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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.
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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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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%.
