coolhabhi wrote:C is 20% more efficient that A. A and B can do a piece of work in 16 days. B and C can do it in 15 days. in how many days can A alone do the work?
a)36
b)42
c)45
d)48
e)54
AnsD
I prefer Mitch's approach, but here's another way to do it...
For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour
Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job
in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
Let's use these rules to solve the question. . . .
A and B can do a piece of work in 16 days.
So according to Rule #1, IN ONE DAY, A and B can complete 1/16 of the job
In other words, the COMBINED rate for A and B is 1/16 of the job EACH DAY
If we let A = the A's DAILY rate and let B = the B's DAILY rate, we can write:
A + B = 1/16
B and C can do it in 15 days
So according to Rule #1, IN ONE DAY, B and C can complete 1/15 of the job
In other words, the COMBINED rate for B and C is 1/15 of the job EACH DAY
If we let C = the C's DAILY rate and let B = the B's DAILY rate, we can write:
C + B = 1/15
So, we have:
C + B = 1/15
A + B = 1/16
Subtract the bottom equation from the top equation to get:
C - A = 1/15 - 1/16 = 1/240
Finally, we have:
C is 20% more efficient that A
So, we can write:
C = 1.2A
Now take
C - A = 1/240, and replace C with
1.2A
We get:
1.2A - A = 1/240
Simplify: 0.2A = 1/240
Or: (1/5)A = 1/240
Multiply both sides by 5 to get: A = 1/48
So, in ONE DAY, A can complete 1/48 of the job
Applying Rule #2 (above), we see that A can complete the entire job in 48 days.
Answer: D
Cheers,
Brent
