Maharashtra Board Class 11 Maths Part 2 Chapter 9 Commercial Mathematics 9.2 Solutions

Exercise 9.2 Solutions Commerce Maths

Question 1. Mr. Sarad purchased a laptop for Rs. 24,000 and sold it for Rs. 30,000. What was the profit percentage?
Answer:Solution:
Cost price (C.P.) = Rs. 24000
Selling price (S. P.) = Rs. 30,000
Profit = S.P. - C.P.
= 30,000 - 24,000
= 6,000
Profit % \( = \frac{\text{Profit} \times 100}{\text{C.P.}} \)
\( = \frac{6000 \times 100}{24000} \)
\( = \frac{6}{24} \times 100 = \frac{100}{4} \)
\( = 25 \)
\( \therefore \) Profit Percentage = 25%
In simple words: To find the profit percentage, first calculate the profit by subtracting the cost price from the selling price, then divide this profit by the cost price and multiply by 100.

🎯 Exam Tip: Always ensure you use the Cost Price (C.P.) as the base for calculating profit or loss percentages.

Question 2. Shraddha purchased a mobile phone and refrigerator for Rs. 18,000 and Rs. 15,000 respectively. She sold the refrigerator at a loss of 20% and the mobile at a profit of 20%. What is her overall profit or loss?
Answer:Solution:
C.P. of mobile phone = Rs. 18,000
Profit percentage on mobile phone = 20%
Selling price (S.P.) of mobile phone \( = 18,000 (1 + \frac{20}{100}) \)
\( = 18,000 (1 + \frac{1}{5}) \)
\( = 18,000 \times \frac{6}{5} \)
\( = \) Rs. 21,600
C.P. of refrigerator = 15,000
Loss percentage on refrigerator = 20%
\( \therefore \) Selling price (S.P.) \( = 15,000(1 - \frac{20}{100}) \)
\( = 15,000(1 - \frac{1}{5}) \)
\( = 15,000 \times \frac{4}{5} \)
\( = \) Rs. 12,000
\( \therefore \) Total selling price for the transaction = 21,600 + 12,000 = Rs. 33,600
Total cost price (purchase price) for the transaction = 18,000 + 15,000 = Rs. 33,000
\( \therefore \) Overall profit made by Shraddha = Total S.P. - Total C.P.
= 33,600 - 33,000
= Rs. 600
Thus, Shraddha made an overall profit of Rs. 600.
In simple words: To calculate the overall profit or loss, find the selling price for each item considering its individual profit or loss percentage, then sum up all selling prices and all cost prices to compare the total.

🎯 Exam Tip: Handle profit and loss for each item separately before combining them for the overall transaction.

Question 3. A vendor bought toffees at 6 for Rs. 10. How many for 10 must he sell to gain 20%?
Answer:Solution:
Vendor bought toffees at the rate of 6 for Rs. 10
\( \therefore \) Cost price of one toffee \( = \frac{10}{6} \)
i.e. C.P. \( = \frac{10}{6} \) .......(i)
Let x be the number of toffees he must sell in Rs. 10 to gain 20%
i.e. S.P. \( = \frac{10}{x} \) .......(ii)
Profit percentage \( = \frac{\text{S.P. - C.P.}}{\text{C.P.}} \)
Using (i) and (ii) we have
\( 20\% = \frac{\frac{10}{x} - \frac{10}{6}}{\frac{10}{6}} \)

\( \implies \frac{20}{100} = (\frac{10}{x} - \frac{10}{6}) \times \frac{6}{10} \)

\( \implies \frac{1}{5} = (\frac{1}{x} - \frac{1}{6}) \times 6 \)

\( \implies \frac{1}{5} = \frac{6}{x} - 1 \)

\( \implies \frac{1}{5} + 1 = \frac{6}{x} \)

\( \implies \frac{6}{5} = \frac{6}{x} \)

\( \implies x = 5 \)
The vendor must sell 5 toffees for Rs. 10 in order to gain 20%.
In simple words: Determine the cost price per toffee. To achieve a desired profit percentage, calculate the new selling price per toffee and then find out how many toffees can be sold for a specific amount.

🎯 Exam Tip: For 'number of items' problems, convert the rate to a per-item cost/selling price for easier calculation.

