Mira can complete a piece of work in 20 days, Nina in 30 days and Sima in 40 days. Mira and Sima worked together for 4 days and then Mira was replaced by Nina. In how many days, altogether, was the work completed?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 16.
LCM(20, 30, and 40) = 120
The efficiency of Mira = 120/20 = 6 units
The efficiency of Nina = 120/30 = 4 units
The efficiency of Sima = 120/40 = 3 units
Mira and Sima worked together for 4 days
Work done in 4 days = 4(6 + 3) = 4 × 9 = 36 units
Remaining work = 120 - 36 = 84 units
Now, Mira was replaced by Nina
So, Nina and Sima are working and will complete the remaining work
Time taken by both = 84/(4 + 3) = 84/7 = 12 days
Total days = 4 + 12 = 16 days