Hi vaibhav101,

We're told that Person A does 80% of a work in 20 days; he then calls Person B and they together finish the remaining work in 3 days. We're asked for the number of days that it would take Person B alone to do all of the work.

Since Person A does 80% of the work in 20 days, we can deduce that.....
20% of the job can be done in 5 days and
100% of the job can be done in 25 days

In addition....
it takes 3 days for the two people to complete the remaining 20% of the job, so
it would take 15 days for the two people to complete 100% of the job

We now know Person A's total time needed and the total time needed for both people working together, so we can use the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the job

(25)(B)/(25+B) = 15
25B = 375 + 15B
10B = 375
B = 37.5 days

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

vaibhav101 wrote:A does 80% of a work in 20 days. He then calls B and they together finish the remaining work in 3 days.. How many days B alone would take to do the whole work?

A 23
B 37
C 37.5
D 40
E 50

The rate of A is (4/5)/(20) = 4/100 = 1/25.

The combined rate of A and B is (1/5)/3 = 1/15.

Thus:

1/25 + 1/B = 1/15

Multiplying by 75B we have:

3B + 75 = 5B

75 = 2B

37.5 = B

Answer: C