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 8 of 10.
Naman said:
8 years ago
Thanks @Sandeep.
Priti said:
8 years ago
Please tell me how to solve the equation of x and y in detail?
Manish said:
8 years ago
Don't consider x & y only consider x.
We know 16 days work of A + 44 days of B = total 1 work.
let work be x by both A & B.
now 16 days of x+44 days of x=1 work.
60 days x=1 work.
x=1/60.
Now find total work of B.
first find how much worked for 44 days ie-44*1/60=11/15.
now for 44 days he completed work of 11/15.
how many days he need to complete 1 work (total work) .
44*15/11=60 days.
We know 16 days work of A + 44 days of B = total 1 work.
let work be x by both A & B.
now 16 days of x+44 days of x=1 work.
60 days x=1 work.
x=1/60.
Now find total work of B.
first find how much worked for 44 days ie-44*1/60=11/15.
now for 44 days he completed work of 11/15.
how many days he need to complete 1 work (total work) .
44*15/11=60 days.
Biswaranjan mohapatra said:
8 years ago
x+y=30.
so if A do a work in x days then B do it in 30- x days.
A's 1-day work is 1/x.
B's 1-day work is 1/y.
Both 1-day work is 1/30.
So according to question.
1/x + 1/30-x = 1/30.
Solve it and find x.
so if A do a work in x days then B do it in 30- x days.
A's 1-day work is 1/x.
B's 1-day work is 1/y.
Both 1-day work is 1/30.
So according to question.
1/x + 1/30-x = 1/30.
Solve it and find x.
Tufail Ashraf Bhat said:
8 years ago
A+B do whole work in 30 days(100% of work or Complete).
A+B's1 day work =1/30.
Let us take assumption as usual.
A's 1 day work = x , & B's 1 day work = y.
=> x+y=1/30 ------------ eq1.
Now people got confused by;
This 16x +44y =1.
(Ans. It is equal to 1 coz 1 here means 100% or mathematically 1/1=1 and in eq1 1/30 means 1/30 100%work--1 divided into 30 parts has been done in 1 day 1/30%=3.3%).
And simply 1 means 100%. 1/1*%. Or 1/1x100.
A+B's1 day work =1/30.
Let us take assumption as usual.
A's 1 day work = x , & B's 1 day work = y.
=> x+y=1/30 ------------ eq1.
Now people got confused by;
This 16x +44y =1.
(Ans. It is equal to 1 coz 1 here means 100% or mathematically 1/1=1 and in eq1 1/30 means 1/30 100%work--1 divided into 30 parts has been done in 1 day 1/30%=3.3%).
And simply 1 means 100%. 1/1*%. Or 1/1x100.
(1)
Deepak said:
7 years ago
A+B can do a work in 30 days.
One day work done by A =1/A.
One day work done by B=1/B.
1/A+1/B=1/30.
A worked for 16 days.
So one day work done by A =16/A.
Remaining work =1-16/A.
One day work done by B=1/B.
In 44day work done by B=44/B.
1-16/A=44/B.
16/A+44/B=1-----> eq1
1/A=1/30-1/B----> eq2
16(1/30-1/B)+44/B=1.
16/30+(44_16/B)=1,
16/30+28/B=1,
28/B=1-16/30,
28/B=30-16/30,
28/B=14/30,
28*30=14B,
B=840/14=60.
B shall finish whole work in 60 days.
One day work done by A =1/A.
One day work done by B=1/B.
1/A+1/B=1/30.
A worked for 16 days.
So one day work done by A =16/A.
Remaining work =1-16/A.
One day work done by B=1/B.
In 44day work done by B=44/B.
1-16/A=44/B.
16/A+44/B=1-----> eq1
1/A=1/30-1/B----> eq2
16(1/30-1/B)+44/B=1.
16/30+(44_16/B)=1,
16/30+28/B=1,
28/B=1-16/30,
28/B=30-16/30,
28/B=14/30,
28*30=14B,
B=840/14=60.
B shall finish whole work in 60 days.
Jeyasurya said:
7 years ago
B finishes the remaining work in 44 days.
A finishes the work in 16 days,
So, B alone, 44 + 16 = 60 days.
A finishes the work in 16 days,
So, B alone, 44 + 16 = 60 days.
(2)
Kaavya said:
7 years ago
Thanks for the answer @Tapash Dey.
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)
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)
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