Aptitude - Time and Work - Discussion

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 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.

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.

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.

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

"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].

The work being done by A & B is in ratio of 1:3.

This means if A does a work in 1 day, than B will do this work in 3 days.

Now let suppose this ratio is multiplied by a factor, say x.

Then ratio becomes x:3x.

Now another relation given is that A can do work 60 days faster then B. Mathematically we can write it as.

x=3x-60.

Solving this, we get x = 30.

Hence the ratio becomes 30:60.

Now we can calculate the time taken by them.

Lets B takes x days to complete the Work,

Then B 's Capacity ==>1/x.
A is 3 times as good as A so A'S capacity is 3/x.

Then Time Taken by B is = x/1.
Time taken by A is = x/3.

Time difference (x-x/3)=60.

Which gives x = 90.
Time taken By B = 90.
Time taken By A = 30.

(A's Work +B's Work) 1 day Work = (1/30)+(1/90).
= 4/90.

Then Time taken to complete work is 90/4 ==> 22.5 days.

How its "4/90 " ?

Guys,

I'll tell by simple method.
Given, A is thrice of B.

So A = 3B---->(1).
A's 1 day work is A=1/60--->(2).

Substitute (2) in (1),
A=3B.
We get,
3B=1/60.
B=1/180.

In question they asked A+B=how many working days?
We know A and B values.

Add A and B.
1/60+1/180=1/Work days.
Take L.C.M.

3+1/180=1/Work days.
4/180=1/work days.
1/45=1/work days.
Work days=45.

By fraction we can write 22 1/2 days.