The capacity of a towns pumping system is 110 x 106 ld The p

The capacity of a town\'s pumping system is 110 x 106 l/d. The present population of the town expected to remain constant at 36L/person/d. The population a decade ago was 1.3 million, and a decade before that, the population was 1.2 million. In what year will the capacity will be fully utilized? (15 points) i· is 1.5 million, and the average consumption of water is

Solution

Given data:

total supply of the city = 110*10⁶l/day

per capita demand of the city = 36 l/day

population details:

deacade at which the full supply is utilized?

demand for given deacade population = population *per capita demand

for 1st decade Q = 1.2*10⁶ * 36 = 43.2 *10⁶l/day

for second decade Q = 1.3*10⁶ * 36 = 46.8 *10⁶l/day

for third decade Q = 1.5*10⁶ * 36 = 54 *10⁶l/day

the actual full supply is 110*10⁶l/day,the above values shows that it does not utilizes the full supply,hence we need to forecast the population at which the supply of town is fully utilized.

by arthimetic mean method the population is forecated in this problem

the formula given by this method is P_n= P + nI

where P_n= populaton after n decades

P = present population

n = number of decades

I = population increase rate

from the given population values 1.5*10⁶ = 1.2*10⁶ + 2*I

where 1.5*10⁶ is the population after 2 decades from the given last population i.e 1.2*10⁶

from the above expression I = 150000

for utilizing the whole demand the required population is 110*10⁶/36=3055555.556

say the required population is obtained at n deacades,so the n decades are

3055555.556 = 1200000+(n*150000)

n = 12.37 deacdes after the decade at which 1.2*10⁶ population has been occured.and 10.37 deaceds after the present deacade.

s.no	no.of decades	population in millions
1	1	1.2
2	2	1.3
3	3	1.5(present year population)