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 5 of 10.
Subhant said:
8 years ago
Solving the equations is tiresome brothers.
Instead take like
16a +44 b = 30 a + 30b.
a/b = 1/1
So if a one day work is 1 and b one day work is one and when they work together they do 2 units of work every day.
this means there is 30x2 = 60 units of work.
B can do it in = (total unit of work)/(B's one day work) = 60 days.
Instead take like
16a +44 b = 30 a + 30b.
a/b = 1/1
So if a one day work is 1 and b one day work is one and when they work together they do 2 units of work every day.
this means there is 30x2 = 60 units of work.
B can do it in = (total unit of work)/(B's one day work) = 60 days.
Sandeep said:
8 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.
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.
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.
Kaavya said:
7 years ago
Thanks for the answer @Tapash Dey.
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.
Nagesh said:
5 years ago
Thanks @Sameer.
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