Maharashtra Board Class 12 Maths Part 2 Chapter 1 Commission Brokerage 1.1 Solutions

Question 1. An agent charges a 12% commission on the sales. What does he earn if the total sale amounts to Rs. 48,000? What does the seller get?
Answer: Solution:
Rate of commission = 12%
Total sales = Rs. 48,000
Agent's commission = \(\frac{12}{100} \times 48,000\)
= Rs. 5,760
Amount received by the seller = Total sales - commission
= Rs. 8,000 - Rs. 5760
= Rs. 2,240
In simple words: This question asks to calculate the agent's commission and the net amount received by the seller based on a given sales amount and commission rate.

🎯 Exam Tip: Remember to calculate the commission first and then subtract it from the total sales to find the seller's net amount. Pay attention to calculating percentages correctly.

Question 2. A salesman receives a 3% commission on sales up to Rs. 50,000 and a 4% commission on sales over Rs. 50,000. Find his total income on the sale of Rs. 2,00,000.
Answer: Solution:
Total sales = Rs. 2,00,000
Rate of commission upto Rs. 50,000 = 3%
= \(\frac{3}{100} \times 50,000\)
= Rs. 1,500
Rate of commission on the sales over Rs. 50,000 = 4%
Sales over Rs. 50,000 is \(2,00,000 - 50,000 = Rs. 1,50,000\)
Commission on sales over Rs. 50,000 = \(\frac{4}{100} \times 1,50,000 = Rs. 6,000\)
His total income = \(Rs. 1,500 + Rs. 6,000 = Rs. 7,500\)
In simple words: This problem involves calculating a salesman's total income, which is determined by different commission rates applied to sales above and below a certain threshold.

🎯 Exam Tip: When commission rates change based on sales tiers, break down the total sales into relevant segments and calculate commission for each segment separately before summing them up.

Question 3. Ms. Saraswati was paid 88,000 as commission on the sale of computers at the rate of 12.5%. If the price of each computer was Rs. 32,000, how many computers did she sell?
Answer: Solution:
Total commission = Rs. 88,000
Rate of commission = 12.5%
Let the number of computers sold be x
since price of each computer = Rs. 32,000
Total sales = Rs. 32,000x
Total commission = 12.5% of total sales
\(88,000 = \frac{12.5}{100} \times 32,000x\)
\( = \frac{125}{1000} \times 32,000x\)
\(X = \frac{88,000}{125 \times 32}\)
\(x = 22\)
In simple words: Given the total commission earned and the commission rate, along with the price per item, this question requires finding out how many items were sold.

🎯 Exam Tip: First, use the total commission and commission rate to find the total sales value. Then, divide the total sales value by the price of one item to get the number of items sold.

Question 4. Anita is allowed 6.5% commission on the total sales made by her, plus, a bonus of \(\frac{1}{2}\)% on the sale over Rs. 20,000. If her total commission amounts to Rs. 3,400. Find the sales made by her.
Answer: Solution:
Let the total sales made by Anita be x
Rate of commission = 6.5% of total sales
= \(\frac{6.5}{100} \times x\)
= \(\frac{65x}{1,000}\)
= \(\frac{13x}{200}\)
Rate of bonus = \(\frac{1}{2}\)% of \((x - 20000)\)
= \(\frac{1}{200} \times (x - 20,000)\)
= \(\frac{x - 20,000}{200}\)
Her total commission = Rs. 3,400
\(\frac{13x}{200} + \frac{x}{200} - 100 = 3,400\)
\(\frac{14x}{200} = 3,500\)
\(x = \frac{3,500 \times 200}{14}\)
\(x = 50,000\)
In simple words: This question involves an agent earning a base commission on total sales and an additional bonus commission on sales exceeding a specific amount, and you need to find the total sales given her total earnings.

🎯 Exam Tip: Set up an equation where the total commission (base + bonus) equals the given amount. Carefully define variables for total sales and express both commission types in terms of that variable.

