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10 Nov 2010, 10:39
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A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?
A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
10 Nov 2010, 11:23
Kudos
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cleetus
A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?
A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
Check this: word-translations-rates-work-104208.html?hilit=time%20work#p812628
Let a, b and c be the time needed for A, B and C respectively to fill the tank alone.
Given:
\(\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}\) - combined rate of B and C is 7/6 of rate of A;
\(\frac{10}{3}*\frac{1}{c}=\frac{1}{a}+\frac{1}{b}\) - combined rate of A and B is 10/3 of rate of C;
\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{60}\) - combined rate of A, B and C is 13/60 tank/hour;
Solving:
\(\frac{1}{a}+\frac{7}{6a}=\frac{13}{60}\) --> \(a=10\);
\(\frac{1}{c}+\frac{10}{3c}=\frac{13}{60}\) --> \(c=20\);
\(\frac{1}{10}+\frac{1}{b}+\frac{1}{20}=\frac{13}{60}\) --> \(b=15\).
Answer: B.
General Discussion
pauc
Joined: 15 Sep 2013
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23 Oct 2013, 05:35
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Bunuel
cleetus
A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank. If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?
A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
A) 10 hrs
B) 15 hrs
C) 20 hrs
D) 25 hrs
E) 30 hrs
Check this: word-translations-rates-work-104208.html?hilit=time%20work#p812628
Let a, b and c be the time needed for A, B and C respectively to fill the tank alone.
Given:
\(\frac{7}{6}*\frac{1}{a}=\frac{1}{b}+\frac{1}{c}\) - combined rate of B and C is 7/6 of rate of A;
\(\frac{10}{3}*\frac{1}{c}=\frac{1}{a}+\frac{1}{b}\) - combined rate of A and B is 10/3 of rate of C;
\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{60}\) - combined rate of A, B and C is 13/60 tank/hour;
Solving:
\(\frac{1}{a}+\frac{7}{6a}=\frac{13}{60}\) --> \(a=10\);
\(\frac{1}{c}+\frac{10}{3c}=\frac{13}{60}\) --> \(c=20\);
\(\frac{1}{10}+\frac{1}{b}+\frac{1}{20}=\frac{13}{60}\) --> \(b=15\).
Answer: B.
Hi Bunuel,
I have a really stupid question, but I hope you can help me out. Why isn't it 6 (1/A) = 7(1/B + 1/C) leading to a final equation of 6/7 (1/A) = 1/B + 1/C?
Thanks in advanced - as always!!
