Aptitude - Time and Work - Discussion

I have one another method.

A can do total work in 4 hr.

B+C can do this in 3 hr.

A+C can do this in 2 hr.

Convert all of this in unit/hr.

Take LCM of 4, 3 and 2 which is 12 Unit (total unit of Work).

A can do work 12/4=3 unit/hr.

A+C can do work in 2 hr means A done 2hr*3unit=6unit. Now remaining work is 6 unit (hint:-12unit-6unit=6unit) which has done by C. So C can do 3 unit (hint:-6unit/2hr=3unit/hr) Work in 1 hr.

Now B+C can do work in 3 hr means C done 3hr*3Unit=9 Unit. Now remaining work is 3 unit (hint:-12unit-9unit=3 unit) which has done by B. So B can do 1 unit (hint:-3unit/3hr=1unit/hr) Work in 1 hr.

B takes 12 hr (hint:-12unit*1hr) to complete whole work.

You can do this method oraly. You need only some practice on this method.

Hey there is no need to do so. Just.

Give as A's one day work is = 1/4.

(B+C) one day work = 1/3.

(A+C) one day work = 1/2.

As we know A = 1/4.

Then.

C = 1/2-1/4 = 1/4.

Then from given.

B = 1/3-1/4 = 1/12.

If A = 4 -(1)
B+C = 3 -(2)
A+C = 2 -(3)

From Eq.(1) and (2)

4C = 2-1, C = 4 (4' is coming from LCM and 4/4 = 1 and 4/2 = 2,
So 2-1 = 1 and 4/1 = 4).

Put the value of C in eq.(2).
12 B = 4-3.

Than B = 12 hours, Option -C.

A=1/4

B+C=1/3

A+C=1/2
----------(subtracting on both sides)
B-A=(-)1/6

B=(- 1/6)+(1/4)

B=1/12

Therefore, 12 hours!!!!

A's 1 day work = 1/4
(B+C)'s 1 day work = 1/3
(A+C)'s 1 day work = 1/2

So, C's 1 day work = (A+C)'s 1 day work - A's 1 day work
= 1/2 - 1/4
= 1/4

Now, B's 1 day work = (B+C)'s 1 day work - C's 1 day work
= 1/3 - 1/4
= 1/12 (taking LCM)

So, B complete the work in = 12 days.

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

b can do it in 12 days....

What is wrong with this approach :
C 's 1 hour work=(A+C)'s 1 hour work -A 's 1 hour work=1/2

then B's i hour work = (B+C)'s 1 hour work-C's 1 hour work =1/6

But the answer as mentioned with another approach is 1/12
Can anybody explain ?

[(b+c)=1/3]-[(a+c)=1/2]

=> b=1/12

=>b's time= 12hrs

A =1/4 (A's ONE HOUR WORK)
B+C =1/3 (B+C's ONE HOUR WORK)
A+C =1/2 (A+C's ONE HOUR WORK)

C =1/2-A

B+1/2-1/4=1/3 (submitting c value in b+c=1/3 for value of b)
B=1/3-1/2+1/4
B=1/12

Just simply i know that A's is 1/4
B+C is 1/3
So do it
1/3 - 1/4
And u get 1/12
B's work 12 hour