Question 4. The percentage profit earned by selling an article for Rs. 2,880 is equal to the percentage loss incurred by selling the same article for Rs. 1,920. At what price the article should be sold to earn a 25% profit?
Answer:Solution:
Let x be C.P. of the article
Let y % be both, the gain and loss made when article is sold at Rs. 2,880 and Rs. 1,920 respectively. Then
\( x + \frac{y}{100} x = 2880 \) ......(i)
\( x - \frac{y}{100} x = 1920 \) .....(ii)
Adding (i) and (ii), we get
\( 2x = 4800 \)
\( \therefore x = 2400 \)
i.e. C.P. of the article = Rs. 2400
Required profit percentage = 25%
S.P. \( = \text{C.P.} [1+ \frac{\text{Profit%}}{100}] \)
\( = 2400 [1+\frac{25}{100}] \)
\( = 2400 [1+\frac{1}{4}] \)
\( = 2400 \times \frac{5}{4} \)
\( = 3000 \)
\( \therefore \) The article should be sold at Rs. 3000 to earn 25% profit.
In simple words: If the percentage profit from one selling price equals the percentage loss from another selling price for the same article, you can set up equations to find the original cost price, and then use that to determine the selling price for a new desired profit.

🎯 Exam Tip: When profit and loss percentages are equal, setting up simultaneous equations based on the cost price is an effective method.

Question 5. A cloth merchant advertises for selling cloth at a 4% loss. By using a faulty meter scale, he is earning a profit of 20%. What is the actual length of the scale?
Answer:Solution:
Let the cost price of the cloth be 'x' per meter
He claims a loss of 4%
\( \therefore \) Selling price of the cloth
S.P. \( = \text{C.P.}(1 - \frac{\text{loss}}{100}) \)
\( = x(1 - \frac{4}{100}) \)
\( = 0.96x \) .....(i)
The actual cost price of the cloth is lower as the cloth is measured by a faulty meter scale.
Given that shopkeeper's profit = 20%
Now, S.P. \( = \text{C.P.} (1+ \frac{\text{Profit%}}{100}) \)

\( \implies \) S.P. \( = \text{C.P.} (1+ \frac{\text{Profit%}}{100}) \)

\( \implies \) Actual C.P. \( = 0.96x (1+ \frac{20}{100}) \) ...[From (i)]
\( = 0.96x (1+\frac{1}{5}) \)
\( = 0.96x \times \frac{6}{5} \)
\( = 0.8x \)
\( \therefore \) The actual cost price is 0.8 times the cost price as advertised.
In other words, the meter scale used for the fraud is 0.8 times the meter scale that should have been used.
\( \therefore \) The length of the faulty meter scale used = 0.8 \( \times \) 1 = 0.8 meter
\( \therefore \) The actual length of the scale is 0.8 meters.
In simple words: A faulty scale means the actual quantity of cloth sold differs from the advertised quantity. To find the actual scale length, use the advertised loss percentage and the actual profit percentage to work back to the true cost price relation.

🎯 Exam Tip: This question combines faulty weight/scale with profit/loss. The key is to understand that the "cost price" for the shopkeeper is based on the actual quantity, not the marked quantity.

Question 6. Sunil sells his bike worth Rs. 25,000 to Rohit at a profit of 20%. After 6 months Rohit sells the bike back to Sunil at a loss of 20%. Find the total profit percent of Sunil considering both the transactions.
Answer:Solution:
Sunil sells his bike to Rohit at 20% profit.
So S.P. of the bike for Sunil
\( = 25000 + \frac{20}{100} \times 25000 \)
\( = 25000 + 5000 \)
\( = 30000 \)
\( \therefore \) Cost price of bike to Rohit = Rs. 30000
Rohit sells the bike back to Sunil at 20% loss
\( \therefore \) S.P. of the bike for Rohit \( = 30000 - \frac{20}{100} \times 30000 \)
\( = 30000 - 6000 \)
\( = 24000 \)
\( \therefore \) In second transaction Sunil pays 24000 to Rohit
In the first transaction, he had received 30000 from Rohit
\( \therefore \) Sunil made a profit of (30000 - 24000) = Rs. 6000
Sunil earned this profit on the bike which costed him Rs. 25000
\( \therefore \) Total profit % that Sunil makes \( = \frac{6000}{25000} \times 100 \)
\( = \frac{600}{25} \)
\( = 24 \)
\( \therefore \) Sunil makes 24% profit considering both the transactions.
In simple words: Track the selling and buying prices of the bike through Sunil's transactions. Calculate Sunil's net profit from these two deals, then express this net profit as a percentage of his initial cost.

