Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 21)
21.
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
Answer: Option
Explanation:
| Suppose A, B and C take x, | x | and | x | days respectively to finish the work. |
| 2 | 3 |
| Then, |  |
1 | + | 2 | + | 3 |  |
= | 1 |
| x | x | x | 2 |
 |
6 | = | 1 |
| x | 2 |
x = 12.
So, B takes (12/2) = 6 days to finish the work.
Discussion:
68 comments Page 2 of 7.
Vidivelli said:
1 decade ago
Let us consider the time taken by B is 2x.
So the time taken by A is "twice of B" then A=4x.
Similarly if time taken by B is x/2, the time taken by A is (2*x/2) = x; the time taken by C is x/3.
So the time taken by A is thrice of C (3* x/3). Hence we get x+x/2+x/3.
Since we consider work for one day we take inverse 1/x+2/x+3/x = 1/2.
So the time taken by A is "twice of B" then A=4x.
Similarly if time taken by B is x/2, the time taken by A is (2*x/2) = x; the time taken by C is x/3.
So the time taken by A is thrice of C (3* x/3). Hence we get x+x/2+x/3.
Since we consider work for one day we take inverse 1/x+2/x+3/x = 1/2.
Manasa said:
1 decade ago
@nayana
GIVEN:
A=2B,A=3C
solution:
consider A can do work in X days
X=2B...B=X/2;X=2C...C=X/3;
B can complete work in X/2days,B's 1 day work is 2/X
C can complete work in X/3days,C's 1 day work is 3/X
A's 1 day work is 1/X.
(A+B+C) 1 days work is[(1/X)+(2/X)+(3/X)]=1/2
6/X=1/2
X=12
therefore b can do work in ;B=X/2=12/2=6 days
GIVEN:
A=2B,A=3C
solution:
consider A can do work in X days
X=2B...B=X/2;X=2C...C=X/3;
B can complete work in X/2days,B's 1 day work is 2/X
C can complete work in X/3days,C's 1 day work is 3/X
A's 1 day work is 1/X.
(A+B+C) 1 days work is[(1/X)+(2/X)+(3/X)]=1/2
6/X=1/2
X=12
therefore b can do work in ;B=X/2=12/2=6 days
Shridhar said:
1 decade ago
As the ques. says,
time taken by A is twice that of B and thrice that of C,so
this means that
A=2*B=3*C ----(eq.1)
dividing the whole equation by lcm(1,2,3)=6,we get
A/6=B/3=C/2
Now
one third of the workdone of B is finished in 2 days
therefore complete workdone of B will be finished in 3*2=6 days.
time taken by A is twice that of B and thrice that of C,so
this means that
A=2*B=3*C ----(eq.1)
dividing the whole equation by lcm(1,2,3)=6,we get
A/6=B/3=C/2
Now
one third of the workdone of B is finished in 2 days
therefore complete workdone of B will be finished in 3*2=6 days.
Tanuja Sinha said:
12 months ago
A = 2B, A = 3C.
So A = 2B = 3C.
A : B : C = (1/1) × 6 : (1/2) × 6 : (1/3)×6.
= 6 : 3 : 2.
A and B together do work in 2 days (Nowhere mention that A, B and C are doing simultaneously, so taking A and B as contains B and we have to find B alone).
So, Total work = (6 + 3) × 2 = 18
B can do alone = 18/3 = 6 days.
So A = 2B = 3C.
A : B : C = (1/1) × 6 : (1/2) × 6 : (1/3)×6.
= 6 : 3 : 2.
A and B together do work in 2 days (Nowhere mention that A, B and C are doing simultaneously, so taking A and B as contains B and we have to find B alone).
So, Total work = (6 + 3) × 2 = 18
B can do alone = 18/3 = 6 days.
(3)
Abhishek said:
5 years ago
Let's assume.
C takes 4 days to do X work.
B takes 6 days for the same X work.
A takes 12 days for the same X work.
so, efficiency
A = 1/12.
B = 1/6.
c = 1/4.
So, as they all together takes 2 days to work,
x/(1/12)+(1/6)+(1/4) = 2
From that, we got X ( total work ) = 1
So time taken alone by;
B = 1/(1/) = 6 days.
C takes 4 days to do X work.
B takes 6 days for the same X work.
