Given: Time taken by Ramesh and Rajesh to do the work together = 12 days Calculation: Let the time taken by Ramesh and Rajesh to do the work alone be x and y respectively. Then, Ramesh’s and Rajesh’s 1 day work is equal to
1
x
and
1
y
respectively ⇒ (
1
x
)+(
1
y
)=
1
12
...(i) Ramesh reduced his efficiency by half then time taken to complete the work by both of them is increased by 50%. ⇒ Ramesh’s 1 day work =
1
2x
⇒ Time taken by them to finish the work =12×(
150
100
)=18 days ⇒
1
2
x+
1
y
=
1
18
...(ii) Solving (i) and (ii) x = 18 and y = 36 ∴ Time taken by Rajesh to finish the work alone is 36 days