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Two typists of varying skills can do a typing job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 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 typing job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 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 15 minutes

Given:

If both typist work together, then they complete the work in = 6 min

Formula:

Total work = Efficiency × Time

Calculation:

Let efficiency of first and second typist be x and y respectively, then

⇒ Total work = (x + y) × 6     ----(1)

If 1/5 of work left, then done work = 1 – 1/5 = 4/5

According second condition

Total work × 4/5 = (4x + 6y)

⇒ Total work = (4x + 6y) × 5/4      ----(2)

From equation (1) and equation (2)

(x + y) × 6 = (4x + 6y) × 5/4

⇒ 24x + 24y = 20x + 30y

⇒ 24x – 20x = 30y – 24y

⇒ 4x = 6y

⇒ x/y = 6/4

⇒ x : y = 3 : 2

Total work = (3 + 2) × 6 = 30 unit

∴ Slower typist can complete the work in = 30/2 = 15 minutes

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