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Question
The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. Find the percentage reduction in the value of the business.
Solution
Let the initial value of the business be ₹ 100.
Original rate of commission = 4%.
∴ The original income of the agent = `100 xx 4/100` = ₹ 4
Let the new value of the business be ₹ x
New rate of commission = 5%
∴ New income of the agent = `x xx 5/100 = (5x)/100`
However, it is given that the original income and new income of agent is the same.
∴ 4 = `(5x)/100`
∴ 5x = 400
∴ x = 80
∴ New value of business is ₹ 80.
Reduction in business
`= ("Old value" - "New value")/"Old value" xx 100`
`= (100 - 80)/100 xx 100`
= 20 %
There is 20% reduction in the value of the business.
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Solution: Total selling Price of three cars = 2,40,000 + 2,22,000 + 2,25,000
= `square`
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= `14/100 xx square`
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= `17.5/100 xx 2,40,000 = square`
∴ Commission on first car = ₹ `square`
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= `12.5/100 xx 2,22,000 = square`
∴ Commission on second car = ₹ `square`
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Commission on third car = `x/100 xx 2,25,000`
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∴ `x/100 xx 2,25,000 = square - {square + square}`
∴ x = `square`
