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In a factory, there are 3 men worker and 4 female worker can do a certain work in 15 days. If the same work can be done by 5 men worker and 3 female worker in 10 days, then find the number of days taken by a 2 men to complete the work?
1. 29 days 
2. 55/2 days
3. 55/4 days 
4. 60 days 

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Correct Answer - Option 2 : 55/2 days

Given

3 men and 4 female can do work in = 15 days 

5 men and 3 female can do work in = 10 days 

Formula Used: 

Work = Time × Efficiency 

Calculation: 

⇒ let the efficiency of men and female be M and W  

⇒ 3M + 4W = 15 , 5M + 3W = 10 

⇒ LCM (15,10) = 30 

⇒ Let total work = 30 

⇒ efficiency of 3M + 4W = 2 ----(1) 

⇒ similarly, 5M + 3W = 3 -----(2) 

multiply the equation (1) by 3 and equation (2) by 4 

⇒ 9M + 12W = 6  ------(1) 

⇒ 20M + 12W = 12 -----(2)

⇒ From (3) and (4)

⇒ M = 6/11 

⇒ total efficiency of 2 men = 12/11 

⇒ No. of days taken by 2 men to complete the work = 30 × 11/12 = 55/2 days 

⇒ No. of days taken by 2 men to complete the work is 55/2 days 

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