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?
Answer: Option
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:
96 comments Page 3 of 10.
Decoder said:
1 decade ago
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 ?
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 ?
Sainath said:
1 decade ago
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....
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....
Dharam Verma said:
1 decade ago
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.
(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.
Sonu said:
1 decade ago
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!!!!
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!!!!
Vinod Anand said:
1 decade ago
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.
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.
Rahul said:
1 decade ago
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.
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.
Amit Raj Modi said:
1 decade ago
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.
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.
Kartik said:
1 decade ago
a = 1/4 B+c = 1/3 a+c = 1/2 on subtracting b+c = 1/3 & a+c = 1/2 we got,
b-a = -1/6 and a = 1/4 (given) on putting these value we got b=12 is 1 day work so now total is 12 days.
It's Very Simple.
b-a = -1/6 and a = 1/4 (given) on putting these value we got b=12 is 1 day work so now total is 12 days.
It's Very Simple.
SIDHARTH said:
1 decade ago
A'S 1 hr work = 1/4.
(B's+ C's) 1hr work = 1/3.
Therefore, (A+B+C's)1 hr work = 1/4+1/3 = 7/12.
Therefore, B's 1hr work = 7/12 - 1/2 = 1/12.
Hence B takes 12 hrs to complete the work.
(B's+ C's) 1hr work = 1/3.
Therefore, (A+B+C's)1 hr work = 1/4+1/3 = 7/12.
Therefore, B's 1hr work = 7/12 - 1/2 = 1/12.
Hence B takes 12 hrs to complete the work.
Sai mounika said:
1 decade ago
It is easy to find out.
A+C = 1/2, A = 1/4.
(A+C) - A = 1/4 we got C = 1/4.
We know B+C = 1/3 then substitute C = 1/4 value here then we will get 1/12.
Hence B takes 12 hrs to complete the work.
A+C = 1/2, A = 1/4.
(A+C) - A = 1/4 we got C = 1/4.
We know B+C = 1/3 then substitute C = 1/4 value here then we will get 1/12.
Hence B takes 12 hrs to complete the work.
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