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:
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'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].

What is the meaning of taking 3/2 in the problem. What's that ratio about?

If A does a work in 1 day.
therefor B does the same work in 3 days since A is thrice as good as workman as B.

Let A completes the work in x days, B will take (x + 60) days more than A takes.

Therefore 1:3 :: x :(x + 60).
Now according to the formula if a:b :: c:d.
Then it is considered as (a * d) = (b*c).

Applying this formula we get 1*(x + 60) = 3*x.
By solving we get x= 30 i.e A takes 30 days to complete the work.
Therefore B will take (30+60)=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.

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.

Let A takes x days and B takes 60+x days.
Its given that A takes 1 days when B takes 3 days.

So,
1/3 = x/x+60.

Cross multiply and we get x = 30 i.e A.
X+60 = 30 + 60 = 90 i.e B.

Remaining as usual.

Simple:

A's work = x.
B's work = y = 3x.

Hence acc. to ques.: 3x - x = 60 ;.
x=30 A's.
y=90 B's.

Now.... 1/30 + 1/90 = 1/z.

z = 90/4 Answer.

Let,

A takes = x days.
B will take = 3x days.

Difference 3x-x = 60.

So 2x = 60.
x = 30 days.

Thus A can do it in 30 days and B in 90 days.

If difference of time is 60 days, B takes 3/2 x 60 = 90 days.

Please explain this statement.

But there is not given difference in question they given A finish work in 60 day?

If B takes y days , A takes (y-60 ) days. Now , their efficiency are A:B = 3x : x.

So total unit of work is 3x*(y- 60 ) man days = x*y man days.

Calculating this we get y = 90. So if B worked for 90 days, A worked for 30 days.

Hence 1/30 + 1/90 = 22 1/2 days :).