CMAT Exam 2023 Shift 2 Solved Paper

Question : 13 of 100

Marks: +1, -0

Three pipes

P, Q

and

R

can fill a tank in 6 hours. After working at it together for 2 hours,

R

is closed and both

P

and

Q

can fill the remaining part in 7 hours. The number of hours that will be taken by

R

alone to fill the tank is

Solution:

It is given that

P, Q

and

R

together can complete the work in

6 {\hrs}

P, Q

and

R

together worked for 2 hours, this implies they completed

1 {/}3

rd of the work.

{\R}

left and remaining work is finished by

{\P}

and

{\Q}

in 7 hours.
Therefore,

{\P}

and

{\Q}

completed

2 {/} 3

rd of the work in 7 hours.
This implies

{\P}

and

{\Q}

together can complete the work in 21/2 hours.
Let the total work be

{\LCM}(6,21 {/} 2)

, i.e. 42 units.

P, Q

and

R

together can complete 7 units in one hour.

P

and

Q

together can complete 4 units in one hour.
This implies,

{\R}

can complete 3 units in one hour.
Time taken by

R

alone to complete the work

=\;{42}/{3}=14

hours
The answer is option C.

Go to Question:

Prev Question

Next Question