# 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:

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.

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.

(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.

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.

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.

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.

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.

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.

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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