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 4 of 10.
Shyam said:
1 decade ago
I got the same answer as Sai and Kaustubha.
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?
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.
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.
Sakshi said:
1 decade ago
I can't understand. Why we have used x? We did not do this in other question.
Tarik Khan said:
1 decade ago
Let total work = 1.
Work done by A is = x.
So remaining work that is done by B = 1-x.
So, total time to complete the whole work by A = 16/x....(1).
Similarly total time to complete the whole work by B = 44/(1-x).....(2).
From (1) and (2) we get.
16/x = 44/(1-x).....(3).
Solving (3) we get.
x = 4/15.
So 1-x = 11/15.
Now for B takes time 44 days to complete 11/15 work.
So total time to complete the whole work alone B = (15/11)x44 = 60 (ans).
Work done by A is = x.
So remaining work that is done by B = 1-x.
So, total time to complete the whole work by A = 16/x....(1).
Similarly total time to complete the whole work by B = 44/(1-x).....(2).
From (1) and (2) we get.
16/x = 44/(1-x).....(3).
Solving (3) we get.
x = 4/15.
So 1-x = 11/15.
Now for B takes time 44 days to complete 11/15 work.
So total time to complete the whole work alone B = (15/11)x44 = 60 (ans).
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.
Sunil kumar said:
1 decade ago
Any easy method better than above all? All are did in same method. Somehow tough above all the methods.
Sunil kumar said:
1 decade ago
Why can't we take 1/x, 1/y instead of x, y as one day work?
Usha said:
1 decade ago
I agree with @Sunil kumar.
Why it has been calculated as x+y=1/30 instead of considering 1/x + 1/Y = 1/30.
Kindly explain, I understood the above calculations but the basic equation why it was altered that I din't got.
Why it has been calculated as x+y=1/30 instead of considering 1/x + 1/Y = 1/30.
Kindly explain, I understood the above calculations but the basic equation why it was altered that I din't got.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers