Question

X takes thrice as much time as Y takes or four times as much time as Z takes to finish a piece of work. Working together, they can finish the work in 6 days. Y alone can do the same work in: 
1. 14 days 
2. 16 days 
3. 17 days 
4. 15 days 

Answer 1

Correct Answer - Option 2 : 16 days 

Given  

They complete the work together = 6 days

Formua Used 

Work = time ×  efficiency

Calculations:

Suppose X, Y and Z take x, x/3​ and x/4​ days respectively to finish the work.

Then,  one days work by them

⇒ (1/x ​+ 3/x​ + 4/x​) = 1/6​

⇒ 8/x ​= 1/6​

⇒ x = 48

⇒ Y takes days to finish the work. = 48/3​ = 16 

∴ The required answer is 16 days