A takes 12 days for the same X work.
so, efficiency
A = 1/12.
B = 1/6.
c = 1/4.
So, as they all together takes 2 days to work,
x/(1/12)+(1/6)+(1/4) = 2
From that, we got X ( total work ) = 1
So time taken alone by;
B = 1/(1/) = 6 days.
(1)
Bharath ECE said:
8 years ago
Simple Method. But I explained Elaborate.
A is twice time as B => A=2B
A is thrice time as c => A=3C
therefore;
B =A/2
C= A/3
A= A, A=2* (A/2)
A taken as X
A, B, C X, X/2, X/3 Days Respectively;
Rule of Flip or Time to Work
1/x +2//x+3/x =1/2
6/x =1/2
x=12
Asking b Alone.
B= x/2
so 12/2
B =6 Days.
A is twice time as B => A=2B
A is thrice time as c => A=3C
therefore;
B =A/2
C= A/3
A= A, A=2* (A/2)
A taken as X
A, B, C X, X/2, X/3 Days Respectively;
Rule of Flip or Time to Work
1/x +2//x+3/x =1/2
6/x =1/2
x=12
Asking b Alone.
B= x/2
so 12/2
B =6 Days.
Raj said:
9 years ago
2A = B.......eqn1.
3A = C.......eqn2.
A + B + C = 2days
A + 2A + C = 2days (from the eqn1),
A + 2A + 3A = 2days(from the run2),
6A = 2days ,
A = 2/6,
A = 1/3 days.
i.e A takes 3days to work.
We have B=2A.
B=2(3),
B=6.
That's B takes 6 days to complete.
3A = C.......eqn2.
A + B + C = 2days
A + 2A + C = 2days (from the eqn1),
A + 2A + 3A = 2days(from the run2),
6A = 2days ,
A = 2/6,
A = 1/3 days.
i.e A takes 3days to work.
We have B=2A.
B=2(3),
B=6.
That's B takes 6 days to complete.
(1)
Mahesh Sarangapani said:
1 decade ago
Suppose A, B and C take x, x/2, x/3 days respectively to finish the work.
work done per day by
A is 1/x
B is 1/(x/2)=2/x
C ix 1/(x/3)=3/x
And the work done by A, B and C together per day is 1/2 (since work is completed in 2 days)
So 1/x + 2/x + 3/x = 1/2
6/x = 1/2
x = 12.
Answer : 6
work done per day by
A is 1/x
B is 1/(x/2)=2/x
C ix 1/(x/3)=3/x
And the work done by A, B and C together per day is 1/2 (since work is completed in 2 days)
So 1/x + 2/x + 3/x = 1/2
6/x = 1/2
x = 12.
Answer : 6
MONA said:
9 years ago
In simple way:
A =2B , A = 3C,So ratio will be = A : B : C = 1 : 2 : 3.
A = 1 unit/day
B = 2unit/day
C = 3unit/day
A + B + C = 6unit/day.
We don't know the total work in units.
So,
A + B + C = 2 Days
TOTAL WORK/DAYS = 6.
TOTAL WORK = 6 * 2 = 12 UNITS.
So,B = 12/2 = 6 Days.
A =2B , A = 3C,So ratio will be = A : B : C = 1 : 2 : 3.
A = 1 unit/day
B = 2unit/day
C = 3unit/day
A + B + C = 6unit/day.
We don't know the total work in units.
So,
A + B + C = 2 Days
TOTAL WORK/DAYS = 6.
TOTAL WORK = 6 * 2 = 12 UNITS.
So,B = 12/2 = 6 Days.
Wangchuk Drukpa said:
1 decade ago
Let C takes x days to complete the work, then:
A, B, C.
3x, 3/2 x and x.
Their respective 1 day's work.
1/3x, 3/2x, 1/x now this is equal to 1/2 (as A+B+C takes 2 days to complete the work, thus their 1 day's work would be half).
Then we get x=4. Now 3/2 of 4 is 6.
A, B, C.
3x, 3/2 x and x.
Their respective 1 day's work.
1/3x, 3/2x, 1/x now this is equal to 1/2 (as A+B+C takes 2 days to complete the work, thus their 1 day's work would be half).
Then we get x=4. Now 3/2 of 4 is 6.
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