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Two typists of varying skills can do a job in 8 minutes if they work together. If the first typist typed alone for 6 minutes and then the second typist typed alone for 8 minutes, they would be left with (1/5) of the whole work. How many minutes would it take the slower typist to complete the typing job working alone?

Two typists of varying skills can do a job in 8 minutes if they work together. If the first typist typed alone for 6 minutes and then the second typist typed alone for 8 minutes, they would be left with (1/5) of the whole work. How many minutes would it take the slower typist to complete the typing job working alone? Correct Answer 40

Let, Efficiency of 1st typist = a/min

Efficiency of 2nd typist = b/min

According to the question, two typists can complete the work in 8 minutes.

⇒ 8a + 8b = 1        ----(1)

Also, 1st typist worked for 6 min. and 2nd typist worked for 8 min. and 1/5 of the work left.

⇒ 6a + 8b = 1 - 1/5

⇒6a + 8b = 8a + 8b - 1/5

⇒ 2a = 1/5

⇒ a = 1/10

Putting a = 1/10 in equation (1) we get,

8/10 + 8b = 1

⇒ 8b = 1/5

⇒ b = 1/40

∴ 1st typist completes the work in 10 minutes.

2nd typist completes the work in 40 minutes.

∴ Time taken by slower typist to complete the work = 40 min 

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