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 9 of 10.
Pranav Jain said:
10 years ago
What happens if the third condition is implemented saying B and C completes work in 16 days and A works for 7 days, B for 5 and C alone completes remaining work for 13 days, then C alone can complete work in how many days, how to solve this, when another variable is involved?
Jitender said:
10 years ago
I want any short method of this question.
Rutika patel said:
10 years ago
I can't understand how we can right 16x+44y = 1.
How you get 1? What is the meaning of 1?
How you get 1? What is the meaning of 1?
Neha said:
10 years ago
@Varun how you take 26.66%?
Can you explain me please?
Can you explain me please?
Varun said:
1 decade ago
Total work: 44+16 = 60 days.
Now a does 26.66% work.
Therefore B does 100-26.66 = 73.34% work in 44 days.
Time in which B can complete the whole work : 100/73.34*44.
= 60 days.
Now a does 26.66% work.
Therefore B does 100-26.66 = 73.34% work in 44 days.
Time in which B can complete the whole work : 100/73.34*44.
= 60 days.
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.
Ray said:
10 years ago
How can you get 1 in the equation: B = 1-16x? I don't understand.
Sunil kumar said:
1 decade ago
Why can't we take 1/x, 1/y instead of x, y as one day work?
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.
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).
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