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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
Three cars were sold by agent for ₹ 2,40,000,
₹ 2,22,000 and ₹ 2,25,000 respectively.
Rates of commission for first and second car were 17.5% and 12.5% respectively.
Overall commission received after sales of three cars is 14%.
∴ Total commission = 14% on Total Sales
`= 14/100 xx (2,40,000 + 2,22,000 + 2,25,000)`
`= 14/100 xx 6,87,000`
= ₹ 96180 .....(i)
Commission on first car = `2,40,000 xx 17.5/100` = ₹ 42000 ......(ii)
Commission on second car = `2,22,000 xx 12.5/100` = ₹ 27750 ....(iii)
Let rate of commission on third car be x%.
Commission on third car = `2,25,000 xx x/100` .....(iv)
Total commission = Commission on first car + Commission on second car + Commission on third car
∴ From (i), (ii), (iii) and (iv),
`96,180 = 42,000 + 27,750 + 2,25,000 xx x/100`
∴ `96,180 = 69,750 + 2,25,000 xx x/100`
∴ `2,25,000 xx x/100 = 96,180 - 69,750`
∴ `2,25,000 xx x/100 = 26,430`
∴ x = `(26,430 xx 100)/225000`
∴ x = 11.75%
∴ Rate of commission on third car is 11.75%.
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