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
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

Therefore B alone will take 12 hours to do the work.

Discussion:
89 comments Page 2 of 9.

Pallabi Sethi said:   3 years ago
A 1 hours work=1/4 ----> (i)
B+C 1 hors work=1/3 ----> (ii)
A+C 1 hour work=1/2 ----> (iii).

By subtracting from (iii) to (ii) we get A-B = 1/6.
Now in place of A put the value of A = 1/4.
1/4-B = 1/6,
1/4-1/6 = B.
1/12 IS B'S 1 Hour's work.
B will take 12 hours.

Abhimanyu said:   3 years ago
A = 4 B + C = 3 A + C = 2.

(B+C) - (A+C) + A = B(Making equation such that we will get value of B)
1/3 -1/2 + 1/4 = B.

B = 4 - 6 + 3/12(By taking kam) = 1/12.
B = 12.

Don said:   4 years ago
How 7/12 - 1/2 = 1/12? Explain this.

Lazy Balu said:   4 years ago
A+(B+C)-(C+A) = 1/4+1/3-1/2.
A+B+C-C-A = (3+4-6)/12.

Therefore B = 1/12.
So B can do in 12 days.

Soumyaranjan said:   5 years ago
A = 4hrs.
B+C = 3hrs.
A+C = 2hrs.

Work=LCM(4, 3,2) = 12.
The efficiency of A = 12/4 = 3.
The efficiency of BC = 12/3 = 4.
The efficiency of AC = 12/2 = 6.

The efficiency of C = efficiency of (AC-A)
= 6-3 = 3
The efficiency of B = efficiency of (BC-C)
= 4-3 = 1
T = W/E
= 12/1 = 12.

So, B alone will take 12hrs for do it.
(2)

Shreya said:   5 years ago
A takes 4hrs.

B+C takes 3 hrs.
A+C takes 2 hrs.
A=a.
B+C=b,
A+C=c
LCM of 4,3,2=12.
a+b+c=12units(total work done).

a=A.
So A takes 4h for 12u.

In 1 hr it does 3u.
b=B+C,
B+C take 3h for 12u.

In 1h does 4u,
c=A+C.
A+C take 2h for 12u,
in 1hr A+C do 6u.

A does 3u/h.
replacing in A+C.
3+C=6.
C=3,
C does 3u/h.

Replacing C in B+C
In 1 hr;
B+3=4.
B=1.
B does 1u/h.

1 unit of work in 1hr.
12 unit of work in 12 hrs.

Sohail said:   5 years ago
How, (7/12 - 1/2) = 1/12?

Explain this step please.

Dev said:   5 years ago
LET THE B CAN DO WORK IN X DAYS.

PART OF THE WORK IS DONE BY B+C = 1/3.
PART OF THE WORK IS DONE BY A+C = 1/2.
Now (B+C) - (A+C) = 1/3-1/2.
B-A = 1/3-1/2.
1/x-1/4 = 1/3-1/2.
1/x = 1/12 part of work.

So Work will be completed by B alone in 12 days.

Akshay Sen said:   6 years ago
Work done by A in one hr = 1/4.

As A+C = 2hr.
so, C's working for 1 hr will be = 1/2 -1/4 (A's working).
C's working for 1hr = 1/4.
Now As B+C = 3hrs.
so, we can find the working of B in 1 hr.
therefore working of B in 1 hr = 1/3 - 1/4.
B's = 1/12.
Hence 12hrs taken by B.

Tejs said:   6 years ago
Thanks for your answer @Bits.


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