Question 5. Priya gets a salary of Rs. 15,000 per month and a commission of 8% on sales over Rs. 50,000. If she gets Rs. 17,400 in a certain month. Find the sales made by her in that month.
Answer: Solution:
Let the total sales made by Priya be x
Salary of Priya = Rs. 15,000
Commission = Total earning - salary
= Rs. 17,400 - Rs. 15,000
= Rs. 2,400
Commission = 8% on the sales over Rs. 50,000
\(2400 = \frac{8}{100} (x - 50000)\)
\(\frac{2,400 \times 100}{8} = x - 50,000\)
\(30,000 = x - 50,000\)
\(30,000 + 50,000 = x\)
∴ \(x = Rs. 80,000\)
In simple words: This problem asks to determine the total sales made by a person who earns a fixed monthly salary plus a commission on sales exceeding a certain threshold.

🎯 Exam Tip: Isolate the commission amount by subtracting the fixed salary from the total earnings. Then, use the commission rate and threshold to set up an equation to find the total sales.

Question 6. The income of the broker remains unchanged though the rate of commission is increased from 4% to 5%. Find the percentage reduction in the value of the business.
Answer: Solution:
Let the original value of business be Rs. 100
Original rate of commission = 4%
.. Original commission = \(\frac{4}{100} \times 100 = Rs. 4\)
Let the new value of business be x
The new rate of commission = 5%
.. New commission = \(\frac{5}{100} \times X = \frac{x}{20}\)
Given, original income = New income
\(4 = \frac{x}{20}\)
.. \(x = Rs. 80\)
Thus there is 20% reduction in the value of the business.
In simple words: This question asks to find the percentage reduction in business value when the commission rate increases, but the broker's income remains the same.

🎯 Exam Tip: Set the original commission equal to the new commission. Express both in terms of original and new business values and rates to find the relationship between the business values.

Question 7. Mr. Pavan is paid a fixed weekly salary plus commission based on a percentage of sales made by him. If on the sale of Rs. 68,000 and Rs. 73,000 in two successive weeks, he received in all 9,880 and Rs. 10,180. Find his weekly salary and the rate of commission paid to him.
Answer: Solution:
Let the weekly salary of Mr. Pavan be x and the rate of commission paid to him be y%
Income = Weekly salary + Commission on the sales
.. \(9,880 = x + \frac{y}{100} \times 68,000\)
i.e. \(9,880 = x + 680y .......(1)\)
Also, \(10,180 = x + \frac{y}{100} \times 73,000\)
i.e \(10,180 = x + 730y .........(2)\)
Subtracting (1) from (2), we get
\(50y = 300\)
∴ \(y = 6\)
Substituting y = 6 in equation (1)
\(9,880 = x + 680(6)\)
.. \(9,880 - 4,080 = x\)
.. \(x = 5,800\)
Weekly salary = Rs. 5,800
Rate of commission = 6%
In simple words: Given two scenarios of weekly sales and corresponding total income, this problem requires determining the fixed weekly salary and the commission rate of an agent.

🎯 Exam Tip: Formulate two simultaneous linear equations, one for each week's income, with weekly salary and commission rate as unknowns. Solve these equations to find the values.

Question 8. Deepak's salary was increased from Rs. 4,000 to Rs. 5,000. The sales being the same, due to a reduction in the rate of commission from 3% to 2%, his income remained unchanged. Find his sales.
Answer: Solution:
Let Deepak's total sales be Rs. x
Original salary of Deepak = Rs. 4,000
Original rate of commission = 3%
His new salary = Rs. 5,000
New rate of commission = 2%
Original income = New income (given)
\(4000 + \frac{3x}{100} = 5000 + \frac{2x}{100}\)
\(\frac{3x}{100} - \frac{2x}{100} = 5,000 - 4,000\)
\(\frac{x}{100} = 1000\)
\(x = Rs. 1,00,000\)
.. His total sales = Rs. 1,00,000
In simple words: This question involves a situation where an individual's salary increases, but the commission rate decreases, yet their total income remains unchanged, and you need to find the total sales.