🎯 Exam Tip: For sequential transactions, carefully identify the cost price and selling price for each party at each step.

Question 7. By selling a book at Rs. 405 bookseller incurs a loss of 25%. Find the cost price of the book.
Answer:Solution:
S.P. = Rs. 405
Loss% = 25
S.P. when there is a loss is given by
S.P. \( = \text{C.P.} \times [1 - \frac{\text{Loss %}}{100}] \)

\( \implies 405 = \text{C.P.} \times [1 - \frac{25}{100}] \)

\( \implies 405 = \frac{100-25}{100} \times \text{C.P.} \)

\( \implies \text{C.P.} = \frac{405 \times 100}{75} \)
\( = \frac{405 \times 4}{3} \)
\( = 135 \times 4 \)
\( = 540 \)
\( \therefore \) The cost price of the book is Rs. 540.
In simple words: If you know the selling price and the loss percentage, you can calculate the original cost price by understanding that the selling price represents a certain percentage of the cost price after the loss.

🎯 Exam Tip: Remember that Selling Price = Cost Price \( \times \) (1 - Loss%/100). Rearrange this formula to find the Cost Price.

Question 8. A cloth costs Rs. 675. If it is sold at a loss of 20%, what is its cost price as a percentage of its selling price?
Answer:Solution:
C.P. = Rs. 675
Loss% = 20%
\( \therefore \) Loss made in selling \( = \frac{20}{100} \times 675 = \) Rs. 135
S.P. = C.P. - Loss
= 675 - 135
= Rs. 540
Let C.P. be x % S.P.,
Then \( 675 = \frac{x}{100} \times 540 \)
\( \therefore x = \frac{675 \times 100}{540} \)
\( = 125 \)
\( \therefore \) Cost price is 125% of the selling price.
In simple words: First, calculate the selling price of the cloth after a 20% loss from its cost price. Then, determine what percentage the original cost price represents in relation to this new selling price.

🎯 Exam Tip: Clearly distinguish between cost price and selling price, and be careful when calculating percentages *of* the selling price versus *of* the cost price.

Question 9. Ashwin buys an article for Rs. 500. He marks it for sale at 75% more than the cost price. He offers a 25% discount on the marked price to his customer. Calculate the actual percentage of profit made by Ashwin.
Answer:Solution:
C.P. = Rs. 500
Marked price \( = \text{C.P.} + \frac{75}{100} \times \text{C.P.} \)
\( = 500 + \frac{75}{100} \times 500 \)
\( = 500 + 75 \times 5 \)
\( = 500 + 375 \)
\( = 875 \)
25% discount was given on marked price
\( \therefore \) Discount \( = \frac{25}{100} \times 875 = \frac{875}{4} \)
Selling price = marked price - discount
\( = 875 - \frac{875}{4} \)
\( = 875(1-\frac{1}{4}) \)
\( = \frac{875 \times 3}{4} \)
Profit = S.P. - C.P.
\( = \frac{875 \times 3}{4} - 500 \)
\( = \frac{2625-2000}{4} \)
\( = \frac{625}{4} \)
Profit percentage \( = \frac{\text{Profit}}{\text{Cost price}} \times 100 \)
\( = \frac{\frac{625}{4}}{500} \times 100 \)
\( = \frac{625}{4 \times 500} \times 100 \)
\( = \frac{625}{20} \)
\( = \frac{125}{4} \)
\( = 31.25 \)
\( \therefore \) Ashwin makes 31.25% profit.
In simple words: Calculate the marked price by adding the profit percentage to the cost price. Then, apply the discount percentage to the marked price to find the actual selling price. Finally, compare this selling price to the original cost price to find the actual profit percentage.

🎯 Exam Tip: This is a multi-step problem involving C.P., M.P. (Marked Price), S.P., and discounts. Process each step sequentially and accurately.

Question 10. The combined cost price of a refrigerator and a mixer is Rs. 12,400. If the refrigerator costs 600% more than the mixer, find the cost price of the mixer.
Answer:Solution:
Let x be the cost price of the mixer.
The cost price of the refrigerator \( = x + \frac{600}{100} X \)
\( = x + 6x \)
\( = 7x \)
Total cost price = 12400 .....[Given]
i.e. \( x + 7x = 12400 \)
i.e. \( 8x = 12400 \)
\( \therefore x = \frac{12400}{8} = 1550 \)
\( \therefore \) The cost price of mixer is Rs. 1550.
In simple words: Set up an equation where the cost of the refrigerator is expressed in terms of the mixer's cost, considering the 600% more cost. Then, use the total combined cost to solve for the mixer's cost.

