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Aptitude - Time and Work - Discussion

@ : Home > Aptitude > Time and Work > General Questions - Discussion

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"I never see what has been done; I only see what remains to be done."
- Marie Curie
26. 

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

[A]. 4 days[B]. 6 days
[C]. 8 days[D]. 12 days

Answer: Option D

Explanation:

(A + B + C)'s 1 day's work = 1 ;
6

(A + B)'s 1 day's work = 1 ;
8

(B + C)'s 1 day's work = 1 .
12

Therefore (A + C)'s 1 day's work
= ( 2 x 1 ) - ( 1 + 1 )
6 8 12
= ( 1 - 5 (
3 24
= 3
24
= 1 .
8

So, A and C together will do the work in 8 days.


Nandakumar said: (Tue, Jan 18, 2011 08:11:34 AM)    
 
How can i take 2*1/8-(1/8+1/12)?

Bhanu said: (Thu, Jan 27, 2011 06:52:43 AM)    
 
(A + B + C)'s 1 day's work = 1/6


(A + B)'s 1 day's work = 1/8


(B + C)'s 1 day's work = 1/12

so c's 1 day's work=1/6-1/8=1/24
and a's 1 day's work=1/6-1/12=1/12
and b's 1 day work=1/6(1/24+1/12)=1/4

so a and c 1'day work=1/12+1/24=1/8

Akiii said: (Sun, Mar 27, 2011 12:02:53 PM)    
 
Good explanation.

Azuu said: (Thu, Aug 11, 2011 10:20:57 AM)    
 
How to take lcm of 1/8+1/12 ?

Sabarimani said: (Mon, Aug 15, 2011 06:17:54 PM)    
 
Is b's 1day work=1/6-(1/24+1/12)?

Gulshan said: (Sat, Oct 22, 2011 02:58:23 PM)    
 
24 is lcm of 8 & 12

Kavitha said: (Mon, Feb 20, 2012 12:52:19 PM)    
 
Why did you take 1/6 (1/12+1/24) ?

Anishkumar said: (Wed, Mar 7, 2012 09:48:55 PM)    
 
Assume A+C as x

so now
2(A+B+C)=1/8+1/12+1/x


2(1/6) =5/24+1/x

finally

x =8

Parveen Verma said: (Tue, Mar 20, 2012 08:30:24 PM)    
 
(A+B+C)=1/6
A's one day work work= (A+B+C)-(B+C)= 1/6-1/12 =1/12
C's one day work work= (A+B+C)-(A+B)= 1/6-1/8= 1/24
(A+C)'s one day work= 1/12+1/24= 1/8
so the work will be completed in 8 days

Sujeet said: (Fri, Apr 20, 2012 12:52:41 AM)    
 
Why 2 is multiplied by 1/6.

Basu said: (Wed, Sep 5, 2012 12:01:48 PM)    
 
How its come on 1/6-1/2=1/12
1/6-1/8= 1/24
1/12+1/24= 1/8

Nice Dreamer said: (Fri, Sep 21, 2012 01:34:15 PM)    
 
Why 2 is multiplied with 1/6 ? please explain any one.

Nik said: (Sat, Sep 22, 2012 07:37:19 PM)    
 
1 day's work of(A+B)=1/8
1 day's work of (B+C)=1/12
lets take 1 day's work of (A+C)=1/x
adding the above we get 2(A+B+C)=1/8+1/12+1/X
dr4 2(1/6)=(1/8)+(1/12)+(1/x)
1/x=(2/6)-(1/8)-(1/12)
1/x=1/8

Dhanshree said: (Tue, Mar 19, 2013 04:04:28 PM)    
 
(A+B) work is = 1/8.

(B+C)work is = 1/12.

(A+B+C)work is = 1/6.

Only A's work = 1/6-1/12

= 1/12.

Only C's work=1/6-1/8

= 1/24.

Hence (A+C)'s complete work is = (1/12+1/24)

= 1/8.

(A+C)'s complete work in 8 day.

Monu said: (Sat, Apr 27, 2013 01:34:02 PM)    
 
Why can't we simply subtract A+B's 1 day work from B+C's 1 day work to get A+C's 1 day work?

Sk.Gopinath said: (Mon, May 20, 2013 06:39:08 PM)    
 
A+B+C = 1/6;
A+B = 1/8;
B+C = 1/12;

C's 1day work is =>1/6 - 1/8
=>1/24.
A's 1day work is =>1/6 - 1/12
=>1/8.

A+C 's 1day's work =>1/24 + 1/12.
= 1/8 = 8 days.

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