Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 1)
1.
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
Answer: Option
Explanation:
| A's 1 day's work = | 1 | ; |
| 15 |
| B's 1 day's work = | 1 | ; |
| 20 |
| (A + B)'s 1 day's work = |  |
1 | + | 1 |  |
= | 7 | . |
| 15 | 20 | 60 |
| (A + B)'s 4 day's work = | |
7 | x 4 | |
= | 7 | . |
| 60 | 15 |
| Therefore, Remaining work = | |
1 - | 7 | |
= | 8 | . |
| 15 | 15 |
Discussion:
344 comments Page 4 of 35.
Arun D C said:
1 decade ago
@Raj, Here is the solution for yours.
Given:
A + B = 1/30 (A and B together can do the work in a single day).
B = 1/40 (B alone can do the work in a single day).
Solution:
A = (A+B) - B.
= 1/30 - 1/40.
= (4-3) / 120.
= 1 / 120.
A = 1 / 120 (A alone can do the work in a single day).
Therefore 'A' alone can complete the work in 120 days.
Given:
A + B = 1/30 (A and B together can do the work in a single day).
B = 1/40 (B alone can do the work in a single day).
Solution:
A = (A+B) - B.
= 1/30 - 1/40.
= (4-3) / 120.
= 1 / 120.
A = 1 / 120 (A alone can do the work in a single day).
Therefore 'A' alone can complete the work in 120 days.
Harry said:
9 years ago
I just came across an extremely easy way of solving this question. So felt like sharing it.
Work = LCM (15, 20) = 60 units.
A does 60/15 i.e. 4 units in a day, B does 60/20 i.e. 3 units in a day.
In 4 days work completed = (4 + 3) * 4 = 28 units.
Work left = Total work - work done by AB
= 60 - 28 = 32
So, Fraction of Work left = 32/60 = 8/15.
Work = LCM (15, 20) = 60 units.
A does 60/15 i.e. 4 units in a day, B does 60/20 i.e. 3 units in a day.
In 4 days work completed = (4 + 3) * 4 = 28 units.
Work left = Total work - work done by AB
= 60 - 28 = 32
So, Fraction of Work left = 32/60 = 8/15.
GANESH said:
9 years ago
A do the work in 1 day is = 1/15.
B do the work in 1 day is = 1/20.
So LCM of 15, 20 is = 60.
Now,
A's work is 1/15 * 60 = 4.
B's work is 1/20 * 60 = 3.
Then (4 + 3/60) = 7/60.
7/60 is one day work of A+B.
We want 4 days work of A+B.
Then,
(4 * 7/60) = 28/60.
=> 7/15.
Now one day work is (1 - 7/15) = 15 - 7/15.
=> 8/15 is the answer.
B do the work in 1 day is = 1/20.
So LCM of 15, 20 is = 60.
Now,
A's work is 1/15 * 60 = 4.
B's work is 1/20 * 60 = 3.
Then (4 + 3/60) = 7/60.
7/60 is one day work of A+B.
We want 4 days work of A+B.
Then,
(4 * 7/60) = 28/60.
=> 7/15.
Now one day work is (1 - 7/15) = 15 - 7/15.
=> 8/15 is the answer.
Sufiyan said:
6 years ago
A' work is (1÷15) in one day,
B's work is (1÷20) in one day,
If both perform the work together then (1÷15)+(1÷20)=(35÷300) work is done in one day.
Now multiplying it by 4 so we get the amount of work done in 4 days.
(35÷300)*4 = (7÷15).
Now we know the total amount of work is 1.
Then subtract (1)-(7÷15)=(8÷15) the remaining work.
B's work is (1÷20) in one day,
If both perform the work together then (1÷15)+(1÷20)=(35÷300) work is done in one day.
Now multiplying it by 4 so we get the amount of work done in 4 days.
(35÷300)*4 = (7÷15).
Now we know the total amount of work is 1.
Then subtract (1)-(7÷15)=(8÷15) the remaining work.
Akash said:
1 decade ago
Try to avoid fraction calculation.
L.C.M of(15,20) = 60.
Let total work is 60 unit.
A can do 60/15 = 4 unit/day.
B can do 60/20 = 3 unit/day.
A+B can do = 4+3 = 7 unit/day.
A+B in 4 day can do = 7*4 = 28 unit.
Total work = 60 unit.
Remaining work = 60-28 = 32 unit.
