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Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work?

Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work? Correct Answer 28

Given:

Newton’s Time = 20 days

Einstein’s Time = 30 days

Tesla’s Time = 60 days

All three together time = (x + 6) days

Calculation:

The data provides three different combinations of working, to do the work completely.

1) Combination 1 -

All three people working for(x+6) days.

(1/20 + 1/30 + 1/60) = 1/(x + 6)

⇒ (6/60) = 1/(x + 6)

⇒ x + 6 = 10

⇒ x = 4 days

2) Combination 2 -

All three people for x days,and two people for(y + 6) days.

(x)/10 + (y + 6)(1/30 + 1/60) = 1

Substituting x=4,

⇒ 4/10 + (y + 6)(1/20) = 1

⇒ (y + 6)(1/20) = 1 – 4/10

⇒ y + 6 = 12

⇒ y = 6

3) Combination 3 –

All three for x days, two people for y days and one person for z days.

x(1/10) + y(1/20) + z/60 = 1

Substituting x=4,y = 6, and simplifying,

⇒ z/60 = 1 – 4/10 –6/20

⇒ z/60 = 3/10

⇒ z = 18 days

∴ Total number of days required under combination 3, is

x + y + z = 4 + 6 + 18 = 28 days

Alternate Method –

1. A, B and C four days work = 4 × 6 = 24

Left work = 60 - 24 = 36

(B + C) complete left work in Time = 36/3 = 12

Y + 6 = 12

Y = 6

2. (B + C) 6 days work 6 × 3 = 18

work left = 60 – 24 – 18 - 18

C = 18 /1 =18 days

Total time = A + B + C = 4 + 6 = 28 days

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