percent
Answer: Let the Cost Price of 1 chair be Rs 1.
Cost Price of 15 chairs = Rs 15
Given that C.P. of 15 chairs = S.P. of 10 chairs.
Therefore, Selling Price of 10 chairs = Rs 15
Cost Price of 10 chairs = \(10 \times 1 =\) Rs 10
Selling Price of 10 chairs = Rs 15
Since \(\text{S.P.} > \text{C.P.}\), there is a profit.
\(\text{Profit} = \text{S.P.} - \text{C.P.} = 15 - 10 =\) Rs 5
\(\text{Gain percent} = \left( \frac{\text{Profit}}{\text{C.P. of 10 chairs}} \right) \times 100 = \frac{5}{10} \times 100 = 50\%\)
In simple words: Assume a unit price for the items, equate the total amounts for a common quantity, and find the profit percentage.

Exam Tip: For quantity-based problems, always calculate the C.P. and S.P. for the exact same number of items.

Question 6. Toffees are bought 8 for a rupee and sold 6 for a rupee. Find the profit percent.
Answer: Let the number of toffees bought and sold be the LCM of 8 and 6, which is 24.
Cost Price of 8 toffees = Re 1
Cost Price of 24 toffees = \(\frac{1}{8} \times 24 =\) Rs 3
Selling Price of 6 toffees = Re 1
Selling Price of 24 toffees = \(\frac{1}{6} \times 24 =\) Rs 4
Total Cost Price for 24 toffees = Rs 3
Total Selling Price for 24 toffees = Rs 4
\(\text{Profit} = 4 - 3 =\) Rs 1
\(\text{Profit percent} = \left( \frac{1}{3} \right) \times 100 = \frac{100}{3}\% = 33\frac{1}{3}\%\)
In simple words: Take the LCM of the quantities to find the common number of items, calculate total cost and selling price, then find the profit.

Exam Tip: Finding the LCM of quantities makes calculation fraction-free and much easier.

Question 7. Anil purchased an article for Rs 4000 and sold it to Arun for a profit of 25%. Arun sold it to Ajay at a loss of 5%. For how much did Ajay buy it?
Answer: Cost price for Anil = Rs 4000
Anil sells to Arun at a profit of \(25\%\):
Selling Price for Anil (Cost Price for Arun) = \(4000 \times \left( \frac{100 + 25}{100} \right)\)
\(= 4000 \times \frac{125}{100} = 40 \times 125 =\) Rs 5000
Arun sells to Ajay at a loss of \(5\%\):
Selling Price for Arun (Cost Price for Ajay) = \(5000 \times \left( \frac{100 - 5}{100} \right)\)
\(= 5000 \times \frac{95}{100} = 50 \times 95 =\) Rs 4750
In simple words: Calculate successive selling prices step-by-step from one person to the next.

Exam Tip: In chain transactions, the selling price of the previous person always becomes the cost price for the next person.

Question 8. A man sold two watches for Rs 480 each. He gains 20% on one and loses 20% on the other. By how much he gains or loses in the whole transaction.
Answer: Selling Price of each watch = Rs 480
Total Selling Price of two watches = \(480 + 480 =\) Rs 960
For the first watch (Gain of \(20\%\)):
\(\text{C.P.}_1 = \frac{\text{S.P.} \times 100}{100 + \text{Gain}\%} = \frac{480 \times 100}{120} = 4 \times 100 =\) Rs 400
For the second watch (Loss of \(20\%\)):
\(\text{C.P.}_2 = \frac{\text{S.P.} \times 100}{100 - \text{Loss}\%} = \frac{480 \times 100}{80} = 6 \times 100 =\) Rs 600
Total Cost Price of both watches = \(400 + 600 =\) Rs 1000
Total Selling Price = Rs 960
Since \(\text{C.P.} > \text{S.P.}\), there is a total loss.
\(\text{Loss} = \text{Total C.P.} - \text{Total S.P.} = 1000 - 960 =\) Rs 40
\(\text{Loss percent} = \left( \frac{40}{1000} \right) \times 100 = 4\%\)
In simple words: Find the individual cost price for each watch separately, add them up, and compare with the total selling price.

Exam Tip: When the selling price and equal percentage of profit and loss are given, there is always a net loss calculated by \(\text{Loss}\% = \left(\frac{\text{Common}\%}{10}\right)^2\).

Question 9. A fruit seller buys oranges for Rs 12 a dozen and sells them for Rs 18 a dozen, Find his profit per cent
Answer: Cost Price of 1 dozen oranges = Rs 12
Selling Price of 1 dozen oranges = Rs 18
\(\text{Profit} = \text{S.P.} - \text{C.P.} = 18 - 12 =\) Rs 6
\(\text{Profit percent} = \left( \frac{\text{Profit}}{\text{C.P.}} \right) \times 100 = \frac{6}{12} \times 100 = \frac{1}{2} \times 100 = 50\%\)
In simple words: Since both buying and selling prices are given for the same quantity (one dozen), calculate the profit directly.

Exam Tip: Always verify that the quantities are identical before calculating profit or loss.

Question 10. If by selling a saree for Rs 200, a shopkeeper suffers a loss of 20%. for what amount should he sell it as to gain a profit of 10%.
Answer: Selling Price (S.P.) = Rs 200
Loss percent = \(20\%\)
First, find the Cost Price (C.P.):
\(\text{C.P.} = \frac{\text{S.P.} \times 100}{100 - \text{Loss}\%} = \frac{200 \times 100}{100 - 20} = \frac{20000}{80} =\) Rs 250
Now, find the new Selling Price to gain a profit of \(10\%\):
Desired Profit percent = \(10\%\)
\(\text{New S.P.} = \text{C.P.} \times \left( \frac{100 + \text{Profit}\%}{100} \right)\)
\(\text{New S.P.} = 250 \times \left( \frac{100 + 10}{100} \right)\)
\(\text{New S.P.} = 250 \times \frac{110}{100} = 25 \times 11 =\) Rs 275
In simple words: First find the cost price using the initial loss condition, then calculate the new selling price using the desired profit percentage.

Exam Tip: You can combine this into a single step: \(\text{New S.P.} = \text{Old S.P.} \times \left( \frac{100 + \text{New Profit}\%}{100 - \text{Old Loss}\%} \right)\).