Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 16)
16.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Answer: Option
Explanation:
| Work done by X in 4 days = |  |
1 | x 4 |  |
= | 1 | . |
| 20 | 5 |
| Remaining work = | |
1 - | 1 | |
= | 4 | . |
| 5 | 5 |
| (X + Y)'s 1 day's work = | |
1 | + | 1 | |
= | 8 | = | 2 | . |
| 20 | 12 | 60 | 15 |
| Now, | 2 | work is done by X and Y in 1 day. |
| 15 |
| So, | 4 | work will be done by X and Y in | |
15 | x | 4 | |
= 6 days. |
| 5 | 2 | 5 |
Hence, total time taken = (6 + 4) days = 10 days.
Discussion:
69 comments Page 2 of 7.
Gouri said:
8 years ago
X=>20 and Y=>12.
L.C.M. of 20&12=>60.
The efficiency of X is 3 and of Y is 5,
3 * 4 = 12 (here 3 is the efficiency of X and 4 is the no: of days he worked alone)
remaining work=60-12=48,
8*x=48 (here 3+5=8),
x=48/8; x=6.
According to the question we want to know how many days work went on
so, 4+6 =10 days.
L.C.M. of 20&12=>60.
The efficiency of X is 3 and of Y is 5,
3 * 4 = 12 (here 3 is the efficiency of X and 4 is the no: of days he worked alone)
remaining work=60-12=48,
8*x=48 (here 3+5=8),
x=48/8; x=6.
According to the question we want to know how many days work went on
so, 4+6 =10 days.
(2)
Shanmugam said:
10 years ago
(1-1/5) = 4/5? Please explain it.
(1)
Kavya said:
1 decade ago
Short cut: A=20, B=12.
4 days left: 20-4 = 16.
B joined : (1/20) + (1/12) = 15/2.
Therefore: (16/20)(15/2) = 6.
Total days = 6+4 = 10.
4 days left: 20-4 = 16.
B joined : (1/20) + (1/12) = 15/2.
Therefore: (16/20)(15/2) = 6.
Total days = 6+4 = 10.
(1)
Chandu said:
1 decade ago
X 1 days work = 1/20.
Y 1 days work = 1/12.
X work for 4 days ---> 4/20 = 1/5.
Remaining work to be done--->1-1/5 = 4/5.
After 4 days Y is join with X to work.
So X+Y 1 day's work = (1/20+1/12) = 2/15 ---> X+Y finish work in 15/2 days.
So X+Y finish 4/5 part of work in 15/2*4/5 ----> 6 days.
Total days ---> 4+6 = 10 days.
Y 1 days work = 1/12.
X work for 4 days ---> 4/20 = 1/5.
Remaining work to be done--->1-1/5 = 4/5.
After 4 days Y is join with X to work.
So X+Y 1 day's work = (1/20+1/12) = 2/15 ---> X+Y finish work in 15/2 days.
So X+Y finish 4/5 part of work in 15/2*4/5 ----> 6 days.
Total days ---> 4+6 = 10 days.
(1)
Shehina.s.p said:
2 decades ago
Please explain how {15/2*4/5} comes?
(1)
Gowtham said:
1 year ago
One days work of X=1/20.
One days work of Y=1/12.
Four days work is. 4[1/X = 1/20],
=> 4/X = 4/20,
=>4/X. = 1/5
1 is the whole work.
1-1/5 = 4/5.
Then 4/5 work is to be done.
X's and Y's one day work is = 1/20+1/12=2/15.
Let "K" be the number of days taken by X and Y to complete the work.
1 day --->2/15.
K days --->4/5.
4/5 ×1 = K× 2/15.
4/5 ×15/2 = K.
K = 2×3 = 6 days.
4 days work of X.
6 days work of X and Y.
4 + 6 =10 days.
One days work of Y=1/12.
Four days work is. 4[1/X = 1/20],
=> 4/X = 4/20,
=>4/X. = 1/5
1 is the whole work.
1-1/5 = 4/5.
Then 4/5 work is to be done.
X's and Y's one day work is = 1/20+1/12=2/15.
Let "K" be the number of days taken by X and Y to complete the work.
1 day --->2/15.
K days --->4/5.
4/5 ×1 = K× 2/15.
4/5 ×15/2 = K.
K = 2×3 = 6 days.
4 days work of X.
6 days work of X and Y.
4 + 6 =10 days.
(1)
Priya said:
9 years ago
One shortcut method.
Total work assumes as 1unit.
Use option to Slove this
1.we know that x's 1day work= 1/20.
Same y's=1/12
Choose option no. a, i.e .6 if x work for 6 days so y work for 2 days because y start working after 4 days so.
6/20+2/12 = 1,
Is not equal to 1.
So, the answer is not 6.
Take another i.e.10.
If x takes 10 days, y takes 6 days.
10/20+6/12 = 1.
Lhs=rhs . So the ans. Is 10days.
Total work assumes as 1unit.
Use option to Slove this
1.we know that x's 1day work= 1/20.
Same y's=1/12
Choose option no. a, i.e .6 if x work for 6 days so y work for 2 days because y start working after 4 days so.
6/20+2/12 = 1,
Is not equal to 1.
So, the answer is not 6.
Take another i.e.10.
If x takes 10 days, y takes 6 days.
10/20+6/12 = 1.
Lhs=rhs . So the ans. Is 10days.
Makvana Disha said:
1 decade ago
@Sachin,
2/15 = 1 day work.
Then for remaining work 4/5 = ?
i.e. (4/5) * (15/2) = 6 days.
Total days are, 6 + 4 = 10 days.
2/15 = 1 day work.
Then for remaining work 4/5 = ?
i.e. (4/5) * (15/2) = 6 days.
Total days are, 6 + 4 = 10 days.
Nik said:
1 decade ago
But here it asked like "how long did they work", why should we consider A's work here?
Shree said:
9 years ago
Clear and detailed explanation. Thank you.
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