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Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)

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Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

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New post 23 Nov 2018, 05:57
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A
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C
D
E

Difficulty:

  75% (hard)

Question Stats:

55% (03:04) correct 45% (02:35) wrong based on 56 sessions

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Three pipes A, B and C can fill a tank in 10, 15 and 25 minutes respectively. All the three taps are used simultaneously to fill the tank. But, due to a leak at the bottom of the tank, only \(\frac{1}{3}\)rd of the tank was filled by the time it was supposed to be full. In how much time could the leak empty a full tank?

    A. \(\frac{75}{31}\)

    B. \(\frac{150}{31}\)

    C. \(\frac{225}{31}\)

    D. \(\frac{15}{2}\)

    E. \(\frac{450}{31}\)


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Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

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New post 23 Nov 2018, 09:03
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This took me a little over 3 minutes but...

First let's figure out how much time it SHOULD take the pipes to fill the tank:

Individual rates of the three pipes are 1/10, 1/15, and 1/25, respectively.

Using W = R*T, and setting W = 1, we know that together, the three pipes can fill the tank in 1/((15+10+6)/150), or 150/31 units of time.

Next we need to find the rate that the tank is leaking. We know that 1/3 of the tank is left after this period (150/31) of time, so we set a new equation with the W = R*T formula:

(1/3) = ((31/150) - (leaking rate)) * (150/31)

After some "quick" algebra, we identify that:

31/450 = 31/150 - leaking rate

Leaking rate = (93/450) - (31/450) = 62/450 or 31/225

FINALLY, we need to know how long it would take the lead to drain an entire tank:

Back to W=R*T, we know that if unit of work is 1, then R and T are reciprocals of each other, so t=225/31 or ANSWER C

I really hope that's right...

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Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)  [#permalink]

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New post 28 Nov 2018, 04:55

Solution


Given:
    • Three pipes, A, B and C can fill a tank in 10, 15 and 25 days respectively
    • All the three taps are used simultaneously to fill the tank
    • Only \(\frac{1}{3}^{rd}\) of the tank was filled by the time it was supposed to be full, due to a leak

To find:
    • The time in which the leak can empty a full tank

Approach and Working:
    • Three taps together can fill the tank in \(\frac{1}{((1/10) + (1/15) + (1/25))} = \frac{150}{31}\) days
      o But only \(\frac{1}{3}^{rd}\) of the tank was filled in \(\frac{150}{31}\) days, which implies that the leak can empty \(\frac{2}{3}^{rd}\) of the tank in \(\frac{150}{31}\) days

    • Thus, it can empty a full tank in \((\frac{150}{31}) * (\frac{3}{2})\) days = \(\frac{225}{31}\) days

Hence the correct answer is Option C.

Answer: C

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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Re: Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...) &nbs [#permalink] 28 Nov 2018, 04:55
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Question of the Week- 24 (Three pipes, A, B , C can fill a tank in...)

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