🎯 Exam Tip: "X% more than" means adding X% of the original value to the original value, i.e., `Original + Original * (X/100)`.

Question 11. Find the single discount equivalent to the discount series of 5%, 7%, and 9%.
Answer:Solution:
Let the marked price be Rs. 100
After 1st discount the price \( = 100(1 - \frac{5}{100}) = 95 \)
After 2nd discount the price \( = 95(1 - \frac{7}{100}) = \frac{95 \times 93}{100} \)
After 3rd discount the price \( = \frac{95 \times 93}{100} (1 - \frac{9}{100}) \)
\( = \frac{95 \times 93 \times 91}{100 \times 100} \)
\( = \frac{803985}{10000} \)
\( = 80.3985 \approx 80.4 \)
Selling price after 3 discounts is Rs. 80.4
Single equivalent discount = Marked price - Selling price
= 100 - 80.4
= Rs. 19.6
\( \therefore \) Single equivalent discount is 19.6%.
In simple words: To find a single equivalent discount for a series of discounts, imagine an original marked price (e.g., Rs. 100), apply each discount sequentially to the remaining price, and then compare the final price to the original marked price.

🎯 Exam Tip: Discounts are always applied to the *remaining* price after the previous discount. Do not simply add the percentages.

Question 12. The printed price of a shirt is Rs. 390. Lokesh pays Rs. 175.50 for it after getting two successive discounts. If the first discount is 10%, find the second discount.
Answer:Solution:
Marked price = Rs. 390
After the first discount of 10%, the price of the shirt
\( = 390 - \frac{10}{100} (390) \)
\( = 390(1 - \frac{1}{10}) \)
\( = 390 (\frac{9}{10}) \)
Let second discount be x %. Then
\( 390 (\frac{9}{10}) (1 - \frac{x}{100}) = 175.5 \)

\( \implies 1 - \frac{x}{100} = \frac{175.5 \times 10}{390 \times 9} \)
\( = \frac{19.5 \times 10}{390} \)
\( = \frac{195}{390} \)
\( = \frac{1}{2} \)

\( \implies 1 - \frac{x}{100} = \frac{1}{2} \)

\( \implies \frac{x}{100} = 1 - \frac{1}{2} = \frac{1}{2} \)

\( \implies x = 50 \)
\( \therefore \) Second discount is 50%
In simple words: After the first discount, calculate the price of the shirt. Then, knowing the final price paid and the price after the first discount, work backward to determine the percentage of the second discount.

🎯 Exam Tip: For successive discounts, always work step-by-step. The second discount is applied to the price *after* the first discount.

Question 13. Amar, a manufacturer, gives a discount of 25% on the list price to his distributor Akbar, Akbar sells at a 10% discount on the list price to his customer Anthony. Anthony paid Rs. 540 for the article. What is the profit percentage of Akbar on his cost price?
Answer:Solution:
Let 'x' be the list price of the article.
Amar gives a discount of 25% on the list price.
\( \therefore \) Selling price for Amar \( = x (1 - \frac{25}{100}) \)
\( = x (1 - \frac{1}{4}) \)
\( = \text{Rs.} \frac{3x}{4} \)
Amar sells the article to Akbar
Cost price of article for Akbar \( = \text{Rs.} \frac{3x}{4} \) ........(i)
Akbar sells the article to Anthony at 10% discount on list price
\( \therefore \) Selling price for Akbar \( = x (1 - \frac{10}{100}) \)
\( = x (1 - \frac{1}{10}) \)
\( = \frac{9x}{10} \) .....(ii)
Profit percentage \( = \frac{\text{S.P. - C.P.}}{\text{C.P.}} \times 100 \)
Using (i) and (ii), we have the profit percentage for Akbar as,
Profit percentage \( = \frac{\frac{9x}{10} - \frac{3x}{4}}{\frac{3x}{4}} \times 100 \)
\( = \frac{\frac{36x-30x}{40}}{\frac{3x}{4}} \times 100 \)
\( = \frac{\frac{6x}{40}}{\frac{3x}{4}} \times 100 \)
\( = \frac{6x}{40} \times \frac{4}{3x} \times 100 \)
\( = \frac{6}{10} \times 100 \)
\( = 20\% \)
\( \therefore \) Akbar gets a profit of 20% on his cost price.
In simple words: Trace the transaction chain: manufacturer to distributor (Akbar) to customer (Anthony). Calculate Akbar's cost price (Amar's selling price) and Akbar's selling price (Anthony's cost price), then find Akbar's profit percentage based on his cost price.

