Question

Ramesh can do 2/5 of a work in 12 days while Mahesh can do \(66\frac2 3\)% of the same work in 16 days. They together work for 10 days. Mahesh alone will complete the remaining work in:

1. 7 days
2. 6 days
3. 5 days 
4. 4 days 

Answer 1

Correct Answer - Option 2 : 6 days

Given 

Ramesh can do 2/5th work = 12 days 

Mahesh can do \(66\frac 2 3\)% = 16 days 

Formula 

Work = Time × Efficiency 

Calculation

⇒ \(66\frac 2 3\)% = 2/3

⇒ Ramesh can do 1 work = 12 × (5/2) = 30 days

⇒ Mahesh can do 1 work = 16 × (3/2) = 24 days

⇒ Let total work be 120 (LCM of 24, 30)

⇒ Using efficiencies of both or one day work  

⇒ (1/R) + (1/M) = (1/30) + (1/24)

 

⇒ (R + M) efficiency = 4 + 5 = 9

⇒ (R + M), 10 days work = 10 × 9 = 90

⇒ Remaining work = 30

⇒ Mahesh required days = 30/5 = 6 days

∴ Mahesh required 6 days to complete the remaining work