Aptitude - Time and Work - Discussion

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.

Ratio of A:B=1:3(efficiency).
=3:1(time will be opposite of efficiency).
Time difference between A:B=2.
2 denotes =60,
1 denotes=60/2=30 A,
3 denotes =60/2*3=90 B calculate L. C. M of A &B = 90,
A+B=90/4= 22(1/2)-Ans.

W1/w2 = d2/d1.
W1 = 3w2.
And d1 = d2-60.
So,
3w2/w2 = d2/d2-60,
d2 = 90,
d1 = d2 - 60 = 90 - 60 = 30.
1/90 + 1/30 = 1/22.5.
Ans 22 * 1/2.

If A completes the work in x days, B will do the same in 3x days.

3x - x = 60.
2x = 60.
Then x = 30 and 3x = 90.
(A + B) 's 1 day's work.
=1/30 + 1/90.
= 4/90.

So, A and B together will do the work in;

= 90/4.
=>22 and 1/2.

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.

Thanks everyone.

a ------ b
x ------ 3x.

1/3 of the work is remaining = 1 - 1/3.
= 2/3.

2/3 of the work is completed by b = 60 days.
one of the work is completed by b = 60 * 3/2.
b = 90.
B one day work = 1/90.
A one-day work = 1/30.
a+b = 1/30 + 1/90.
a+b = 4/90
a+b = 2/45.

A and B together can do the work = 45/2.

The ratio of time taken by A and B is 1:3.
Now, if B do the work in x days, then A can do it in x-60 days.
So for A its ---> 1/x-60.
And for B its ---> 3/x.

So, 1/ x-60 = 3/x.
x = 3x - 180.
x = 90.

Now A can do it in 90-60 = 30 days.
B can do it in 90 days.

If they work together 1/30 + 1/90 = 45/2 => 22 1/2.