Aptitude - Time and Work - Discussion

Simple that how get 7/60. 15 + 20/15 * 20 = 35 / 300.
So, 7 * 5 = 35 & 60 * 5 = 300. Thats it!

A's 1 day's work = 1/15;
B's 1 day's work = 1/20;

(A + B)'s 1 day's work = (1/15 + 1/20)

LCM = 60

5 | 15 , 20
__________
3 , 4
= 5*3*4 = 60

(A + B)'s 1 day's work = (4/60 + 3/60) ( 4/60 = 1/15 AND 3/60 =1/20 )
= 7/60

(A + B)'s 4 day's work = 7/60*4
= 28/60
= 7/15 .

Therefore, Remaining work = (1 - 7/15)
= (15-7)/15
= 8/15.

A can do the work in 15days, hence he does 1/15 of the work in a day.
B can do the work in 20days, hence he does 1/20 of the work in a day.
Working together, they will do (1/15)+(1/20)= 7/60 of the total work.

In 4 days, they would have done 4 * (7/60) = 7/15 of the total work (E.g they have built 7 houses out of the 15 houses they were to build).

Hence, they need to build 8 more houses to complete their work. That is how we get 8/15 as the FRACTION of work remaining.

I hope that was comprehensive enough.

How to find the solution of this question? Please solve this by easy method.

Please give the short trick 'with efficiency' then the sum will be solved very quickly.

@ Vishwanath.

7/60 * 4 = 7/15.
This is how;
It's like multiplying 7/60 by 4/1 = 7 * 4/60 * 1
This gives us 28/60.
We get a common divisor of the numerator and denominator which is 4.

Hence it is 7/15.

Why 1 - 7/15? Explain it.

Here,
A works 1/15 in 1 day.
B works 1/20 in 1 day.

So, A + B works (1/15 + 1/20) = 7/60 in 1 day.

So, if A + B works together 7/60 in 1 day.
Then A + B works together (7/60 * 4) = 8/15 in 4 day.

If we assume that 1 is the full work and A+B works together 8/15 in 4 days .
The remaining works we get by {full work - (A + B)'s 4 days completed works}.
So , (1 - 8/15) = 7/15.
So, the answer is 7/15.

Since our target is to crack for the competitive exam which means we must do problems as fast as we can to save time, in other words in a short cut way.

Now, for this question, lets suppose they are making chairs (the work).
A takes 15 days. B takes 20 days. Then LCM of 15, 20 is 60.
Capacity of A = 4 chair/day and capacity of B = 3 chairs/day.
So A + B capacity in one day = 4 + 3 = 7 chairs/day,
The question says for 4 days they worked together. ie (7 * 4 = 28).
Remaining = 60 - 28 = 32.
Fraction of work remaining = 32/60 = 8/15.

For the Question of @Raju,

(A + B)'s completion days = (A * B/(A + B)),

=> 15 * 20/(20 + 15),

=> 300/35 = 8.6 days.