Lalit can finish a work in 15 days. Laxman can finish the same work in 25 days. They work together for 5 days. If the rest of the work is finished by Lalit and Deven in 4 days, then in how many days can Deven alone finish the work?
Show answer & explanation
Correct answer: D
Explanation
Given:
Lalit completes the work in 15 days
Laxman completes the work in 25 days
Both work together for 5 days
Lalit and Deven complete the remaining work in 4 days
Lalit's rate = 1/15
Laxman's rate = 1/25
Work done in 5 days
= 5 × (1/15 + 1/25)
= 5 × (5/75 + 3/75)
= 5 × (8/75)
= 40/75
= 8/15
Remaining work = 1 − 8/15 = 7/15
Lalit and Deven complete 7/15 of the work in 4 days
4 × (1/15 + 1/x) = 7/15
1/15 + 1/x = 7/60
1/x = 7/60 1/15
= 7/60 − 4/60
= 3/60
= 1/20
x = 20 days
Deven alone will complete the work in 20 days