Question

The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water treatment plant has a design capacity of 6000 $m^3/d$. It is expected that the population will increase to 48000 during the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth?

• A. 16.5 years
• B. 15.0 years
• C. 8.6 years
• D. 12.0 years

Answer 1

The correct option is D 12.0 years

Population after n years,
$P_n=P_0+n\overline{x}$

$\overline{x}$ is arithmetic design growth rate
$Given{P}_0=28000$

$Forn=20;P_{20}=48000$

$\therefore \overline{x}=\frac{48000-28000}{20}=1000peryear$

The population when design capacity will be required,

$P_n=\frac{6000\times 1000}{150}=40,000$

$\therefore$ Number of years to reach the plant at design capacity,

$n=\frac{P_n-P_0}{\overline{x}}=\frac{40000-28000}{1000}$


= 12.0 years

Note: Since design capacity of treatment plant is done on the basis of 2 times average daily demand not maximum daily demand, but in the given question solution is done on the basis of simply average daily demand otherwise answer will not match from any of the given option (data will be improper).