Fraction of work = (Remaining work/Total work) = 32/60 = 8/15 (ans).
L.C.M of(15,20) = 60.
Let total work is 60 unit.
A can do 60/15 = 4 unit/day.
B can do 60/20 = 3 unit/day.
A+B can do = 4+3 = 7 unit/day.
A+B in 4 day can do = 7*4 = 28 unit.
Total work = 60 unit.
Remaining work = 60-28 = 32 unit.
Fraction of work = (Remaining work/Total work) = 32/60 = 8/15 (ans).
Mukesh gautam said:
10 years ago
Simple method:
A-15.
B-20.
LCM is 60.
60/15 = 4.
60/20 = 3.
Total work 60 an total unit work done by a and b is 7.
In q4 day work are done than total 4 day work is 7x4 = 28.
Remaining work 60-28 = 32.
Fraction of remaining work is 32/60 = 8/15. Solution are done in only 20 sec. This method is very simple and less time consuming.
A-15.
B-20.
LCM is 60.
60/15 = 4.
60/20 = 3.
Total work 60 an total unit work done by a and b is 7.
In q4 day work are done than total 4 day work is 7x4 = 28.
Remaining work 60-28 = 32.
Fraction of remaining work is 32/60 = 8/15. Solution are done in only 20 sec. This method is very simple and less time consuming.
Ashutosh Sharma said:
4 years ago
A takes 15 days & B takes 20 days.
L.C.M. of 15 and 20 is 60 ( Total work)
Then
A works in a day 60÷15 = 4 &,
B works in a day 60÷20 = 3.
When both works together;
A+B works in a day (4+3) = 7.
They works for 4 days then 7*4 = 28,
Remaining work is 60 - 28 = 32,
The fraction of left work is 32/60 = 8/15.
L.C.M. of 15 and 20 is 60 ( Total work)
Then
A works in a day 60÷15 = 4 &,
B works in a day 60÷20 = 3.
When both works together;
A+B works in a day (4+3) = 7.
They works for 4 days then 7*4 = 28,
Remaining work is 60 - 28 = 32,
The fraction of left work is 32/60 = 8/15.
Atma kumar vishwakarma said:
8 years ago
Let both making toffee.
The total toffee they made is 60 it LCM of 20 and15.
mins A make 60 toffee in 15 days it mins A make 4 toffee a day,
B makes 60 toffee in 20 days it mins B make 3 toffy a day they work together for day
it mins (3+4)*4=28.
In 4 days they made 28 toffee they need to make 60 toffee.
It mins 28/60=7/15.
The total toffee they made is 60 it LCM of 20 and15.
mins A make 60 toffee in 15 days it mins A make 4 toffee a day,
B makes 60 toffee in 20 days it mins B make 3 toffy a day they work together for day
it mins (3+4)*4=28.
In 4 days they made 28 toffee they need to make 60 toffee.
It mins 28/60=7/15.
James said:
1 decade ago
We can solve this problem more easily by taking efficiency.
Since work=efficiency *time
To take efficiency take lcm of A&B.it is 60
60/15=4 60/20=3
A'efficiency=4 & B's=3
Work=4*15 or 3*20 =60
Work=60
Since a b works together for 4 days
a+b effi=4+3=7
7*4=28
Total work-work done
60-28=32(work remaining)
32/60=8/15.
Since work=efficiency *time
To take efficiency take lcm of A&B.it is 60
60/15=4 60/20=3
A'efficiency=4 & B's=3
Work=4*15 or 3*20 =60
Work=60
Since a b works together for 4 days
a+b effi=4+3=7
7*4=28
Total work-work done
60-28=32(work remaining)
32/60=8/15.
Prashant said:
1 decade ago
@Deepa.
Actually when fraction occur.
Then base must be same while doing it.
1/15 + 1/20 in this situation to calculate it base must be same. We can make it by multiply 1/15 By 4 and 1/20 By 3 so that it will be:
4/60 and 3/60 so.4/60 + 3/60 now we can do calculation result 7/60.
I hope you understand what I mean to say?
Actually when fraction occur.
Then base must be same while doing it.
1/15 + 1/20 in this situation to calculate it base must be same. We can make it by multiply 1/15 By 4 and 1/20 By 3 so that it will be:
4/60 and 3/60 so.4/60 + 3/60 now we can do calculation result 7/60.
I hope you understand what I mean to say?
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