Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 9)
9.
A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
23 days
37 days
37
40 days
Answer: Option
Explanation:
| Whole work is done by A in |  |
20 x | 5 |  |
= 25 days. |
| 4 |
| Now, | |
1 - | 4 | |
i.e., | 1 | work is done by A and B in 3 days. |
| 5 | 5 |
Whole work will be done by A and B in (3 x 5) = 15 days.
| A's 1 day's work = | 1 | , (A + B)'s 1 day's work = | 1 | . |
| 25 | 15 |
 B's 1 day's work = |
|
1 | - | 1 | |
= | 4 | = | 2 | . |
| 15 | 25 | 150 | 75 |
| So, B alone would do the work in | 75 | = 37 | 1 | days. |
| 2 | 2 |
Discussion:
166 comments Page 16 of 17.
Siva said:
1 decade ago
Hi Guys,
General Concept: Time and work
A can complete work in X days
1.e., A can complete 100% of work in X Days
A's 1 day work = (Amount of work completed) /(number of days)
so,
A's 1 day work = 100%/X => 100%(1/X)
Now,
A completed 80% of work in 20 Days
so, A's 1 day work = 80%/20 => 1/25
A+B completed 20% of work in 3 days
so, (A+B)'s 1 days work = 20%/3 => 1/15
A+B = 1/15
B = (1/15-1/25) => 10/375
B's 1 day work = 100%/(10/375) => 100%(375/10)
B alone completed 100% of work in 375/10 Days
B = 37.5 Days => 37 1/2 Days
General Concept: Time and work
A can complete work in X days
1.e., A can complete 100% of work in X Days
A's 1 day work = (Amount of work completed) /(number of days)
so,
A's 1 day work = 100%/X => 100%(1/X)
Now,
A completed 80% of work in 20 Days
so, A's 1 day work = 80%/20 => 1/25
A+B completed 20% of work in 3 days
so, (A+B)'s 1 days work = 20%/3 => 1/15
A+B = 1/15
B = (1/15-1/25) => 10/375
B's 1 day work = 100%/(10/375) => 100%(375/10)
B alone completed 100% of work in 375/10 Days
B = 37.5 Days => 37 1/2 Days
Nazeem said:
1 decade ago
Great explanation by baskar. Thanks.
Mathi said:
1 decade ago
A = (1/20) * (80/100) = 1/25
1/A + 1/B =1/3(20/100)
1/B=(1/15) - (1/25) =2/75
1/A + 1/B =1/3(20/100)
1/B=(1/15) - (1/25) =2/75
(1)
Mayank said:
1 decade ago
thankx rajendra.........
Ganesh said:
1 decade ago
For A
Here 80% work is done by A in 20 days.
so 80/20 = 4% work per day.
So,remaining 20% will take 20/4= 5 days.
so A will take 20+5= 25 days to complete 100% of work.
so A's 1 day work is 1/25 --------------(1)
---------------------------------------------------------
Similarly, remaining 20% is done by both (A & B) in 3 days.
so (20/3)% work per day.
Now, 100% work will be completed in 100/(20/3)
i.e. 100 x 3/20 =15 days.
(A + B)'s one day work is 1/15.
So,
A + B = 1/15
1/25 + B = 1/15
B = 1/15 - 1/25
SO B's one day work = 4/150 = 2/75
So B will take 75/2 days. i.e. 37 1/2 days.
Here 80% work is done by A in 20 days.
so 80/20 = 4% work per day.
So,remaining 20% will take 20/4= 5 days.
so A will take 20+5= 25 days to complete 100% of work.
so A's 1 day work is 1/25 --------------(1)
---------------------------------------------------------
Similarly, remaining 20% is done by both (A & B) in 3 days.
so (20/3)% work per day.
Now, 100% work will be completed in 100/(20/3)
i.e. 100 x 3/20 =15 days.
(A + B)'s one day work is 1/15.
So,
A + B = 1/15
1/25 + B = 1/15
B = 1/15 - 1/25
SO B's one day work = 4/150 = 2/75
So B will take 75/2 days. i.e. 37 1/2 days.
Pratswinz said:
2 decades ago
@Bhaskar your explanation was superb. Carry on dude.
(1)
Shanmug said:
2 decades ago
@Baskar you have done great job. Just carry on.
(1)
Balaji said:
2 decades ago
Thank you very much rajendra.
(1)
Rajendra said:
2 decades ago
A does 80% in 20 days..so
A does 100% in 25 days..
A's 1 day work=1/25
A+B does 20% in 3 days..so
A+B does 100% in 15 days
A+B's 1 day work=1/15
1/25+B=1/15
B=1/15-1/25
B,s 1 day work=2/75
so B,s work=75/2 i.e 37 1/2 days..
A does 100% in 25 days..
A's 1 day work=1/25
A+B does 20% in 3 days..so
A+B does 100% in 15 days
A+B's 1 day work=1/15
1/25+B=1/15
B=1/15-1/25
B,s 1 day work=2/75
so B,s work=75/2 i.e 37 1/2 days..
(2)
Rahul said:
2 decades ago
@ baskar: thanks dude
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