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?
[A].
30 days
[B].
40 days
[C].
60 days
[D].
70 days
Answer: Option D
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.
A having worked for 16 days
B finishes the remaining work alone in 44 days
so,
B finish the whole work alone is = A having worked+B finishes the remaining work alone
B alone = 16 days + 44 days
= 60 days
Guest said:
(Fri, Aug 13, 2010 09:37:20 AM)
Selvi: its wrong... because, we dont know a & b's one day work.
Vishal said:
(Sun, Aug 29, 2010 01:49:01 PM)
Above solution is not properly explained.
Let me try to make it more clear (mathematically or logically).
1 day = 24 Hours.
A worked x hours in 1 day (24 hours).
B worked y hours in 1 day (24 hours).
So, x + y = 24 hours ----- Eq 1.
Now A's 16 days' work in hours = 16 * x = 16x.
And B's 44 days' work in hours = 44 * y = 44y.
16x + 44y = 30 days together worked of A + B in hours = 30 * 24 = 720 hours.
So 16x + 44y = 720 ----- Eq 2.
Now Eq 2 - 16 * Eq 1.
16x + 44y = 720.
16x + 16y = 384.
0 + 28y = 336.
Y = 336 / 28 = 12 hours in 1 day.
So x = 12 hours in 1 day.
If A doesn't work then to B has to work 24 hours in order to finish 1 day work which is equal to 2 days for B.
So for 30 days work, B has to work 60 days (answer = 60 days).
Ranjit said:
(Sun, Nov 14, 2010 11:12:48 PM)
How you got 16x + 44y = 1, thy said 16 days alone a worked remainig work finished by b is 44 days then how can you frame the equation from this given data, I cant get please make me to understand.
Student said:
(Thu, Dec 23, 2010 08:25:30 AM)
How can we write 16x+44y=1. I cant understand.
Santh said:
(Mon, Dec 27, 2010 01:26:01 PM)
Selvi. You are wrong absolutely.
Kanna said:
(Mon, Jan 10, 2011 06:00:47 AM)
Let A's 1 day's work = x and B's 1 day's work = y.
Both A's and B's 1 day work=1/30
i.e (A's 1 day + B's 1 day)=1/30
i.e x + y = 1/30........eq1
now,
A having worked for 16 days, B finishes the remaining work alone in 44 days
i.e work done by A in 16 days = 16x
Remaining work done B= 1 - 16x
but Remaining work is done by B in 44days i.e 44y
i.e. 44y=1-16x
i.e 16x+44y=1........eq2
solving eq1 & eq2,
we get,x = 1/60 and y = 1/60
B's 1 day's work = 1/60.
Hence, B alone shall finish the whole work in 60 days.
Akiii said:
(Sun, Mar 27, 2011 12:33:33 PM)
Kanna you are right.
Bangaram said:
(Sun, Jun 5, 2011 03:52:20 AM)
Kanna your explaination was good.
Manasa said:
(Sat, Jun 11, 2011 12:49:42 AM)
A's 1 day work ,consider X
B's 1 day work ,consider Y
(A+B) 1 day work=(X+Y)=1/30
next condition:
A works for 16 days=16*X
B works for 44 days for remaining work to complete=44*Y
to complete whole work;16X+44Y=1
by solving both equations ,we get
X=1/60,Y=1/60
B can complete work in 60 days.
Vidhya said:
(Mon, Jul 4, 2011 09:25:49 AM)
What is the need to write number of days as a ratio?
Why cant we take it as x+y=30 ?
Yogi said:
(Wed, Jul 27, 2011 05:29:18 PM)
@Manasa
Yes you are corrrect.
Sheik said:
(Thu, Jul 28, 2011 10:42:09 PM)
@Kanna
Your explanation is good and easily understandable.
Soniya said:
(Tue, Aug 9, 2011 01:56:06 PM)
@kanna.
You are right. Thanks.
Thangeswari said:
(Sat, Sep 10, 2011 08:35:14 AM)
Kanna.
Thanks a lot. Your explanation was excellent.
Pandit said:
(Thu, Sep 15, 2011 12:12:52 AM)
@Kanna.
You explain very easly. Thanks a lot.
Priyanka said:
(Thu, Nov 3, 2011 02:04:23 PM)
@vidya :- we are taking 1/30 , becoz we are talking about work completed by x and y in one day .
B's 1 day's work =