Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 30)
30.
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Answer: Option
Explanation:
Let A's 1 day's work = x and B's 1 day's work = y.
| Then, x + y = | 1 | and 16x + 44y = 1. |
| 30 |
| Solving these two equations, we get: x = | 1 | and y = | 1 |
| 60 | 60 |
 B's 1 day's work = |
1 | . |
| 60 |
Hence, B alone shall finish the whole work in 60 days.
Discussion:
97 comments Page 3 of 10.
NIshil said:
6 years ago
a+b = can do a work in 30 days.
A work for 16 day means 14 days work left.
B do the work for 44 days means extra 14-day work from 30-day timeline.
That is 14. a = 14.b (14day work left is don by b in extra 14-day work).
a/b = 1/1.
Total work = 30.(1+1)= 60 ( 30 days and both efficiency).
B alone can do= total work/b efficiency= 60/1.
60 is the answer.
A work for 16 day means 14 days work left.
B do the work for 44 days means extra 14-day work from 30-day timeline.
That is 14. a = 14.b (14day work left is don by b in extra 14-day work).
a/b = 1/1.
Total work = 30.(1+1)= 60 ( 30 days and both efficiency).
B alone can do= total work/b efficiency= 60/1.
60 is the answer.
(1)
Hetal said:
1 decade ago
Yes I also get the same answer like @Sai and @Kaustubha Sen.
a+b = 1/30 (1 day's work).
So (a+b) work together for 16 days.
So, 1/30*16 = 16/30. So we get 8/15 work done together for 16 days.
Now remaining work = 1-8/15 we get 7/15.
That's why if 7/15 remaining work b takes 44 days then work done by b in 1 day.
= 1*7/44*15.
I got 94.28.
a+b = 1/30 (1 day's work).
So (a+b) work together for 16 days.
So, 1/30*16 = 16/30. So we get 8/15 work done together for 16 days.
Now remaining work = 1-8/15 we get 7/15.
That's why if 7/15 remaining work b takes 44 days then work done by b in 1 day.
= 1*7/44*15.
I got 94.28.
IOvd said:
1 decade ago
@Sneha.
x+y = 1/30 .....(i).
16x+44y = 1 .....(ii).
Multiply equation (i) by 16 we get,
16x+16y = 8/15(ie 16/30).....(iii).
Now subtract equation (iii) from equation (ii).
16x+44y = 1.
- 16x+16y = 8/15.
-----------------
+28y = 7/15 (ie 1-8/15).
Now y = 7/15*1/28.
y = 1/15*1/4.
y = 1/60.
I hope u get it now.
x+y = 1/30 .....(i).
16x+44y = 1 .....(ii).
Multiply equation (i) by 16 we get,
16x+16y = 8/15(ie 16/30).....(iii).
Now subtract equation (iii) from equation (ii).
16x+44y = 1.
- 16x+16y = 8/15.
-----------------
+28y = 7/15 (ie 1-8/15).
Now y = 7/15*1/28.
y = 1/15*1/4.
y = 1/60.
I hope u get it now.
Subhant said:
8 years ago
Solving the equations is tiresome brothers.
Instead take like
16a +44 b = 30 a + 30b.
a/b = 1/1
So if a one day work is 1 and b one day work is one and when they work together they do 2 units of work every day.
this means there is 30x2 = 60 units of work.
B can do it in = (total unit of work)/(B's one day work) = 60 days.
Instead take like
16a +44 b = 30 a + 30b.
a/b = 1/1
So if a one day work is 1 and b one day work is one and when they work together they do 2 units of work every day.
this means there is 30x2 = 60 units of work.
B can do it in = (total unit of work)/(B's one day work) = 60 days.
Sameer said:
5 years ago
A's 1 day work = x.
B's 1 day work = y.
They work together x+y= 1/30; x = 1/30-y.
A having work for 16 days and B finishes remaining work alone 44 days 16x+44y = 1.
16*(1/30-y)+ 44y =1.
16/30-16y + 44y =1.
16/30 -28y =1.
28y= 1-16/30.
28y=7/15.
y=7/15*28.
y=1/60.
B's alone do the work in = 1/60 days = 60days.
B's 1 day work = y.
They work together x+y= 1/30; x = 1/30-y.
A having work for 16 days and B finishes remaining work alone 44 days 16x+44y = 1.
16*(1/30-y)+ 44y =1.
16/30-16y + 44y =1.
16/30 -28y =1.
28y= 1-16/30.
28y=7/15.
y=7/15*28.
y=1/60.
B's alone do the work in = 1/60 days = 60days.
Harish said:
1 decade ago
I don't think we should bother about 30 days' combined work. That piece of problem is, I think, meant to confuse us. Because he wishes to know B's individual capacity of doing what is left out by A's individual work.
Whatever A leaves behind, B finishes it.
Hence it is as simple as 16+44 = 60 days.
Whatever A leaves behind, B finishes it.
Hence it is as simple as 16+44 = 60 days.
Sai said:
1 decade ago
If 8/15 of the work is done by A in 16 days, then remaining 7/15 of the work is done by B in 44 days right....then why not cross multiply for 15/15 of the work.
I am getting a wrong answer doing this. Can anyone explain please.
7/15 work ----- 44 days.
15/15 work ----- k days.
k = 44*15/7 = 94.28.
I am getting a wrong answer doing this. Can anyone explain please.
7/15 work ----- 44 days.
15/15 work ----- k days.
k = 44*15/7 = 94.28.
Sagar parida said:
8 years ago
Please, anyone help me out from this question--.
A and B can do a work together in 10 days, B and C can do the same work in 18 days, if A starts the work and after working 5 days B do the work for 15 days and remaining work in done by C than find in how many days will C complete the work alone?
A and B can do a work together in 10 days, B and C can do the same work in 18 days, if A starts the work and after working 5 days B do the work for 15 days and remaining work in done by C than find in how many days will C complete the work alone?
Manasa said:
1 decade ago
A's 1 day work ,consider X
B's 1 day work ,consider Y
(A+B) 1 day work=(X+Y)=1/30
next condition:
A works for 16 days=16*X
B works for 44 days for remaining work to complete=44*Y
to complete whole work;16X+44Y=1
by solving both equations ,we get
X=1/60,Y=1/60
B can complete work in 60 days.
B's 1 day work ,consider Y
(A+B) 1 day work=(X+Y)=1/30
next condition:
A works for 16 days=16*X
B works for 44 days for remaining work to complete=44*Y
to complete whole work;16X+44Y=1
by solving both equations ,we get
X=1/60,Y=1/60
B can complete work in 60 days.
Avi said:
1 decade ago
For completion of one work it took A, B for 30 days.
So let A's one day work is x & B's one day work is y.
From above we can write 1 work=30x+30y.
But in second case a worked for 16 days & B worked for 44days.
Therefore,
16x+44y=1 work.
By solving we can get y=1/60 work.
So let A's one day work is x & B's one day work is y.
From above we can write 1 work=30x+30y.
But in second case a worked for 16 days & B worked for 44days.
Therefore,
16x+44y=1 work.
By solving we can get y=1/60 work.
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