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In 1975, the consumption of water for human use was about 3850 cu.km/year. It increased to about 6000 cu.km/year in the year 2000. Find the percent increase in the consumption of water from 1975 to 2000. Also, find the annual percent increase in consumption (assuming water consumption increases uniformly)

Solution:

Water consumption in 1975 = 3850 cu. km/year

Water consumption in 2000 = 3850 cu. km/year

Percentage increase in water consumption from year 1975 to 2000:

% increase = [(6000 - 3850)/3850] × 100

= (2150/3850) × 100

= (43/77) × 100

= 0.5584 × 100

= 55.84%

Annual Percentage increase in water consumption assuming uniform increase in consumption :

Since 25 years have elapsed we get:

Annual % increase = 55.84/25

= 2.23%

Alternative Method: The Compounding Formula

A = P(1 + g/100)ⁿ

A = 6000

P = 3850

g = ?

n = 25

6000 = 3850(1 + g/100)²⁵

1 + g/100 = (6000/3850)^1/25

1 + g/100 = (1,558)^1/25

1 + g/100 = 1.018

g/100 = 1.018 - 1

g = 0.018 × 100

g = 1.8%

The annual rate of increase in consumption of water from 1975 to 2000 is 1.8%.

✦ Try This: Find the percent decrease of the price of a TV unit from Rs. 25,999 to Rs. 19,999.

The percentage decrease =[ (25999-19999)/25999 ] × 100

= [ 6000 /25999]× 100 = 23.077%

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 8

NCERT Exemplar Class 8 Maths Chapter 9 Problem 77

In 1975, the consumption of water for human use was about 3850 cu.km/year. It increased to about 6000 cu.km/year in the year 2000. Find the per cent increase in the consumption of water from 1975 to 2000. Also, find the annual per cent increase in consumption (assuming water consumption increases uniformly)

Summary:

In 1975, the consumption of water for human use was about 3850 cu.km/year. It increased to about 6000 cu.km/year in the year 2000. The the per cent increase in the consumption of water from 1975 to 2000 is 55.34%. The find the annual per cent increase in consumption (assuming water consumption increases uniformly) is 2.23 percent and 1.8% using the compounding formula

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