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. - Mathematics and Statistics

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.

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.

= ("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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Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Commission, Brokerage and Discount
Exercise 1.1 | Q 6 | Page 5