Two typist of varying skills can do a 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 $$\frac{1}{5}$$ of the whole work. How many minutes would it take the slower typist to complete the typing job working alone ?
a) 10 minutes
b) 15 minutes
c) 12 minutes
d) 17 minutes

Answer: b
Explanation: Working efficiency of both typist together,
= $$\frac{{100}}{6}$$ = 16.66% per minute

Now, let work efficiency of first typist be x and then second typist will be (16.66 – x)
First typist typed alone for 4 minutes and second typed alone for 6 minutes and they left with $$\frac{1}{5}$$ (i.e 20%) of job, means they have completed 80% job
First Typist typed in 4 minute + Second typed in 6 minutes = 80%
4 × x + 6 × (16.66 – x) = 80%
4x + 100% – 6x = 80%
x = 10%
First Typist typed 10% per minutes. Then second typed (16.66 – 10) = 6.66% per minute
Then, Second typist complete the whole job in $$\frac{{100}}{{6.66}}$$ = 15.01 = 15 minutes.