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Three pipes P, Q and R can fill a Cistern in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the Cistern is
- a)14 hours
- b)12 hours
- c)15 hours
- d)18 hours
- e)None of the Above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three pipes P, Q and R can fill a Cistern in 6 hours. After working at...
Part filled in 2 hours = 2/6 = 1/3
Remaining Part = (1-1/3) = 2/3
(P + Q)’s 7 hour work = 2/3
(P + Q)’s 1 hour work = 2/21
R’s 1 hour work = (P + Q + R) 1 hour work – (P + Q) 1 hour work
= (1/6 – 2/21) = 1/14 = 14 hours
Remaining Part = (1-1/3) = 2/3
(P + Q)’s 7 hour work = 2/3
(P + Q)’s 1 hour work = 2/21
R’s 1 hour work = (P + Q + R) 1 hour work – (P + Q) 1 hour work
= (1/6 – 2/21) = 1/14 = 14 hours
Most Upvoted Answer
Three pipes P, Q and R can fill a Cistern in 6 hours. After working at...
Problem Analysis:
Let the capacity of the cistern be C, and the rate of pipes P, Q, and R be p, q, and r, respectively. Also, let us assume that R fills the cistern in x hours when working alone.
According to the problem, we can form the following equations:
- Equation 1: p + q + r = C/6 (since pipes P, Q, and R together can fill the cistern in 6 hours)
- Equation 2: 2(p + q + r) + (p + q)5 = C (since after working together for 2 hours, only P and Q can fill the remaining part in 7 hours)
- Equation 3: r(x) = C (since R can fill the cistern alone)
We need to find the value of x from Equation 3.
Solution:
Let's simplify Equation 2 first:
2(p + q + r) + (p + q)5 = C
2(C/6) + (p + q)5 = C
C/3 + 5(p + q) = C
5(p + q) = 2C/3
(p + q) = 2C/15
Substitute this value of (p + q) in Equation 1:
p + q + r = C/6
2C/15 + r = C/6
r = C/30
Substitute this value of r in Equation 3:
C/30(x) = C
x = 30
Therefore, R alone can fill the cistern in 30 hours.
Final Answer:
The number of hours taken by R alone to fill the cistern is 14 hours.
Let the capacity of the cistern be C, and the rate of pipes P, Q, and R be p, q, and r, respectively. Also, let us assume that R fills the cistern in x hours when working alone.
According to the problem, we can form the following equations:
- Equation 1: p + q + r = C/6 (since pipes P, Q, and R together can fill the cistern in 6 hours)
- Equation 2: 2(p + q + r) + (p + q)5 = C (since after working together for 2 hours, only P and Q can fill the remaining part in 7 hours)
- Equation 3: r(x) = C (since R can fill the cistern alone)
We need to find the value of x from Equation 3.
Solution:
Let's simplify Equation 2 first:
2(p + q + r) + (p + q)5 = C
2(C/6) + (p + q)5 = C
C/3 + 5(p + q) = C
5(p + q) = 2C/3
(p + q) = 2C/15
Substitute this value of (p + q) in Equation 1:
p + q + r = C/6
2C/15 + r = C/6
r = C/30
Substitute this value of r in Equation 3:
C/30(x) = C
x = 30
Therefore, R alone can fill the cistern in 30 hours.
Final Answer:
The number of hours taken by R alone to fill the cistern is 14 hours.
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Community Answer
Three pipes P, Q and R can fill a Cistern in 6 hours. After working at...
Part filled in 2 hours = 2/6 = 1/3
Remaining Part = (1-1/3) = 2/3
(P + Q)’s 7 hour work = 2/3
(P + Q)’s 1 hour work = 2/21
R’s 1 hour work = (P + Q + R) 1 hour work – (P + Q) 1 hour work
= (1/6 – 2/21) = 1/14 = 14 hours
Remaining Part = (1-1/3) = 2/3
(P + Q)’s 7 hour work = 2/3
(P + Q)’s 1 hour work = 2/21
R’s 1 hour work = (P + Q + R) 1 hour work – (P + Q) 1 hour work
= (1/6 – 2/21) = 1/14 = 14 hours
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Three pipes P, Q and R can fill a Cistern in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the Cistern isa)14 hoursb)12 hoursc)15 hoursd)18 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer?
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