Question

p completes 80% of a certain work in 20 days. then with the help of Q ,he is able to finish it in 3 more days. How many days will Q take to finish the work, if he works alone ?

Answer 1

Answer:

Q take 37.5 or 75/2 days to finish the work.

Step-by-step explanation:

Consider the provided information.

P completes 80% of a certain work in 20 days. then with the help of Q ,he is able to finish it in 3 more days.

P completes the 80% of the work in 20 days.

If P work for 20 days then task complete by P is = 80/100 = 4/5

Work done by P in one day is 80/20 = 4%

That means P can complete the whole work in 25 days.  

P's 1 day work is = 1/25

Now the remaining work is = 1 - 4/5 = 1/5

Assume that Q can complete the whole work in x days  

Q's 1 day work is = 1/x

If they both work together for one day then work done

1/25 + 1/x  = (25+x)/25x

As it is given that they work for 3 days, so the work done in 3 days is 3(x+25)/25x

They complete the remaining work which was 1/5.

$\frac{1}{5}=\frac{3(x+25)}{25x}\\1=\frac{3x+75)}{5x}\\5x=3x+75\\2x=75\\x=37.5$

Hence, Q take 37.5 or 75/2 days to finish the work.