Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 4)
4.
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
20 days
22 1 days
2
25 days
30 days
Answer: Option
Explanation:

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

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

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

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

So, A takes 30 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 + 1 = 4 = 2
30 90 90 45

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

Discussion:
281 comments Page 4 of 29.

OM PRAKASH REDDY said:   7 years ago
NO RATIO'S.

A is thrice as good as B.
This implies that if B take '' T '' days to complete the work, then A takes just ''T/3" days for same amount of the work.

Now coming to the second point in the question, A takes 60 days less than what B takes.

T/3 = T - 60.

----> T=90, ao B takes 90 days alone which implies A takes 30 days alone to complete work.

If A and B work together then no.of days required would be (1 / (1/30)+(1/90) ) which results in 22.5days.

Sundar said:   2 decades ago
Hi Friends!

The statement "A is thrice as good as workman as B" states that, If A complete a work in 1 day, B will take 3 days to complete the same work.

Therefore, if A takes 1 day, B takes 3 days, the time difference is 2 days.

If the time difference is 2 days, B takes 3 days to complete the work.

Similarly if the time difference is 60 days, then B takes (3/2*60) = 90 days.

Then A takes 90 - 60 = 30 days to complete the work.

It is very simple man.
(1)

Pratim Pal said:   10 years ago
Hi friend.

This is one of easiest problem.

Here given that the ratio of time taken of A and B to complete one work in individually is 1:3.

So let us take A can do this work in X days and that of B is 3X days.

According to conditions B took 60 days more than A.

3X-X = 60.

2*X = 60.

X = 30.

So time taken by B is 3*30 = 90 days and by A is 30 days.

When A&B together do this work. The required time is:

= 1/(1/30+1/90).

= 1/((3+1)/90).

= 45/2 days.

Man said:   3 years ago
Given A:B = 1:3 => B = 3A.'

Let assume A can complete work in x days which implies B = 3x
and also given B-A = 60 => 3x-x = 60 => 2x = 60 => x = (60/2) => 30

therefore A can complete the work in 30 days. and B can complete the work in 3*30 = 90 days
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 = 1.
x = 90/4 = 45/2 = 22 1/2.
(47)

Aravind said:   6 years ago
Hi, friends, it's a bit tricky.

First, they found the time difference to do work between a and b.
Because the data we have is time difference in qn for 60 days consider.

Then. If a takes 1 day. B takes 3 days. So.

For 2 days time difference : 3 days for b

Then multiply both sides by 30 since the time difference is given

For 60 days time difference: 90 days of b.

I hope you all get it.

Then use ratio. A takes 30 days to complete work.

Anonymous said:   9 years ago
Hello friends,

I just want to clear out something and that is according to the formula given. Here the answer is not correct.

There has been a mistake and that is it is wrongly solved becomes as the question goes hereby,

1) A is thrice as good as B so the ratio would be like 3:1. But it has been mentioned as 1:3 which is wrong according to my perception.

So please make it correct or give the correct sort of explanation to prove me wrong.

Pranay said:   1 decade ago
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.

Soniya said:   9 years ago
Let t1 &t2 are time taken by A and B.
w1 & w2 are work done by A and B.

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

Then, A = x, B = 3x (x is some constant).
We know that t1 = t2 - 60 (A takes 60 days less than B).
t2 - t1 = 60
3x - x = 60 (t1 = x, t2 = 3x)
x = 30.
Then t1=30 and t2 = 90.
Total work done by A& B(W) = w1 + w2.
W =1/t1 + 1/t2.
= 1/30 + 1/90 = 2/45.
Then time taken by A&B to finish the work is 45/2days.

HMJ said:   4 years ago
A=3B,
A can finish the job 60 days less then B,
Say, work=60.

Capacity of B = (60/x) ----> 1
Cap of A = (60/x-60) ----> 2.

As per the condition A=3B.

Compare the above equation by putting the Capacity of A = 3 times Capacity of B.

You will get x=90.
Now put this x in above equations 1 and 2.
You will get the cap of A = 2 and Cap of B = 0.66.

Working together,
Days= Work/(cap of A + cap of B).
= 60/2.66,
= 22.5.
(1)

Sai said:   6 years ago
A is thrice as B, A:B=1:3.

B takes 60 days more than A to complete the work.

Lets consider A to complete the work in x days, therefore, B completes the same work in (x+60) days, x:(x+60).

Therefore,
As these are equally related to one and other;
1:3::x:(x+60).
Cross multiply we get x=30 days ie A can finish the work in 30 days,
Therefore B can do it in 90 days ie 3 times more days given.
Therefore:
(1÷30)+(1÷90).
= 22.5 days.


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