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.

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.

A completed this in 15 days.
Then, A completed this work in 1 days = (1/15).

B completed this work in 20 days
Then, B completed this work in 1 days = (1/20).

Both A and B both completed this work in 1 days = (A+B)
= ((1/15)+(1/20)).
then, the LCM of 15 and 20 is 60;

we get,
((1*4)+(1*3)/60))
= 7/60.

A and B both completed the same work in 4 days = ((7/60)*4)
= 7/15.

Let's take total work is = 1.
then we know that,

Rest work= total work - completed work.
= 1 - (7/15).
= (15-7)/15.
= 8/15 Answer.

@Rashmi, @Satish : 1/15 + 1/20 Now to make the denominator value equal take LCM i.e. ,
= (1*20) / (15*20) + (1*15) / (15*20) Now simplify these,
i.e. , multiply the values i.e. ,
= (20/300) + (15/300).
Now, both the denominator are equal, so you can add the numerator values i.e. , = (20+15) /300 = 35/300,
Now simplifying this i.e. , cancelling both numerator and denominator by 5 (a common value which both will get cancel) ,
We get 7/60. Hope this will help you to understand the problem.

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),
= 20+15/300(cross multiplication),
= 35/300,
= 7/60.

(A+B)'s 4 day's work= 7/60 * 4,
= 7/15(60/4 is division it is 15).

Therefore remaining work=1 - 7/15,
= 15-7/15,
= 8/15.

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

OK. Then we calculate how much A + B can do in 1 day.

i.e. 1/15 + 1/20 ( in fraction if denominator is different first we find the l.c.m of denominator). So we calculate the l.c.m of 15 and 20 i.e 60(15 and 20 is divided by 5 we get the answer 3 and 4 so we find l.c.m by multiplying 5*3*4=60). 1/15*60+1/20*60 = 4+3/60 = 7/60.

If A and B do work in 4 days = 7/60*4 = 7/15.

Remaining work = 1-7/15 = 8/15 [ (15*1-7)/15 = 8/15.

Hi friends,

A's 1 day work=1/15; B's 1 day work=1/20
OK.Then we calculate how much A + B can do in 1 day.
ie 1/15 + 1/20 ( in fraction if denominator is different first we find the l.c.m of denominator).so we calculate the l.c.m of 15 and 20 ie 60(15 and 20 is divided by 5 we get the answer 3 and 4 so we find l.c.m by multiplying 5*3*4=60).1/15*60+1/20*60=4+3/60=7/60.
if A and B do work in 4 days=7/60*4=7/15

Remaining work=1-7/15 = 8/15 [ (15*1-7)/15 = 8/15 ].

LCM 15, 20 will give you 60 (the total work).

LCM of 15 and 20,

5*3 = 15.
5*4 = 20.

THEREFORE, 3*4*5 = 60.

1 day work of A = 60/15 = 4.
1 day work of B = 60/20 = 3.

1 day work of A and B together = 4 + 3 = 7 / 60.

A and B worked together for 4 days = 4 * 7/60 = 28/60 = 7 / 15.

Therefore,

Work left = Total work - Work done in 4 days by A and B together.

Work left (IN FRACTIONS) = 1 - 7/15 = (15-7)/15 = 8/15.

Thank you for giving me an opportunity.

@Pravin Hambire

Q. How 7/60 came ?

See 1/15 +1/20

Now find the lcm of 15 and 20, it is 60.

Now if you divide 60 by 15 quotient is 4. So mulitply 1/15 with 4, it will become 4/15 .

Again divide 60 by 20. Quotient is 3, now multiply 1/20 with 3. It will become 3/20.

Now you alredy know that lcm of 15 nd 20 is 60. So write 60 in denominator.

Now add the quotient which is 3 nd 4 and write it in numerator.

So finally 7/60 .

Hope you got it.

A, completes the work in 15 days so, the work done by A in 1 day = 1/15.

Similarly, B completes the work in 20 days therefore work done by B in 1 day = 1/20.

A and b work together = 1/15+1/20 i.e. => 14/120 => 7/60.
Now, they both worked for 4 days which will be = 4*7/60 => 7/15.

Let's suppose the total work is x and they have already worked for 4 days.
Therefore remaining work is x -7/15 (for more clarity take x-7/15 = 0) => 8/15.