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Question
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`
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Solution
Total selling Price of three cars = 2,40,000 + 2,22,000 + 2,25,000
= 687000
Commision on total sale = 14%
= `14/100 xx 687000`
= ₹ 96,180
Selling price of First car = ₹ 2,40,000
Rate of commission = 17.5%
= `17.5/100 xx 2,40,000` = 42000
∴ Commission on first car = ₹ 42000
Selling price of Second car = ₹ 2,22,000
Rate of commission = 12.5%
= `12.5/100 xx 2,22,000` = 27,750
∴ Commission on second car = ₹ 27,750
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 = 96180 - {42000 + 27,750}`
∴ `x/100 xx 2,250` = 26,430
∴ x × 2,250 = 26,430
∴ x = `(26,430)/(2,250)`
∴ x = 11.75%
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