🎯 Exam Tip: Set the original total income (salary + commission) equal to the new total income. Represent commission in terms of sales and rates, then solve for the sales amount.

Question 9. An agent is paid a commission of 7% on cash sales and 5% on credit sales made by him. If on the sale of Rs. 1,02,000 the agent claims a total commission of Rs. 6,420, find his cash sales and credit sales.
Answer: Solution:
Total Sales = Rs. 1,02,000
Let cash sales x
.. Credit sales = Rs. (1,02,000 - x)
Agent's commission on cash sales = 7%
= \(\frac{7}{100} \times x\)
= \(\frac{7x}{100}\)
Commission on credit sales = 5%
= \(\frac{5}{100} (1,02,000 - x)\)
Given, Total commission = Rs. 6,420
.. \(\frac{7x}{100} + \frac{5}{100} (1,02,000 - x) = 6420\)
.. \(\frac{7x}{100} + 5100 - \frac{5x}{100} = 6,420\)
.. \(\frac{2x}{100} = 6,420 - 5,100\)
.. \(\frac{2x}{100} = 1320\)
∴ \(x = Rs. 66,000\)
.. Cash sales = Rs. 66,000
.. Credit sales = \(1,02000 - 66,000 = Rs. 36,000\)
In simple words: An agent earns different commission rates for cash sales and credit sales. Given the total sales and total commission, you need to find the values of cash sales and credit sales.

🎯 Exam Tip: Let cash sales be 'x', so credit sales will be 'Total sales - x'. Formulate an equation for total commission based on both types of sales and their respective rates, then solve for x.

Question 10. Three cars were sold through an agent for Rs. 2,40,000, Rs. 2,22,000 and Rs. 2,25,000 respectively. The rates of the commission were 17.5% on the first, 12.5% on the second. If the agent overall received 14% commission on the total sales, find the rate of commission paid on the third car.
Answer: Solution:
Total selling price of three cars = \(2,40,000 + 2,22,000 + 2,25,000 = Rs. 6,87,000\)
Commission on total sales = 14%
= \(\frac{14}{100} \times 6,87,000\)
= 96,180
Selling price of first car = Rs. 2,40,000
Rate of commission = \(17.5\% = \frac{17.5}{100} \times 2,40,000\)
.. Commission on first car = Rs. 42,000
Selling price of second car = Rs. 2,22,000
Rate of commission = \(12.5\% = \frac{12.5}{100} \times 2,22,000\)
.. Commission on second car = Rs. 27,750
Selling price of third car = Rs. 2,25,000
Let the rate of commission be x%
Commission on third car = \(\frac{x}{100} \times 2,25,000\)
\(96,180 - (42,000 + 27,750) = \frac{x}{100} \times 2,25,000\)
\(\frac{26,430 \times 100}{2,25,000} = x\)
.. \(x = 11.75\)
.. Rate of commission on the third car = 11.75%
In simple words: This problem involves three separate sales with known prices and two commission rates. Given the total commission earned and the third car's price, you need to find the commission rate for the third car.

🎯 Exam Tip: Calculate the total commission from all sales. Subtract the commissions from the first two cars to find the commission for the third car. Then, use the third car's sales price to calculate its commission rate.

Question 11. Swatantra Distributors allows a 15% discount on the list price of the washing machines. Further 5% discount is giver for cash payment. Find the list price of the washing machine if it was sold for the net amount of 38,356.25.
Answer: Solution:
Let the list price of the washing machine be Rs. 100
Trade discount = \(15\% = \frac{15}{100} \times 100 = Rs. 15\)
.. Invoice price = \(100 - 15 = Rs. 85\)
Cash discount = \(5\% = \frac{5}{100} \times 85 = 4.25\)
.. Net price = \(85 - 4.25 = Rs. 80.75\)
Thus if List price is 100 than Net price is 80.75
if List price is x than Net price is 38,356.25.
.. \(x = \frac{38356.25 \times 100}{80.75}\)
.. \(x = Rs. 47,500\)
The list price of the washing machine is 47,500
In simple words: This question deals with multiple discounts (trade and cash) applied sequentially to an item's list price to reach a net selling price. You need to find the original list price.

