Question

Bheem and Arjun can finish a piece of work in 24 days while Arjun and Nakul can finish the same work in 36 days, Nakul and Bheem can finish same work in 48 days. Find how many days will Bheem take to complete the work alone.
1. 37(1/2)
2. 72
3. 48
4. 12(1/2)
5. 57(3/5)

Answer 1

Correct Answer - Option 5 : 57(3/5)

Given 

Bheem and Arjun complete a piece of work in = 24 days

Arjun and Nakul complete same work in = 36 days 

Nakul and Bheem complete same work in = 48 days 

Concept used 

Work = time × efficiency 

Calculation 

LCM of 24, 36 and 48 = 144  i.e, total work = 144 units

Efficiency of Bheem and Arjun = 6 units / per day

Efficiency of Arjun and nakul = 4 units / per day

Efficiency of Nakul and bheem = 3 units / per day 

Efficiency of Bheem, Arjun and nakul = 13/2 = 6.5 units/ per day 

Efficiency of bheem per day = efficiency of bheem, arjun, and nakul - efficiency of Arjun and nakul 

So, Efficiency of bheem per day = 6.5 - 4 = 2.5 

No. of days taken by Bheem to complete the work = 144/ 2.5 = 57(3/5) days

∴ Bheem takes 57(3/5) days to complete the work separately.