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Question

P and Q can do a piece of work in 12 days, Q and R in 15 days,R and P in 20 days. in how many days can R alone can do the same work?

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Solution

P can do a piece of work in p days

The work done by P in 1 day =

Q can do a piece of work in q days

The work done by Q in 1 day =

R can do a piece of work in r days

The work done by R in 1 day =

P and Q together work in 1 day =

…………..(1)

Q and R together work in 1 day =

…………..(2)

P and R together work in 1 day =

…………..(3)

Adding eqn (1) , (2) and (3)

We get 2( )=

=

=

=

= ………………(4)

Subtracting eqn (1) from (4)

We get , ( ) – ( =

= =

Hence, R alone can do a piece of work in 60 days


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