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 10 of 10.
Sakshi said:
1 decade ago
I can't understand. Why we have used x? We did not do this in other question.
Ram said:
1 decade ago
1/A + 1/B = 1/30 ------ 1.
16/A + 44/B = 1 ------- 2.
Solving these 2 equation:
B = 60.
16/A + 44/B = 1 ------- 2.
Solving these 2 equation:
B = 60.
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.
Sneha said:
1 decade ago
Yet I don't get anything how the answer is 60. Please explain it.
x+y = 1/60 and 16x+44y = 1/60.
How it comes?
x+y = 1/60 and 16x+44y = 1/60.
How it comes?
Shyam said:
1 decade ago
I got the same answer as Sai and Kaustubha.
Kaustubha Sen said:
1 decade ago
I think there is a mistake in the understanding.
"A having worked for 16 days, B finishes the remaining work alone in 44 days"
Look at this line.
- A worked for 16 days
- B finishes remaining work "ALONE" in 44 days.
So, it is never mentioned that A worked 16 days alone. I think it should be interpreted as - A worked with B for 16 days and then stopped. B did the remaining in 44 days.
Thus Solution is -
Let A's 1 day's work = x and B's 1 day's work = y
Then, x + y = 1/30 and 16*(x + y) + 44y = 1
Solving we get,
16 * (x + y) + 44y = 1.
or 16 * 1/30 + 44y = 1.
or 44y = 1 - 16/30.
or y = (14/30)/44.
Thus B finishes the work in (44 * 30)/14 = 94.285714.
"A having worked for 16 days, B finishes the remaining work alone in 44 days"
Look at this line.
- A worked for 16 days
- B finishes remaining work "ALONE" in 44 days.
So, it is never mentioned that A worked 16 days alone. I think it should be interpreted as - A worked with B for 16 days and then stopped. B did the remaining in 44 days.
Thus Solution is -
Let A's 1 day's work = x and B's 1 day's work = y
Then, x + y = 1/30 and 16*(x + y) + 44y = 1
Solving we get,
16 * (x + y) + 44y = 1.
or 16 * 1/30 + 44y = 1.
or 44y = 1 - 16/30.
or y = (14/30)/44.
Thus B finishes the work in (44 * 30)/14 = 94.285714.
Achesh said:
1 decade ago
This answer can still be solved by only having the basic formulas in mind.
Let A take x and B take y days to complete the whole work.
From question, we know,
1/x+1/y = 30 . By solving this we get,
xy = 30x+30y ... (1).
Now, work done by A in 1 day is 1/x. Therefore in 16 days = 16/x.
Remaining work = 1-(16/x).
This remaining work is done by B in 44 days.
And we have assumed that B takes y days to complete the job.
So for B.
WORK : Days
1 : y
1-(16/x) : 44
Solving this equation we get,
xy = 44x+16y ... (2).
Comparing (1) and (2),
30x+30y = 44x+16y.
Solve this and we get x=y.!
Put this in first equation , i.e.
1/y+1/y = 1/30.
2/y = 30.
Therefore, y = 60!
Hence 60 days.
Lengthy, but easy and precise :).
Let A take x and B take y days to complete the whole work.
From question, we know,
1/x+1/y = 30 . By solving this we get,
xy = 30x+30y ... (1).
Now, work done by A in 1 day is 1/x. Therefore in 16 days = 16/x.
Remaining work = 1-(16/x).
This remaining work is done by B in 44 days.
And we have assumed that B takes y days to complete the job.
So for B.
WORK : Days
1 : y
1-(16/x) : 44
Solving this equation we get,
xy = 44x+16y ... (2).
Comparing (1) and (2),
30x+30y = 44x+16y.
Solve this and we get x=y.!
Put this in first equation , i.e.
1/y+1/y = 1/30.
2/y = 30.
Therefore, y = 60!
Hence 60 days.
Lengthy, but easy and precise :).
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers