| A B and C are three taps connected to a tank. A and B together can fill the tank in \[6\,\,h,\] B and C together can fill it in \[10\,\,h\] and A and C together can fill it in \[7\frac{1}{2}h.\] In how much time all three would take to fill the tank? |
A) \[10\,\,h\]
B) \[12\,\,h\]
C) \[20\,\,h\]
D) \[5\,\,h\]
Correct Answer: D
Solution :
| Given, time taken by (A + B) to fill the tank \[=6\,\,h\] |
| \[\therefore \]Part of tank filled by (A + B) in \[1\,\,h=\frac{1}{6}\] ... (i) |
| (if a pipe fills a tank in x h, then the part of tank filled in \[1\,\,h=\frac{1}{x}\]) |
| Similarly, part of tank filled by (B + C) in\[1\,\,h=\frac{1}{10}\] ... (ii) |
| and part of tank filled by (C + A) in \[1\,\,h=\frac{2}{15}\]...(iii) |
| On adding Eqs. (i), (ii) and (iii), we get |
| \[A+B+B+C+C+A=\frac{1}{6}+\frac{1}{10}+\frac{2}{15}\] |
| \[\Rightarrow \] \[2A+2B+2C=\frac{5+3+4}{30}\] |
| \[\Rightarrow \] \[2\,\,(A+B+C)=\frac{12}{30}\] |
| \[\Rightarrow \]\[(A+B+C)=\frac{12}{60}\]\[\Rightarrow \]\[(A+B+C)=\frac{1}{5}\] |
| Hence, A, B and C all three can fill the tank in 5 h. |
| (if a pipe fills \[\frac{1}{x}\]part of the tank in \[1\,\,h,\] then the time taken by the pipe to fill the full tank \[=x\,\,h\]) |
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