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प्रश्न
Deepak’s salary was increased from ₹ 4,000 to ₹ 5,000. The sales being the same, due to reduction in the rate of commission from 3% to 2%, his income remained unchanged. Find his sales.
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उत्तर
Let the sales made by Deepak be ‘x’.
Existing Salary received is ₹ 4,000
Rate of commission is 3%
∴ Initial income of Deepak = Salary + Commission on sales
= 4000 + 3% on x
= `4000 + (3x)/100` ...(i)
Salary was increased to ₹ 5,000 and rate of commission decreased to 2%. However, sales was still the same.
∴ New income of Deepak = Salary + Commission on sales
= 5000 + 2% on x
= `5000 + (2x)/100` ...(ii)
It is given that the income of Deepak remained unchanged.
∴ `4000 + (3x)/100 = 5000 + (2x)/100` .....[From (i) and (ii)]
∴ ` (3x)/100 - (2x)/100 = 5000 - 4000`
∴ `x/100 = 1000`
∴ x = 1,00,000
∴ Sales made by Deepak is ₹ 1,00,000.
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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
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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`
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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
Commission on ₹5000 = ₹ `square`
∴ the rate of commission = `square/5000 xx 100` = 6%
Commission on ₹68,000 at 6% = ₹`68000 xx6/100 = square`
From (1) and (3), we get Salary = ₹(9880 - 4080) = `square`
Hence, fixed weekly salary is ₹5800 and the rate of commission is 6%.