🎯 Exam Tip: Pay close attention to whose perspective (manufacturer, distributor, customer) the cost price and selling price refer to at each stage of the transaction.

Question 14. A man sells an article at a profit of 25%. If he had bought it at a 10% loss and sold it for Rs. 7 less, he would have gained 35%. Find the cost price of the article.
Answer:Solution:
Let 'x' be the C.P. of the article
\( \therefore \) Article was sold at 25% profit
\( \therefore \) S.P. of the article \( = X (1+ \frac{25}{100}) \)
\( = X (1+ \frac{1}{4}) \)
\( = 1.25x \)
If the article was bought at 10% loss
i.e., the new C.P. \( = x (1 - \frac{10}{100}) \)
\( = X (\frac{9}{10}) \)
\( = 0.9x \)
and sold at Rs. 7 less
\( \therefore \) New S.P. = 1.25x - 7
Then, the profit would have been 35%
Using profit percentage \( = \frac{\text{S.P.-C.P.}}{\text{C.P.}} \times 100 \)

\( \implies 35 = \frac{(1.25x-7)-0.9x}{0.9x} \times 100 \)

\( \implies \frac{35}{100} = \frac{0.35x-7}{0.9x} \)

\( \implies \frac{7}{20} = \frac{0.35x-7}{0.9x} \)

\( \implies 6.3x = 20(0.35x-7) \)

\( \implies 6.3x = 7x - 140 \)

\( \implies 7x - 6.3x = 140 \)

\( \implies 0.7x = 140 \)

\( \implies x = \frac{140}{0.7} \)

\( \implies x = 200 \)
\( \therefore \) Cost price of the article is Rs. 200
In simple words: Set up equations based on two scenarios: the initial sale with 25% profit, and a hypothetical sale where the article was bought at a loss and sold for less but still yielded a 35% gain. Solve these equations to find the original cost price.

🎯 Exam Tip: Problems involving hypothetical scenarios ("If he had bought...") often require setting up and solving algebraic equations based on the profit/loss formulas.

Question 15. Mr. Mehta sold his two luxury cars at Rs. 39,10,000 each. On one he gains 15% but on the other, he loses 15%. How much does he gain or lose in the whole transaction?
Answer:Solution:
Let x, y be the C.P. of two cars.
S.P. of both the cars = Rs. 39,10,000 .....[Given]
\( \therefore \) One car is sold at 15% loss
\( \therefore \) S.P. of the first car \( = x - \frac{15}{100} X \)
\( \therefore \frac{85}{100} x = 39,10,000 \)
\( \therefore x = \frac{39,10,000 \times 100}{85} \)
\( \therefore x = 46,000 \times 100 \)
\( \therefore x = 46,00,000 \)
Other car is sold at 15% gain
\( \therefore \) S.P. of second car \( = y + \frac{15}{100} y \)
\( \therefore y + \frac{15}{100} y = 39,10,000 \)
\( \therefore \frac{115}{100} y = 39,10,000 \)
\( \therefore y = \frac{39,10,000 \times 100}{115} \)
\( \therefore y = 34,000 \times 100 \)
\( \therefore y = 34,00,000 \)
x + y = Total C.P. of two cars
= 46,00,000 + 34,00,000
= 80,00,000
Total S.P. = 39,10,000 + 39,10,000 = 78,20,000
\( \therefore \) S.P. < C.P.
\( \therefore \) There is a loss of Rs. (80,00,000 - 78,20,000) = Rs. 1,80,000
\( \therefore \) Loss % \( = \frac{1,80,000}{80,00,000} \times 100 \)
\( = \frac{18}{8} \)
\( = 2.25 \)
\( \therefore \) Mr. Mehta bears a 2.25% loss in the whole transaction.
In simple words: For each car sold, use the selling price and the profit/loss percentage to calculate its individual cost price. Then, sum up the total cost prices and total selling prices to determine if there was an overall gain or loss in the entire transaction.

🎯 Exam Tip: For multiple items, calculate individual cost prices from known selling prices and profit/loss percentages. Then sum totals to find the overall outcome.