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:
68 comments Page 2 of 7.
Gowtham said:
4 months 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)
Shehina.s.p said:
2 decades ago
Please explain how {15/2*4/5} comes?
(1)
Chandu said:
10 years 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)
Shanmugam said:
9 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)
Nishesh kumar singh said:
4 years ago
@All.
4/5 is the remaining work which is divided by 2/15 which is 1-day work by x and y to find the no. Of days i.e.4/5/2/15.
4/5 is the remaining work which is divided by 2/15 which is 1-day work by x and y to find the no. Of days i.e.4/5/2/15.
(1)
Akil Prakash said:
7 years ago
Thank you @Inna Reddy Chilakala.
Akhil said:
1 decade ago
Can anyone explain this problem clearly.
Sonu jangra said:
10 years ago
x can do a work in 20 days.
y can do a work in 12 days.
To find total work, take LCM of 20 and 12 i.e. 60.
So x+y total 1 day's work = (1/20+1/1/12) = 2/15.
But x work alone = 1/4 day's. Remain work = (1-1/4) = 3/4.
Now, work will be done by x and y = 2/15*3/4 = 1/10.
So 10 day's.
y can do a work in 12 days.
To find total work, take LCM of 20 and 12 i.e. 60.
So x+y total 1 day's work = (1/20+1/1/12) = 2/15.
But x work alone = 1/4 day's. Remain work = (1-1/4) = 3/4.
Now, work will be done by x and y = 2/15*3/4 = 1/10.
So 10 day's.
Suraj said:
10 years ago
They said in question in a piece of so how it's possible whole work done by them.
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