Two pipes A and B can fill a tank in \[10\] and \[15\] minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Part filled by pipe A in \[1\] minute \[=\frac{1}{10}\]
Part filled by pipe B in \[1\] minute \[= \frac{1}{15}\]
Net part filled by pipe A and B in \[1\] minute
\[= \frac{1}{10}+\frac{1}{15}\]
\[=\frac{1}{10}+\frac{1}{15}\]
\[=\frac{2+3}{30}\]
\[=\frac{5}{30}\]
\[=\frac{1}{6}\]
i.e, pipe A and B together can fill the tank in \[6\] minutes.
Three pipes A, B and C can fill a tank in \[10, 15\] and \[20\] minutes respectively. If all the pipes are used together, then how long will it take to fill the tank?
Part filled by pipe A in \[1\] minute \[=\frac{1}{10}\]
Part filled by pipe B in \[1\] minute \[= \frac{1}{15}\]
Part filled by pipe C in \[1\] minute \[= \frac{1}{30}\]
Net part filled by pipe A, B and C in \[1\] minute
\[=\frac{1}{10}+\frac{1}{15}+\frac{1}{30}\]
\[=\frac{6+4+2}{60}\]
\[=\frac{12}{60}\]
\[=\frac{1}{5}\]
i.e, pipe A, B and C together can fill the tank in \[5\] minutes.
Four pipes A, B, C and D can fill a tank in \[2, 3, 4\] and \[6\] hours respectively. If all the pipes are used together, then how long will it take to fill the tank?
Part filled by pipe A in \[1\] hour \[=\frac{1}{2}\]
Part filled by pipe B in \[1\] hour \[= \frac{1}{3}\]
Part filled by pipe C in \[1\] hour \[= \frac{1}{4}\]
Part filled by pipe D in \[1\] hour \[= \frac{1}{6}\]
Net part filled by pipe A, B, C and D in \[1\] hour
\[=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\]
\[=\frac{30+20+15+10}{60}\]
\[=\frac{75}{60}\]
i.e, pipe A, B, C and D together can fill the tank in
\[=\frac{60}{75}\] hours
\[=\frac{60}{75}\times 60\] minutes
\[=48\] minutes
Three pipes A, B, and C can together fill a tank in \[4\] hours. B and C can together fill the tank in \[5\] hours. What time will pipe A take to fill the tank?
Part filled by pipe A, B and C in \[1\] minute \[= \frac{1}{4}\]
Part filled by pipe B and C in \[1\] minute \[= \frac{1}{5}\]
\[\therefore\] Part filled by pipe A in \[1\] minute \[=\frac{1}{4}-\frac{1}{5}\]
\[=\frac{5-4}{20}\]
\[=\frac{1}{20}\]
\[\therefore\] Time taken by pipe \[A\] to fill the tank is \[20\] minutes.
Pipe A takes \[15\] minutes to fill a tank. Pipe B and C together take \[10\] minutes to fill the same tank. In how much time will the tank be fully filled if all the pipes work together?
Part filled by pipe A, B and C in \[1\] minute \[=\frac{1}{15}+\frac{1}{10}\]
\[=\frac{2+3}{30}\]
\[=\frac{5}{30}\]
\[=\frac{1}{6}\]
\[\therefore\] The tank will be fully filled in \[6\] miniutes.
Two pipes A and B can fill a tank in \[20\] minutes and \[30\] minutes respectively. How long will it take to fill the tank if both the pipes are working?
Method 1
Part of the tank filled by both pipes in one minute
\[=\frac{1}{20}+\frac{1}{30}\]
Required time \[=\frac{1}{\frac{1}{20}+\frac{1}{30}}\]
\[=\frac{60}{5}\]
\[=12\]
\[\therefore\] Required time \[=12\] minutes
Method 2
Two taps A and B can fill a tank in \[x\] minutes and \[y\] minutes respectively. If both the taps are opened together, then how much time it will take to fill the tank?
