# Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 7)
7.
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
8 hours
10 hours
12 hours
24 hours
Explanation:

 A's 1 hour's work = 1 ; 4

 (B + C)'s 1 hour's work = 1 ; 3

 (A + C)'s 1 hour's work = 1 . 2

 (A + B + C)'s 1 hour's work = 1 + 1 = 7 . 4 3 12

 B's 1 hour's work = 7 - 1 = 1 . 12 2 12

B alone will take 12 hours to do the work.

Discussion:
89 comments Page 1 of 9.

How the answer for a+b+c = 7/12?

A=1/4 (given)
(B+C)=1/3 (given)
(A+B+C)=(1/4+1/3) then take L.C.M
3+4/12=7/12
FIND FOR B
A+B+C=7/12
B=7/12-(A+C) given(A+C=1/2)
B=7/12-(1/2)=1/12
ANS:12

A's 1 hour work is 1/4
(A+C)'s 1 hour work is 1/2
(B+C)'s 1 hour work is 1/3
so, A+C=1/2 ->X and B+C=1/3 ->Y
subtract X-Y
we will get A-B=1/6
now, substitute A's value in d equation u vl get B's value as 1/12.
which is 1 day,s work of B...
hence B alone require 12 days...

I HOPE IT VL B HELPFULL...

Hi friends,

(A+C-A)=C
(1/2-1/4)=1/4

so C's 1 hour work will be 1/4.

Similarly

(B+C-C)=B
(1/3-1/4)=1/12

Therefore B's 1 hour work is 1/12.

Good question. Reasoning is difficult for this one.

Take the given data as 2 equations as follows

A=1\4 ,B+C=1\3--eq1 and A+C=1\2---eq2

put A=1\4 in eq2

1\4+C=1\2

C=1\2-1\4 we get

C=1\4

put C=1\4 in eq1

B+1\4=1\3

B=1\3-1\4 we get

B=1\12

Therefore B alone take 12hours to do a work

C=1/2-1/4=>1/4(C'S 1 DAY WORK)
B=1/3-1/4=>1/12(B'S 1 DAY WORK)
SO 12 DAYS TO COMPLETE THE WORK

Jayanth babu said:   1 decade ago
Hi friends, in above problem

A=1/4----->(1)
B+C=1/3----->(2)
A+C=1/2------>(3)
now solving (2)
B+C=1/3
c=B-1/3--------->(4)
substitute (1) and (4) in (3)
then..
(1/4)+B-(1/3)=1/2
by solving this equation
B=1/12

Thus, B alone take 12hrs.

Hi friends

b+c=1/3;
a+c=1/2;
a=1/4;
c=1/2-1/4=1/4;
b=1/3-1/4=1/12;

time taken for B alone to complete is 12 hours