Aptitude - Time and Work - Discussion

A+B = (1/30 + 1/90) = 2/45.

How we are getting this?

A - 30d.
B - 90d.
lcm - 90(total work).
Efficiency of A - 3.
Efficiency of B - 1.

Total Efficiency = 4 total.

work/totalEfficiency=90/4=22.5.

Here a simple calculation is;
A takes 1 part and B takes 3 parts.
\
So A:B ratio is 1:3.
total 4p.and the difference is 2,they did work in 60 days so 60p.
4p=60.
p=15/1.
B total working days 15*3=45.
W/t is 45/2.

3/1 = (B)/(B-60).
As work done and time are inversely related,
so, B=90, A=30.
(1/90+1/30)=(2/45),
So, 22 1/5.

@All (Must read if you have any doubts)

If B takes 3 days then A takes 1 day to complete the task.

Time taken Ratio => A : B = 1 day : 3 days.

1 3 (difference is 2)

10 30 (diff 20)

30 90 (diff 60) <= Here diff is 60 days, So this is the correct ratio to be used in calculation, since it was mentioned in the given question.

A alone can finish the task in 30 days.
B alone can finish the task in 90 days.

Work done by A alone in 1 day = 1/30
Work done by B alone in 1 day = 1/90

Work done by A and B in one day (1/30 + 1/90) = 3+1/90 = 4/90

The no. of days required to complete the task by A and B is
= 90/4
= 22.5 days.

////**** Important Note: ****////

We cannot take other ratios like 1:3, 10:30, 40:120, 60:180 for the calculation. Since the diff is mentioned as 60 days.

Because, it will give different answers for each different ratios used for calculation.

If we take 1:3 => (1/1 + 1/3) = 4/3

If we take 10:30 => (1/10 + 1/30) = 4/30

If we take 40:120 = (1/40 + 1/120) = 4/120

If we take 60:180 => (1/60 + 1/180) = 4/180 ... so on.

I hope this will help you. Have a nice day!

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.

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.

Hi Guys,
I think following simple method (alternate) will make you more clear,

A can complete work in N days => A's 1day work = (1/N)----1
B can complete work in n days => B's 1day work = (1/n)----2

Given data,
A thrice as B so , A=3B
A complete work 60 days less than B so, (N=n-60)

Apply in 1 & 2

A's 1day work = (1/(n-60))-----3
B's 1day work = (1/n)--------4

we know that A=3B ; B=(1/n) so,Apply B in A we get[A=3/n]

Apply in 3

3/n=(1/(n-60))
by solving,
3n-180=n
n=90
so, B can complete work in 90 Days => B's 1 Day work =(1/90)
we know that N=n-60,
so, A can complete work in 30 Days => A's 1 Day work = (1/30)

(A+B) 1 Day work = (1/30 + 1/90)
by solving we get,
A+B 1 Day work = 2/45,
so A and B together can complete work in 45/2 Days.

A is thrice as good as workman as B so the ratio of time taken by A and B is = 1:3.
Let, A completed the work in x days.
B completed the work in 3x days.

A's 1-day work= 1/x and B's 1-day work= 1/3x,
So, A+B 's 1-day work= 1/x+1/3x,
=4/3x.

So, A+B completed the work in 3x/4 days.
Since,
A finishes a job in 60 days less than B.
therefore , 3x-x=60.
x=30.
therefore, Working together A+B completed the work in 3x/4 days.
= 3*30/4.
= 45/2.
= 22 1/2 days.

Work=3:1.
Time 1:3.
2 part=60 (difference).
1 part=30.

1*30:3*30=30:90.

He asked work of B( 90)can do by both in how many days.
90/(1+3)= 90/4=22.5 days.