Aptitude - Time and Work - Discussion

Workman.

A : B.
3 : 1.

Time taken;

A : B.
1 : 3.

A) if B finish work in 30 days then, A can finish it in 10 days. Now the difference in a day is 20.

B) if B finish work in 60 days then, A can finish it in 20 days. Now the difference in a day is 40.

C) if B finish work in 90 days then, A can finish it in 30 days. Now the difference in a day is 60.

Given question. The difference is 60 days. Hence, condition c) satisfies.

A 1-day work is 1/30.

B 1-day work is 1/90.

A + B 1 day work is 1/30 + 1/90 = 4/90.

Days to complete the work is 90/4 => 22 1/2.

Ratio of times taken by A and B to finish a work is 1 : 3.
A:B=1:3 OR A/B=1/3 or 3A=1B --(1).

B-A = 60.
B-(1/3)B = 60 (Substituting the value of A from eq 1).
3B-B = 180 (Multiply through by 3).
2B = 180.
B = 180/2.
B = 90.
A = (1/3)*90.
A = 30.

So, A can do the job in 30 days.
Therefore, A can do 1/30 of the job per day.

And B can do the job in 90 days.
Therefore, B can do 1/90 of the job per day.

Work they can do per day:
= (1/30) + (1/90).
= (3/90)+(1/90).
= (3+1)/90.
= 4/90.

So the job will take 90/4 days, which is 45/2 or 22.5 days.

Hi friends, Here is a simple technique to calculate the above problem....

Given,

If the If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes......?

We can represent the above relation like this,

2------->3
60------>....?

By cross multiplying the above terms we will get... 60*3/2 = 90.

Note:- Always individual term should come in the denominator.

By applying the above procedure you can solve any problem of this type....

I think this technique will help you while doing with this type of problems...

A clear approach:

Given: A's time taken:B's time taken=1:3

So A's proportion of time taken=1/(1+3)=>1/4*some x
B's proportion of time taken=3/(1+3)=>3/4*some x

As it is said that difference of time is 60 days

B's time-A's time=60
=> 3x/4-x/4=60
=>x=120

So A's proportion of time taken =x/4=120/4=30 days
B's proportion of time taken =3x/4=3*120/4=90 days

A's 1 day's work = 1/30
B's 1 day's work = 1/90
(A + B)'s 1 day's work = (1/30 + 1/90)= 4/90=2/45

A and B together can do the work in 45/2 = 22 1/2 days.

It is said A is 3 time as good as B.
ie. A=3*B
Again given,
A is able to finish a job in 60 days less than B.

say, B takes x days to complete 1 work
therefore A takes x-60 days to complete 1 work(same work)
A's 1 day work=1/x-60
B's 1 day work=1/x.
Substituting;

Applying in formula,
A=3B
ie. 1/x-60=3/x
so,x=90
x-60=30
so we got the number of days A alone and B alone worked i.e 60 and 90
1 day work of (A+B)=1 / 60 + 1 / 90 = 2/45,
So,nobr of days (A+B) worked = 45/2,
Answer is option B.

Ratio of times taken by A and B = 1 : 3.

That is If A takes 1 day B takes 3 days
Time Difference is 3-1 = 2 days

Here is the tricky part :
If A takes 1/2 day B takes 3/2 days
Time Difference is 3/2 - 1/2 = 1 days

When time difference is 60 days (Just mulitply by 60)
A takes 60/2 and B takes 3*60/2

So, A takes 30 days to do the work.
and B takes 90 days to do the work.

A's 1 day's work = 1/30
B's 1 day's work = 1/90

(A + B)'s 1 day's work = (1/30 + 1/90)= 4/90 = 2/45

A and B together can do the work in 45/2 = 22+1/2

Let A complete work in = x days.
B will complete work in = 3x days.

(As a is 3x sufficient so b will take 3x much time)
Also, A take 60 days less,
So days were taken by B - 60 = days taken by A
So equation will be;
3x - 60 = x,
2x = 60,
x = 30.

So A completes work in 30 days and B in 30 X x = 90
A 1-day work = 1/30,
B 1 day work = 1/90,

1 day work of A & B together = 1/30 + 1/90 = 4/90.

If they both do 4/90 work in one day so to complete the whole 1 work they will take
4/90 X x = 1.
x = 90/4 = 45/2 = 22 1/2.

Let A completes work in x days.
So no of days taken by B to complete the same work will be 3x days.

A takes 60 days less than B.

So 3x-60 = x.
2x = 60.
x = 30 days (number of days taken by A).
3x = 90 days (number of days taken by B).

Work done by A per day is 1/30.
Work done by B per day is 1/90.

Work done the together in 1 day will be (1/30+1/90) = 4/90.

So work done by them in 10 days will be 40/90.

Work done in 20 days 80/90.

Number of days require to do the remaining 10/90 will be 2.5 days.

Ans = 22.5 days.

@All.

Please refer to Sheetal's response as given below. Its the best and easiest way to solve such questions.

PS:Thanks sheetal.

"A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1.

SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA.

K * X / K'S SQUARE - 1
=3 * 60 / 9 - 1
=3 * 60 / 8
=180 / 8
=22.5 DAYS.

AS MENTIONED OPTION B.

The ratio of work done by A & B= 1:3.
(Because A is thrice as good as B)
A' s work done = Less than 60 days than B.
So take B's work done = x days---(1)
Then A's work done = x-60---(2)
So, 1=x-60,
3= x.

So cross mutiply as per the ratio simplification.
x * 1= 3(x-60),
x=3x-180,
3x-x=180,
x =90.

As per (1) & (2)
B's work done = 90 days,
A's work done = 90-60 = 30 days,
(A+B)'s 1 day work done = 1/30 +1/90=4/90=2/45,
Total work done = 45/2= 22 1/2 days.