Aptitude - Time and Work - Discussion

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.

@All.

This is the easiest & shortest!.

Let a be x whereas b = 3x.
So, 3x " x = 60. x = 30.
therefore a = 30, b = 90.
so when they work together-> 1/30+1/60 = 4/90 = 2/45.

Together they can do the work in 22 (1/2) days.

Your explanation is easy, thanks @Showry.

3A = B.

If 60 is less than b(then 60 is two times of a)
then A=30,
b = 3 * 30 = 90,
a+b=1/30+1/90,
3*1/90+1/90,
(3+1)/90.

Where 4/90(to get days upside down).
90/4 = 22(1/2) days.

It's simply.
3a = b.

A+B = 1/60 + 1/180.

A is three times more efficient than B.

(So that if a takes 60 days then B takes 180 days).
And therefore;
2(A+B) = 180/4 = 22 * 1/2.

A : B
TIME 1/3 : 1.
DAYS X-60 : X.

X-60/X = 1/3,
X= 90,
X-60 = 30.
A work efficiency = 1/90,
B work efficiency = 1/30,
A+B work efficiency = 1/90+1/30,
= 2/45,
work efficiency = work/time.
work is constant,so time = 45/2.
= 22.5.

Thank you, excellent explanation.

a = 3b --> (1).

a-b = 60.
3b-b = 60.

2b = 60.
b = 30.
If b = 30 then from 1a = 3 x 30 = 90.

Now,
= 1/30+1/90.
= 3+1/90.

= 4/90 = 2/45.
= 45/2 = 22.5 days.

Let A=X ,B=X+60 (GIVEN A TAKES 60 DAYS LESS THAN B,I CONSIDERED B TAKES 60 MORE DAYS THAN A).

Now, LCM OF X,(X+60) = X*(X+60),
Efficiency of A=(X*(X+60)) / X = X+60,
Efficiency of B=(X*(X+60)) / (X+60) = X.

Total work of A&B = (X(X+60))/(X+X+60),
We have A=3B (GIVEN).
X = 3(X+60),
X = 30.

Put in the equation and get the answer 45/2 =22(1/2).

The solution is;

A = x ,
B = 3x
x = 3x-60
x = 30
A = 30; B = 90;
1/30 + 1/90 = 2/45 = 22.5 days.