Aptitude - Time and Work - Discussion

"A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B."

Solution:
*********
'A' able to finish a job in 60 days 'less than B'.
Let A's work is = x days.
Let B's work is = 3x days.
A able to do a work in 60 less than B.

Therefore,

A's work = B's work - 60.
So,
x=3x-60.
Then x=30.

A can complete the work in 30 days.
B can complete the work in 3*30 = 90 days.

A's one day work = 1/30 days.
B's one day work = 1/90 days.
A+B one day work = (1/30)+(1/90) = 4/90 days.
Therefore A and B can finish the work in = 90/4.
So the answer is : Option [B].

Friends, don't make it complex: Here we go.

Ratio of time taken by A & B = 1:3

And A takes 60 days less then B

Suppose, days taken by B = x then days taken by A = (x - 60)

Thus,

A : B = (x - 60) : x
1 : 3 = (x - 60) : x
1/3 = (x - 60) / x
X = 3 (x - 60)
X = 3x - 180
180 = 3x - x
180 = 2x
X = 180 / 2 = 90

Hence,
Days taken by B = x = 90 days
Days taken by A = (x - 60) = 90 - 60 = 30 days

1 day work of A and B = 1/30 + 1/90
= 4/90
= 2/45

So,
Total days taken by A & B to complete the work = 45/2 = 22.5 days

Let us understand this in a much simpler way.

Let the time taken by B to finish the work be X days.
Then according to the question Time is taken by the A is (X-60).
Work done by B in one day is (1/X),
Work done by A in one day is (1/X-60),

And we know that A is three times faster than B, So work done by A in one day is three times the work done by B in one day.

So 3*(1/X)=(1/X-60), 3X-180=X, X=90, Therefore B takes 90 days to complete the work hence A take 30 days to complete the work, therefore together they take 1/(1/30+1/90) days, which is equal to 45/2.

Thank you all.

Hi friends,.

Though content is big it is easy to understand.

Work done by A as compared to B=3:1.

Time taken by A as compared to B=1:3.

So, time difference is 2.

A will finish the work 60 days lesser than B.

Therefore time difference is 60.

Time taken for A = 60/2 = 30.

Hence time taken for B=3* time taken by A = 90.

If A+B can do a piece of work in n days, then (A+B) 's 1day's work=1/n.

Working together (A+B) 's one day work = (1/30) + (1/90) =2/45.

If (A+B) 's 1day's work=1/n, then A+B can finish the work in n days.

Therefore total time taken = 45/2= 22. 5 Days.

A is thrice as good as workman as B and therefore can finish a job in 60 days - question
Just think A thrice is 90;
How means;

A is thrice as b;
For A assume as x;
then B assume as 2x;
then C assume as 3x;

in question they thrice -- so we can assume thrice as 3x;
if one is 30 means.
then twice as 60.
then thrice as 90.
So , one day of the work is 1/30, then thrice day of the work is 1/90.

Working together A+B;
1/30+1/90;then.
Then take lcm it will give 90.
Then check whether the 90 is in a and b
3+1/90;
4/90;
2/45;
Then reciprocal it or div it will give 22 1/2.

Hi Guys,

Don't be confused in data given in question.

I have one short cut to solve such kind of question.

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.

I HOPE U WILL UNDERSTAND THIS THING & WILL APPLY IN QUESTION BASED ON THIS.

All the best. Have nice day!

First thing, the work done is always same, i.e. Work done by A = work done by B = work done by A+B.

So, if A does a work in x days then B does it in 60-x days.

Now, we can write A=3B

So, work done by A will be = 1*x = x
Work done by B will be = 3*(60-x)

As we know work done remains same then

x = (60-x)*3.
x = 45,

So, A's total time = 45.
B's total time = 60-x = 60-45 = 15.

So, now we can find the total time taken by A+B to complete the work as,
1/15 + 1/45 = 4/45.

It's one day work of A+B so reciprocal it to get the total time taken by them.
45/4 = 22.5 days

A is thrice as good as workman as B and therefore can finish a job in 60 days less than B. Working together, they can do it in:

A = 3x, B= 1x ----> {1}
Here A's efficiency = 3.
B's efficiency = 1.

The Sum of their efficiency is 4 (we will need this later on).

According to the question:
A = 3x - 60.

Therefore 1 day's work of A and B is:
1/(3x-60) = 1/(x).
By solving we get x = 30
By putting the value of x in eqn {1}
We get A= 3 X 30 = 90 days.
B = 30 days.

By working together, they can do it in:
90/4 days.
By further solving, we get 22 1/2 days.

Hi Guys,

Let me do the same thing with different values.

Given statement : "A is thrice as good as workman as B"
Time difference : 60 days.


If B takes 12 days to complete a work, A will take only 4 days to complete the same work.

So, B takes 12 days whereas A takes 4 days only (because A is thrice as good as B).

Here time difference is 12 - 4 = 8 days.

If the time difference is 8 days, B takes 12 days.

Similarly if the time difference is 60 days, then B takes (12/8 * 60) = 90 days.

...Rest thing you can understand from the explanation part.

Let the time taken by A be x days,
then time taken by B will be 3x days.
Given that,
time taken by A to finish the work = time taken by B -60
i.e, x=3x-60
=> x=30.
Therefore, time taken by A to finish the work is 30 days.
so B takes 90 days.
Now ,work done by A & B in 1 day=1/30 + 1/90
=4/90
=2/45
Time taken by A & B to complete the work=45/2 days
=22 1/2 days