Question

X takes twice as much time as Y and four times as much time as Z to complete a work. If X, Y and Z together can complete the work in 16 days, then in how many days Y alone can complete the same work?
1. 56 days
2. 28 days
3. 33 days
4. 66 days

Answer 1

Correct Answer - Option 1 : 56 days

Given:

The X Y, and Z can complete the work together = 16 days

Formula used:

W = E × T     (W = Work, E = Efficiency and T = Time)

Calculation:

Let us assume X can complete the work in 4P days, Y can complete the work in 2P days and Z can complete the work in P days

⇒ The efficiency of X = \({1\over4P }\)

⇒ The efficiency of Y = \({1\over 2P}\)

⇒ The efficiency of Z = \({1\over P}\)

⇒ \({1\over 4P}\ +\ {1\over 2P}\ +\ {1\over P}\ =\ {1\over 16}\) 

⇒ By solving 

⇒ P = 28 days

⇒ Y alone can complete the work = 2P = 2 × 28 = 56 days

∴ The required result will be 56 days.