Aptitude - Time and Work - Discussion

Total work= 299.
A+B= 13+10=23.

Total time= 299/23= 13.

A takes 23 days to finish a work.

Since A is 30% more efficient than B, so obviously B will take 30% of time more than A to complete a work.

B=(A+30% of A),
=(23+(30/100)*23),
=(23+(69/10)),
=299/10.

So B takes 299/10 days to complete the work alone.

Now, A and B together 1 days work ((1/23)+(10/299)),
=1/13.
So both complete the work in 13 days.
HOPE THIS WILL HELP U TO UNDERSTAND THE PROBLEM IN A SIMPLE WAY.

A alone takes 23 days to finish a job.

since A is 30% more efficient,
so B takes( A+30%(A) ) days,
i.e.,B takes ( 1.3*A = 1.3*23 ) days to complete it alone [ since A=23],
(A+B)'s one day work = ( 1/23 )+( 1/(1.3*23) ),
(A+B)'s one day work= 1/13.

Hence it takes 13 days for A alone to finish the work.

A is R% more than B, then B is less than A by.

(((R/(100+R)) * 100)%

Based on this formula,

We cant use A = 100% B = 70%.

As per the given data;

A = 130%B.
then
A = 130/100 B.
1/23 = 130/100 B. (as we know A=1/23)
B = 10/(13*23),
B = 10/299.

A and B together work is;
1/23 + 10/299,
23/299,
= 1/13.
Hence 13 days.

Thank you @Pratyusha.

Since A is more efficient, hence the ratio of time taken by A and B is 100:130 Or A:B = 10:13.

A alone can do the whole work in 23 days(time taken by A to complete the whole work)

Let time taken by B to complete the whole work be=x

Since time ratio is already with us, hence
23/x=10/13,
X=23 *13/10,

Hence
A 1day Work = 1/23,
B 1day work=10/23 * 13,

(A+B) 1day work=1/23 + 10/23*13,
(A+B) 1day work=(10+13)/23*13,
(A+B) 1day work=1/13.

Therefore (A + B) takes 13 days to complete the work if they work together.

Thanks @Nishant. Your answer is understandable.

As A is 30% efficient then B.
A = 13 work per day.
B = 10 work per day.
Total Work= 13 * 23 = 299.
No of days by (A & B) = 299/23 = 13.

A is 30% more efficient than B --A=1.3B.
A's 1 day work=1/23

Since A=1.3B
B's 1day work= 1/(1.3*23)=1/29.9.
A+B 's 1day work= (1/23+1/29.9)=1/13.
So 13 days.