# 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 1 of 9.
Rucha said:
1 decade ago

How the answer for a+b+c = 7/12?

Varseyny said:
1 decade ago

A=1/4 (given)

(B+C)=1/3 (given)

(A+B+C)=(1/4+1/3) then take L.C.M

3+4/12=7/12

FIND FOR B

A+B+C=7/12

B=7/12-(A+C) given(A+C=1/2)

B=7/12-(1/2)=1/12

ANS:12

(B+C)=1/3 (given)

(A+B+C)=(1/4+1/3) then take L.C.M

3+4/12=7/12

FIND FOR B

A+B+C=7/12

B=7/12-(A+C) given(A+C=1/2)

B=7/12-(1/2)=1/12

ANS:12

Nagarjun said:
1 decade ago

A's 1 hour work is 1/4

(A+C)'s 1 hour work is 1/2

(B+C)'s 1 hour work is 1/3

so, A+C=1/2 ->X and B+C=1/3 ->Y

subtract X-Y

we will get A-B=1/6

now, substitute A's value in d equation u vl get B's value as 1/12.

which is 1 day,s work of B...

hence B alone require 12 days...

I HOPE IT VL B HELPFULL...

(A+C)'s 1 hour work is 1/2

(B+C)'s 1 hour work is 1/3

so, A+C=1/2 ->X and B+C=1/3 ->Y

subtract X-Y

we will get A-B=1/6

now, substitute A's value in d equation u vl get B's value as 1/12.

which is 1 day,s work of B...

hence B alone require 12 days...

I HOPE IT VL B HELPFULL...

Nagendramurthy said:
1 decade ago

Hi friends,

(A+C-A)=C

(1/2-1/4)=1/4

so C's 1 hour work will be 1/4.

Similarly

(B+C-C)=B

(1/3-1/4)=1/12

Therefore B's 1 hour work is 1/12.

(A+C-A)=C

(1/2-1/4)=1/4

so C's 1 hour work will be 1/4.

Similarly

(B+C-C)=B

(1/3-1/4)=1/12

Therefore B's 1 hour work is 1/12.

Ashish said:
1 decade ago

Good question. Reasoning is difficult for this one.

Hindu said:
1 decade ago

Take the given data as 2 equations as follows

A=1\4 ,B+C=1\3--eq1 and A+C=1\2---eq2

put A=1\4 in eq2

1\4+C=1\2

C=1\2-1\4 we get

C=1\4

put C=1\4 in eq1

B+1\4=1\3

B=1\3-1\4 we get

B=1\12

Therefore B alone take 12hours to do a work

A=1\4 ,B+C=1\3--eq1 and A+C=1\2---eq2

put A=1\4 in eq2

1\4+C=1\2

C=1\2-1\4 we get

C=1\4

put C=1\4 in eq1

B+1\4=1\3

B=1\3-1\4 we get

B=1\12

Therefore B alone take 12hours to do a work

HARRY said:
1 decade ago

C=1/2-1/4=>1/4(C'S 1 DAY WORK)

B=1/3-1/4=>1/12(B'S 1 DAY WORK)

SO 12 DAYS TO COMPLETE THE WORK

B=1/3-1/4=>1/12(B'S 1 DAY WORK)

SO 12 DAYS TO COMPLETE THE WORK

Jayanth babu said:
1 decade ago

Hi friends, in above problem

A=1/4----->(1)

B+C=1/3----->(2)

A+C=1/2------>(3)

now solving (2)

B+C=1/3

c=B-1/3--------->(4)

substitute (1) and (4) in (3)

then..

(1/4)+B-(1/3)=1/2

by solving this equation

B=1/12

Thus, B alone take 12hrs.

A=1/4----->(1)

B+C=1/3----->(2)

A+C=1/2------>(3)

now solving (2)

B+C=1/3

c=B-1/3--------->(4)

substitute (1) and (4) in (3)

then..

(1/4)+B-(1/3)=1/2

by solving this equation

B=1/12

Thus, B alone take 12hrs.

Pavan@9966606261 said:
1 decade ago

Hi friends

b+c=1/3;

a+c=1/2;

a=1/4;

c=1/2-1/4=1/4;

b=1/3-1/4=1/12;

time taken for B alone to complete is 12 hours

b+c=1/3;

a+c=1/2;

a=1/4;

c=1/2-1/4=1/4;

b=1/3-1/4=1/12;

time taken for B alone to complete is 12 hours

Piyus said:
1 decade ago

(b+c)of 1 hour-(a+c) of 1 hour = 1/3-1/2

=> b(1hr)-a(1hr)=(-1/6)

=> b(1hr)=1/4-1/6

=>b's 1hr work= 1/12

=>b ll take 12 hr to complete the work alone

=> b(1hr)-a(1hr)=(-1/6)

=> b(1hr)=1/4-1/6

=>b's 1hr work= 1/12

=>b ll take 12 hr to complete the work alone

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