Required time \[=\frac{xy}{x+y}\] minutes
Here, \[x = 20, y = 30\]
Required time \[=\frac{xy}{x+y}\] minutes
\[=\frac{20\times30}{20+30}\] minutes
\[=\frac{600}{50}\] minutes
\[=12\] minutes
Two taps A and B can fill a tank in \[x\] hours and \[y\] hours respectively. How long will it take to fill the tank if both the taps are opened?
Two taps A and B can fill a tank in \[x\] hours and \[y\] hours respectively. If both the taps are opened together, then the time it will take to fill the tank is
\[\left(\frac{xy}{x+y}\right)\] hours
A tap A can fill a tank in \[4\] hours and B can empty the tank in \[5\] hours. How long will it take to fill the tank if both the taps are opened?
Part filled by tap A in \[1\] hour \[=\frac{1}{4}\]
Part emptied by tap B in \[1\] hour \[=\frac{1}{5}\]
\[\therefore\] Part filled by tap (A+B) in \[1\] hour
\[=\frac{1}{4}-\frac{1}{5}\]
\[=\frac{5-4}{20}\]
\[=\frac{1}{20}\]
\[\therefore\] the tank will be fully filled in \[20\] hours.
A tap A can fill a tank in \[x\] hours and B can empty the tank in \[y\] hours. How long will it take to fill the tank if both the taps are opened?
A tap A can fill a tank in ‘\[x\]’ hours and B can empty the tank in \[y\] hours. Then time taken to fill the tank when both are opened is
\[\left(\frac{xy}{y-x}\right)\] hours
A tap A can fill a tank in \[5\] hours and B can empty the tank in \[4\] hours. How long will it take to empty the tank if both the taps are opened?
A tap A can fill a tank in \[x\] hours and B can empty the tank in \[y\] hours. Then time taken to fill the tank when both are opened is
\[\left(\frac{xy}{y-x}\right)\] hours
\[\therefore\] Required time \[=\frac{4\times 5}{5-4}=20\] hours.If pipes A & B can fill a tank in time \[x\], B & C in time \[y\] and C & A in time \[z\]. How long will it take to fill the tank if all the taps are opened?
If pipes A & B can fill a tank in time \[x\], B & C in time \[y\] and C & A in time \[z\]. Then the time taken to fill the tank by pipe (A + B + C) together \[=\frac{2xyz}{xy+yx+zx}\]
If pipes A & B can fill a tank in \[10\] minutes, B & C in \[15\] minutes and C & A in time \[30\] minutes. How long will it take to fill the tank if all the taps are opened?
If pipes A & B can fill a tank in time \[x\], B & C in time \[y\] and C & A in time \[z\]. Then the time taken to fill the tank by pipe (A + B + C) together \[=\frac{2xyz}{xy+yx+zx}\]
\[\therefore\] Required time
\[=\frac{2\times 10\times 15\times 30}{\left(10\times 15\right)+\left(15\times 30\right)+\left(30\times 10\right)}\]
\[=\frac{9000}{150+450+300}\]
\[=\frac{9000}{900}\]
\[=10\] minutes
Two taps can fill a tank in ‘\[x\]’ and ‘\[y\]’ hours respectively. If both the taps are opened together and \[1st\] tap is closed before ‘\[m\]’ hours of filling the tank, then in how much time the tank will be filled?
Two taps can fill a tank in ‘\[x\]’ and ‘\[y\]’ hours respectively. If both the taps are opened together and \[1st\] tap is closed before ‘\[m\]’ hours of filling the tank, then the time required to fill the tank
\[=\frac{\left(x+m\right)y}{x+y}\] hours
Two taps can fill a tank in \[4\] and \[6\] hours respectively. If both the taps are opened together and \[1st\] tap is closed before \[2\] hours of filling the tank, then what is the time required to fill the tank?
Two taps can fill a tank in ‘\[x\]’ and ‘\[y\]’ hours respectively. If both the taps are opened together and \[1st\] tap is closed before ‘\[m\]’ hours of filling the tank, then the time required to fill the tank
\[=\frac{\left(x+m\right)y}{x+y}\] hours
\[\therefore\] Required time
\[=\frac{\left(x+m\right)y}{x+y}\]
\[=\frac{\left(4+2\right)6}{4+6}\]
\[=\frac{\left(6\right)4}{10}\]
\[=\frac{24}{10}\]
\[=2.4\] hours
Two taps can fill a tank in ‘\[x\]’ and ‘\[y\]’ hours respectively. If both the taps are opened together and \[2nd\] tap is closed before ‘\[m\]’ hours of filling the tank, then in how much time the tank will be filled?
