Question

Pand Q together can do a piece of work in 12 days. Q and R together can do the same work in 16 days. After Phas
been working at it for 5 days and Q for 7 days, R finishes it in 13 days. In how many days will R alone be able to
do the work?​

Answer 1

Answer: 24 days

Step-by-step explanation:

Let's assume work done = 1.

Let's say P can complete work in p days

Amt of work done by P in 1 day = 1/p

Similarly for Q&R, work done in 1 day is 1/q & 1/r

Hence, 12×(1/p+1/q)=1

1/p+1/q=1/12 =>Eq. 1

Similarly, 16×(1/q+1/r)=1

1/q+1/r=1/16 => Eq. 2

And 5/p+7/q+13/r=1 => Eq. 3

Multiply Eq. 1 by 5

5/p+5/q=5/12 =>Eq. 4

and Eq. 2 by 2

2/q+2/r=2/16

2/q+2/r=1/8 => Eq. 5

Add Eq. 4 and Eq. 5,

5/p+5/q+2/q+2/r=5/12+1/8

5/p+7/q+2/r=5/12+1/8

5/p+7/q+2/r=5*2/12*2+1*3/8*3

5/p+7/q+2/r=10/24+3/24

5/p+7/q+2/r=13/24 => Eq. 6

Subtract Eq. 6 from Eq. 3

5/p+7/q+13/r-(5/p+7/q+2/r)=1-13/24

11/r=24/24-13/24

11/r= 11/24

1/r=1/24

R can complete 1/24th work in 1 day

Hence, it takes 24 days to complete the work.