SSC MTS Model Paper 7

Question : 94 of 99

Marks: +1, -0

Three pipes P, Q and R can separately fill a cistern in 4,8 and 12 hours respectively. Another pipe S can empty the completely filled cistern in 10 hours. Which of the following arrangements will fill the empty cistern in Iess time than others ?

Q alone isopen.
P and S are open.
P, R andS are open.
P, Q and S are open.

Validate

Solution:

(d) Part of the cistern filled in 1 hour
when pipes P and S are open

= { 1 }/ { 4 } - { 1 } /{ 10 } = { 5 - 2 }/ { 20 } = { 3 }/ { 20 }

Hence, the cistern w ill be filled in

{ 20 }/ { 3 }

hours

≈ 6.6

hours
Part of the cistern filled in 1 hour
when pipes P, R and S are open

= { 1 }/ { 4 } + { 1 }/ { 12 } - { 1 } /{ 10 }

= { 15 + 5 - 6 } /{ 60 } = { 14 }/ { 60 } = { 7 } /{ 30 }

Hence, the cistern w ill be filled in

30/7

hours ≈4.3 hours
Part of the cistern filled in 1 hour
when pipes P, g and S are open

= { 1 } /{ 4 } + { 1 } /{ 8 } - { 1 } /{ 10 }

= { 10 + 5 - 4 }/ { 40 } = { 11 } /{ 40 }

Hence, the cistern will be filled in40—hours ≈ 3.6 hours

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