Two taps can fill a tank in ‘\[x\]’ and ‘\[y\]’ hours respectively. If both the taps are opened together and \[2nd\] tap is closed before ‘\[m\]’ hours of filling the tank, then the time required to fill the tank
\[=\frac{\left(y+m\right)x}{x+y}\] hours
Two taps can fill a tank in \[4\] and \[6\] hours respectively. If both the taps are opened together and \[2nd\] tap is closed before \[2\] hours of filling the tank, then what is the time required to fill the tank?
Two taps can fill a tank in ‘\[x\]’ and ‘\[y\]’ hours respectively. If both the taps are opened together and \[2nd\] tap is closed before ‘\[m\]’ hours of filling the tank, then the time required to fill the tank
\[=\frac{\left(y+m\right)x}{x+y}\]
\[\therefore\] Required time
\[=\frac{\left(6+2\right)4}{4+6}\]
\[=\frac{\left(8\right)4}{10}\]
\[=3.2\] hours
Pipes A & B can fill a tank in \[3\] minutes, B & C in \[4\] minutes and C & A in \[5\] minutes, How long will it take to fill the tank if only pipe A is working?
If pipes A & B can fill a tank in time \[x\], B & C in time \[y\] and C & A in time \[z\], then the time required/taken to fill the tank by pipe A alone
\[=\frac{2xyz}{xy+yz-zx}\]
\[\therefore\] required time
\[=\frac{2\times 3\times 4\times 5}{xy+yz-zx}\]
\[=\frac{2\times 3\times 4\times 5}{\left(3\times 4\right)+\left(4\times 5\right)+\left(5\times 3\right)}\]
\[=\frac{120}{12+20+15}\]
\[=\frac{120}{47}\]
\[=2\frac{26}{47}\] minutes
Pipes A & B can fill a tank in \[5\] minutes, B & C in \[6\] minutes and C & A in \[7\] minutes, How long will it take to fill the tank if only pipe B is working?
If pipes A & B can fill a tank in time \[x\], B & C in time \[y\] and C & A in time \[z\], then the time required/taken to fill the tank by pipe B alone
\[=\frac{2xyz}{yz+zx-xy}\]
\[\therefore\] Required time
\[=\frac{2\times 5\times 6\times 7}{\left(6\times 7\right)+\left(7\times 5\right)-\left(5\times 6\right)}\]
\[=\frac{420}{42+35-30}\]
\[=\frac{420}{47}\]
\[=8\frac{44}{47}\] minutes
Pipes A & B can fill a tank in \[2\] minutes, B & C in \[3\] minutes and C & A in \[4\] minutes, How long will it take to fill the tank if only pipe C is working?
If pipes A & B can fill a tank in time \[x\], B & C in time \[y\] and C & A in time \[z\], then the time required/taken to fill the tank by pipe C alone
\[\frac{2xyz}{zx+xy-yz}\]
\[\therefore\] Required time
\[=\frac{2\times 2\times 3\times 4}{\left(4\times 2\right)+\left(2\times 3\right)-\left(3\times 4\right)}\]
\[=\frac{48}{8+6-12}\]
\[=\frac{48}{2}\]
\[=24\] minutes
Two taps A and B can fill a tank in \[5\] hours and \[10\] hours respectively. If both the pipes are opened together, then after how much time pipe B should be closed so that the tank is full in \[3\] hours
Two taps A and B can fill a tank in \[x\] hours and \[y\] hours respectively. If both the pipes are opened together, then time after which pipe B should be closed so that the tank is full in \[t\] hours
\[=y\left(1-\frac{t}{x}\right)\] hours
\[\therefore\] Required time
\[=10\left(1-\frac{3}{5}\right)\]
\[=10\left(\frac{5-3}{5}\right)\]
\[=10\left(\frac{2}{5}\right)\]
\[=2\times 2\]
\[=4\] hours