Aptitude - Time and Work - Discussion

For those who have difficulty with fractions, here is an alternative.

Let the total work be to lay 120 bricks. (I chose 120 as it can be divided easily by both 15 and 20).

Takes 15 days to lay 120 bricks, That means in one day he can lay 8 bricks.

B takes 20 days to lay 120 bricks. That means B can lay only 6 bricks in one day.

Together they can lay 8+6=14 bricks.

Therefore, in 4 days, they will lay 14*4= 56 bricks only.

Remaining bricks to be layed is 120-56=64 bricks.

That means, 64/120=8/15 of the work is remaining.

Fraction of work done in 4 days = 7/15.
(It means that out of 15 parts, 7 parts has been done. So 8 parts left)

Therefore, the fraction of work left = 8/15.

Why you subtract 7/15 from 1?

Thank you, everyone those have written explanation here. It really helps.

In how many days A & B together complete the same job?

Elaborate how you do this (1/50+1/20) where did you get 1/50?

For the Question of @Raju,

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

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

=> 300/35 = 8.6 days.

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.

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.

Why 1 - 7/15? Explain it.