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Two workers P and Q started a job. For the first three hours only P works and then Q joins him to complete remaining work. When work completed it comes to know that P done 2/3rd of work and Q completed remaining work. After first four hours, there is still 3/5 of work is remaining. The number of days taken by alone P to complete work is what percent less than number of days taken by alone Q to complete the work?

Two workers P and Q started a job. For the first three hours only P works and then Q joins him to complete remaining work. When work completed it comes to know that P done 2/3rd of work and Q completed remaining work. After first four hours, there is still 3/5 of work is remaining. The number of days taken by alone P to complete work is what percent less than number of days taken by alone Q to complete the work? Correct Answer 20%

Calculation:

Let number of days taken by P alone and by Q alone to complete the work be p days and q days respectively.

P's 1 day's work = 1/p

Q's 1 day's work = 1/q

Work completed in first four hours = 1 - 3/5 = 2/5

⇒ 4/p + 1/q = 2/5    ----(1)

P completes 2/3 of work and Q completes (1 - 2/3 = 1/3) of work.

⇒ 2p/3 - q/3 = 3    ----(2)

Solving (1) and (2),

⇒ p = 12 and q = 15

P and Q alone complete the work in 12 days and 15 days respectively.

∴ Required percentage = (15 - 12)/15 × 100 = 20%

Important Points

For the first four hours, P works for all four hours while Q works for only one hour.

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