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प्रश्न
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.
उत्तर
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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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: 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
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∴ 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%.
