A cistern can be filled by two pipes in 20 and 30 minutes respectively. Both pipes being opened, when the first pipe must be turned off so that the cistern may be filled in 10 minutes more.
A. After 10 minutes
B. After 12 minutes
C. After 20 minutes
D. After 8 minutes
Answer: Option D
Solution (By Examveda Team)
% Cistern is filled by 1st pipe in one minute = $$\frac{{100}}{{20}}$$ = 5% % Cistern is filled by 2nd pipe in one minute = $$\frac{{100}}{{30}}$$ = 3.33% % cistern filled by 1st and 2nd pipes in one minute = 8.33% According to question, Cistern is totally filled by 2nd pipe in last 10 minute. That means 2nd pipe filled 33.3% of the cistern in last 10 minute and 66.66% of cistern is filled by 1st and 2nd pipe together in = $$\frac{{66.66}}{{8.33}}$$ = 8 minutes Thus, after 8 minute, 1st pipe must be turned off.This Question Belongs to Arithmetic Ability >> Time And Work
(t/20) + {(t+10)/30} = 1
t = 8 min
In 1 minute both pipes can fill =1/20 + 1/30 = 1/12
part of the cistern
In 10 minutes, second pipe can fill = 10/30 =1/3 part
Cistern filled by both pipes = 1 - 1/3 =2/3
∴ Time taken by both the pipes to fill 2/3 part of cistern =
12 × 2/3
= 8 minutes
Therefore, the first pipe can be turned off after 8 minutes.
2nd pipe fill in 30min=1part
1min=1/30
. . . 10min=10/30=1/3
Remaining=2/3part
Both pipes filled=(1/20+1/30)=1/12part
1/12 part=1min
2/3part=2*12/3=8min
Lets suppose time taken to fill the tank is x minutes.
pipe 1 and 2 will fill the tank in x-10 minutes.
while pipe 2 will fill tank for 10 minutes after we switch off pipe 1.
if pipe 1 & 2 work together they will work for x-10 minutes.
so, 1/12 * x-10 + 1/30 * 10 = 1
x = 18 minutes.
so pipe 1 should be turned off after 18-10= 8 minutes which is also the time they work together.
Suppose 60units of work to be done (LCM based 20min for A and 30min for B)..So that means A can do 3 units work per min and B can do 2 units of work per min..
So if both can work together they can do 5 units of work per min..So total 12 min needed to complete 60units of work.
Last 10 min work should be done by B only, so total 20units of work to be done by B.
So A and B together can do 40units of work in 8min..after 8min A can be turned off to continue B for 10more min to complete the work...