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A takes 20% more days than B to complete the work, when they work alone. To complete 1/4th of work, A alone works. A and B works together to complete 1/2th of the work. Remaining work gets completed by B in 5 days. Find the number of days in which total work gets completed.

A takes 20% more days than B to complete the work, when they work alone. To complete 1/4th of work, A alone works. A and B works together to complete 1/2th of the work. Remaining work gets completed by B in 5 days. Find the number of days in which total work gets completed. Correct Answer 16.4 days

Calculation:

Remaining work completed by B = 1 - 1/2 - 1/4 = 1/4

Number of days in which B alone can complete the work = 4 × 5 = 20

A alone can complete the work in = 20 × 120/100 = 24 days

⇒ A's 1 day's work = 1/24

⇒ B's 1 day's work = 1/20

⇒ (A + B)'s 1 days work = 1/24 + 1/20 = 11/120

1/4 of the work gets completed by A in = 1/4 × 24 = 6 days

1/2 of the work completed by A and B in = 1/2 × (120/11) = 60/11 days

∴ Total time in which work gets completed = 6 + 60/11 + 5 = 181/11 ≈ 16.4 days

Important Points

Fraction of work completed by B in five days = 1 - 1/2 - 1/4 = 1/4

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