Aptitude - Time and Work - Discussion

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.

@ 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.