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 2 of 10.
Muzzi said:
5 years ago
LCM Method
(A + B) 30 = 16A + 44B.
14A = 14B.
A/B = 1/1.
So one day work.
A = 1 unit.
B = 1 unit.
Total work = 30 x (1 + 1) = 60 units.
Time taken by B = 60/1 = 60 days.
(A + B) 30 = 16A + 44B.
14A = 14B.
A/B = 1/1.
So one day work.
A = 1 unit.
B = 1 unit.
Total work = 30 x (1 + 1) = 60 units.
Time taken by B = 60/1 = 60 days.
(22)
Shubham Nale said:
5 years ago
A+B takes 30 days to complete whole work.
Their 1-day work
A=1/2 unit/day.
B=1/2 unit/day.
That means the total work of 30 days.
B alone will take 60 days.
Their 1-day work
A=1/2 unit/day.
B=1/2 unit/day.
That means the total work of 30 days.
B alone will take 60 days.
(1)
Prithivi chhetri said:
5 years ago
A+B do 1 work in 30 days
A+B do 1/30 work in 1 day. --------> (1)
A+B do X work in 16 days
A+B do X/16 work in 1 day. --------> (2)
Eq 1 and eq 2 are eqaul, so.
1/30 = X/16
I.e. X= 8/15.
B alone work (1-X)work in (44-16)days.
Therefore, 1- 8/15 work in 28 days.
7/15 work in 28 days
1 work in 28 * 15/7 = 60 days,
Hence B finishes the whole work in 60 days.
A+B do 1/30 work in 1 day. --------> (1)
A+B do X work in 16 days
A+B do X/16 work in 1 day. --------> (2)
Eq 1 and eq 2 are eqaul, so.
1/30 = X/16
I.e. X= 8/15.
B alone work (1-X)work in (44-16)days.
Therefore, 1- 8/15 work in 28 days.
7/15 work in 28 days
1 work in 28 * 15/7 = 60 days,
Hence B finishes the whole work in 60 days.
(5)
Nagesh said:
5 years ago
Thanks @Sameer.
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.
Swarupa said:
6 years ago
A worked 16 days.
A+B worked 30 days.
A+B = 1/30.
16 days A work = 1/30x16 = 8/15 remaining work 7/15. done by B.
B alone work 44-16 = 28.
So Alone B work done =28 x 15/7 = 60.
A+B worked 30 days.
A+B = 1/30.
16 days A work = 1/30x16 = 8/15 remaining work 7/15. done by B.
B alone work 44-16 = 28.
So Alone B work done =28 x 15/7 = 60.
(2)
Viky said:
6 years ago
A work is x. ie. x work completed in 16 days.
B work is 1-x. ie. Remaining 1-x work completed in 44 days.
We need whole work completed ie. 1.
So,
A work + B work=1.
Therefore;
16+44 = 60days.
B work is 1-x. ie. Remaining 1-x work completed in 44 days.
We need whole work completed ie. 1.
So,
A work + B work=1.
Therefore;
16+44 = 60days.
(2)
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)
Shashikanth said:
6 years ago
x + y = 1/30 -----> (i)
16x + 44y = 1 ------> (ii)
Cross Multiply 30 in equation (i).
Now 30x + 30y = 1.
Now equate equation (i) and (ii) , since both equations are equal to 1,
We can write;
30x + 30y = 16x + 44y.
30x - 16x = 44y - 30y.
14x = 14y.
x = y.
Since x = y, apply to any one of the equation, let me put to equation (i)
Now, x+x = 1/30,
2x = 1/30,
x = 1/60,
Since x = y,
y = 1/60.
16x + 44y = 1 ------> (ii)
Cross Multiply 30 in equation (i).
Now 30x + 30y = 1.
Now equate equation (i) and (ii) , since both equations are equal to 1,
We can write;
30x + 30y = 16x + 44y.
30x - 16x = 44y - 30y.
14x = 14y.
x = y.
Since x = y, apply to any one of the equation, let me put to equation (i)
Now, x+x = 1/30,
2x = 1/30,
x = 1/60,
Since x = y,
y = 1/60.
(2)
Kaavya said:
7 years ago
Thanks for the answer @Tapash Dey.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers