Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
4 hours
2 hours
6 hours
3 hours
Explanation:
Suppose pipe A alone can fill the cistern in x hours.
Then pipe B alone can fill the cistern in (x+6) hours.
Part filled by pipe A in 1 hr =1/x
Part filled by pipe B in 1 hr =1/x+6
Part filled by pipe A and pipe B in 1 hr =1/x+1/x+6
It is given that pipes A and B together can fill the cistern in 4 hours.
i.e., Part filled by pipes A and B in 1 hr =1/4
⇒1/x+1/x+6=1/4
From here, it is better to find the value of x from the choices which will be easier. Or we can solve it as follows.
4(x+6)+4x=x(x+6)
4x+24+4x=x^2+6x
x^2−2x−24=0
(x−6)(x+4)=0
x=6 or −4
Since x cannot be negative, x=6
i.e.,pipe A alone can fill the cistern in 6 hours
Suppose pipe A alone can fill the cistern in x hours.
Then pipe B alone can fill the cistern in (x+6) hours.
Part filled by pipe A in 1 hr =1/x
Part filled by pipe B in 1 hr =1/x+6
Part filled by pipe A and pipe B in 1 hr =1/x+1/x+6
It is given that pipes A and B together can fill the cistern in 4 hours.
i.e., Part filled by pipes A and B in 1 hr =1/4
⇒1/x+1/x+6=1/4
From here, it is better to find the value of x from the choices which will be easier. Or we can solve it as follows.
4(x+6)+4x=x(x+6)
4x+24+4x=x^2+6x
x^2−2x−24=0
(x−6)(x+4)=0
x=6 or −4
Since x cannot be negative, x=6
i.e.,pipe A alone can fill the cistern in 6 hours