Question

Two friends X and Y started typing work and were hopeful to complete the work in 10 days and 15 days respectively. They started the work together, but due to an emergency, X left after just 5 days and asked his friend Z to join at his place, who could alone complete this work in 60 days. In how many days did the work get completed?
1. 14
2. 6
3. 7
4. 5

Answer 1

Correct Answer - Option 3 : 7

Given:

Time taken by X to complete the work alone = 10 days

Time taken by Y to complete the work alone = 15 days

Time taken by Z to complete the work alone = 60 days

Formula Used:

Efficiency = Total work/Time taken

Calculation:

Let the total work be 60x units (LCM of 10,15, 60)

Efficiency of X = 6x units/day

Efficiency of Y = 4x units/day

Efficiency of Z = x units/day

Work done in 5 days by X and Y = (6x + 4x) × 5

= 50x units

⇒ Remaining work = 60x – 50x = 10x units

This work is completed by Y and Z

Time taken to complete the remaining work = 10x/[(4x + x)]

= 10x/5x = 2 days

Total time taken to complete the whole work = 5 + 2 = 7 days

∴ The total time taken to complete the whole work is 7 days