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प्रश्न
An agent is paid a commission of 4% on cash sales and 6% on credit sales made by him. If on the sale of ₹ 51,000 the agent claims a total commission of ₹ 2,700, find the sales made by him for cash and on credit.
उत्तर
Let x be the cash sales made by the agent.
∴ Commission on cash sales = 4% of cash sales
`= 4/100 xx x = "4x"/100`
Now, Credit sales = Total sales - Cash sales
∴ Credit sales = 51,000 – x
Commission on credit sales
= 6% of credit sales
`= 6/100 xx (51,000 - x)`
Total commission = Commission on cash sales + Commission on credit sales
∴ `2700 = (4x)/100 + 6/100 (51000 - x)`
∴ `2700 = (4x + 306000 - 6x)/100`
∴ 270000 = - 2x + 306000
∴ 2x = 306000 - 270000
∴ 2x = 36000
∴ x = ₹ 18000
∴ Cash sales is ₹ 18,000.
∴ Credit sales = 51,000 – 18,000 = ₹ 33,000
∴ Sales made by agent for cash is ₹ 18,000 and on credit is ₹ 33,000.
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Three cars were sold through an agent for ₹ 2,40,000, ₹ 2,22,000 and ₹ 2,25,000 respectively. The rates of 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.
Solution: Total selling Price of three cars = 2,40,000 + 2,22,000 + 2,25,000
= `square`
Commision on total sale = 14%
= `14/100 xx square`
Selling price of First car = ₹ 2,40,000
Rate of commission = 17.5%
= `17.5/100 xx 2,40,000 = square`
∴ Commission on first car = ₹ `square`
Selling price of Second car = ₹ 2,22,000
Rate of commission = 12.5%
= `12.5/100 xx 2,22,000 = square`
∴ Commission on second car = ₹ `square`
Selling price of third car = ₹ 2,25,000
Let the rate of commission be x
Commission on third car = `x/100 xx 2,25,000`
∴ Commission on third car = Total commission − (commission on first car + commission on second car)
∴ `x/100 xx 2,25,000 = square - {square + square}`
∴ x = `square`
Mr. Pavan is paid a fixed weekly salary plus commission based on percentage of sales made by him. If on the sale of ₹68,000 and ₹73,000 in two successive weeks, he received in all ₹9880 and ₹10, 180. Complete the following activity to find his weekly salary and the rate of commission paid to him.
Solution: Income of Mr. Pavan = Weekly salary + Commission on sales
Salary + Commission on ₹68,000 = ₹9880 ... (1)
Salary+ Commission on ₹73,000 = ₹10,180 ... (2)
Subtracting (1) from (2), we get
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From (1) and (3), we get Salary = ₹(9880 - 4080) = `square`
Hence, fixed weekly salary is ₹5800 and the rate of commission is 6%.