🎯 Exam Tip: Work backward from the net selling price. Understand that discounts are applied on the remaining amount after the previous discount. Alternatively, set up an equation where list price is 'x' and apply discounts to find the final net price.

Question 12. A bookseller received Rs. 1,530 as a 15% commission on the list price. Find the list price of the books.
Answer: Solution:
Let the list price of the books be x
Rate of commission = 15%
Book seller's commission = Rs. 1,530
.. \(\frac{15}{100} \times x = 1,530\)
.. \(x = \frac{1,530 \times 100}{15}\)
∴ \(x = Rs. 10,200\)
In simple words: Given the total commission received by a bookseller and the commission rate on the list price, this question asks to find the original list price of the books.

🎯 Exam Tip: If commission is a percentage of the list price, set up a direct proportion or an equation to find the list price using the given commission amount and rate.

Question 13. A retailer sold a suit for 8,832 after allowing an 8% discount on market price and a further 4% cash discount. If he made 38% profit, find the cost price and the market price of the suit.
Answer: Solution:
Let the marked price of the suit be 100
Trade discount = \(8\% = \frac{8}{100} \times 100 = Rs. 8\)
Invoice price = \(100 - 8 = Rs. 92\)
Cash discount = \(4\% = \frac{4}{100} \times 92 = 3.68\)
.. Net price = \(92 - 3.68 = Rs. 88.32\)
Thus if list price is 100 then net price is 88.32, if list price is x then net price is 8,832
.. \(x = \frac{8,832 \times 100}{88.32}\)
.. \(x = Rs. 10,000\)
The retailer made 38% profit.
Let the CP of the suit be 100
.. SP of the suit = \(100 + 38 = Rs. 138\)
Thus if the SP of the suit is 138 then its CP is 100
If the SP of the suit is 88.32 then its
CP = \(\frac{88.32 \times 100}{138} = Rs. 6400\)
In simple words: This problem involves calculating the cost price and market price of a suit, given its selling price after two successive discounts and the profit percentage made by the retailer.

🎯 Exam Tip: Start by working backward from the net selling price through the discounts to find the market price. Then, use the selling price and profit percentage to find the cost price.

Question 14. An agent charges 10% commission plus 2% delcredere. If he sells goods worth Rs. 37,200, find his total earnings.
Answer: Solution:
Total sales = Rs. 37,200
Rate of commission = 10%
Agents commission = \(\frac{4}{100} \times 37200 = Rs. 3720\)
Rate of delcredere = 2%
Amount of delcredere = \(\frac{2}{100} \times 37,200 = Rs. 744\)
Total earning of the agent = \(Rs. 3,720 + Rs. 744 = Rs. 4,464\)
In simple words: This question asks for the total earnings of an agent who receives a standard commission plus a delcredere commission on goods sold.

🎯 Exam Tip: Calculate the regular commission and the delcredere commission separately based on the total sales. Sum these two amounts to find the agent's total earnings.

Question 15. A whole seller allows a 25% trade discount and 5% cash discount. What will be the net price of an article marked at 1600?
Answer: Solution:
Marked price of the article = Rs. 1,600
Trade discount = 25%
= \(\frac{25}{100} \times 1,600\)
= Rs. 400
.. Invoice price = \(1,600 - 400 = Rs. 1,200\)
Cash discount = 5%
= \(\frac{5}{100} \times 1,200\)
= Rs. 60
.. Net price = \(1,200 - 60 = Rs. 1,140\)
In simple words: This question asks to find the final net price of an article after applying a trade discount and then a cash discount consecutively on its marked price.

🎯 Exam Tip: Apply the trade discount first to the marked price to get the invoice price. Then, apply the cash discount to the invoice price (the reduced amount) to get the net price.