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Sum

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.

Concept: Commission and Brokerage Agent

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