A can do a certain piece of work in 2.4 times the number of days in which B and C together can do it. If A and B together can do the said piece of work in 27 days and C alone can do it in 75 days, then how many days will B take to do this piece of work alone?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 45.
Given that
A can do a certain piece of work in 2.4 times the number of days in which B and C together can do it
A and B together can do the said piece of work in 27 days
C alone can do it in 75 days
Total work = LCM (27, 75) = 675
The efficiency of C = 675/75 = 9
The combined efficiency of A and B = 225/27 = 25
As we know, the efficiency is inversely proportional to the time taken
The time ratio of A and (B + C) is 24 : 10
So, the efficiency ratio of A and (B + C) = 10 : 24
Now, the efficiency of B = 24 - 9 = 15
Hence, the work is done by B alone in = 675/15 = 45