Question

X is 20% more efficient than Y and Y is 25% more efficient than Z. When they work together, they can finish work in 12 days. Find it how many days Y takes to finish the work?
1. 30 days
2. 36 days
3. 45 days
4. 64 days

Answer 1

Correct Answer - Option 2 : 36 days

Given:

Efficiency of X = 120% of Y

Efficiency of Y = 125% of Z

Time taken by (X + Y + Z) = 12 days

Formula Used:

Efficiency × total days taken to complete the work = Total work

Calculation:

Efficiency of X = 120% of Y

⇒ X/Y = 120/100

⇒ X/Y = 6/5      ----(i)

Efficiency of Y = 125% of Z

⇒ Y/Z = 125/100

⇒ Y/Z = 5/4      ----(ii)

From (i) and (ii)

Ratio of efficiency of X, Y, and Z = 6 : 5 : 4

∴ Efficiency of X = 6x

∴ Efficiency of Y = 5x

∴ Efficiency of Z = 4x

∴ Efficiency of (X + Y + Z) = 6x + 5x + 4x

⇒ 15x

∴ Total work done by X, Y, and Z = 15x × 12

∴ No. of days taken by Y = 15x × 12/5x

⇒ 3 × 12

⇒ 36 days

∴ Y takes 36 days to complete the whole work.