Aptitude - Time and Work - Discussion

'A' is 30% more Efficient than 'B' that means


A --------- B
100% -------- 130%

to complete 100% of work 'A' took 23 Days i.e;
100% -----------------> 23 days.
130% -----------------> x days (need to find) 130% = (130/100) & 100% = (100/100).

By Cross Multiplying we get;

(130/100) *23 = x * (100/100).

=> x = (130/100) * (100/100) * 23.

=> x= (299/10) --------------------> This is the B value that we found now substitute these A and B values i.e

(A+B) = (1/23) + (10/299).

After Calculation we'll get;

(A+B) = (23/ 299) = 1/13,

Therefore Answer is 1/13.
That's It.

A is 30% more efficient than B.

This means;

A ------------ B
100%--------- 130%

Now this 100% of work done by A in 23days.
Now
100% ---------------------> 23.
130%----------------------> x.
By Cross Multiplication We get;

100% * x = 23 * 130%,
=> (100/100) * x = 23 * (130/100),
=> x = 23 * (13/10),
=> x= (299/10),

this X work now we got is B's Total Work.

Now Calculate A & B work Together.

ie. (A+B)'s 1 day Work = (1/24) + (10/299)/ LCM is 299.
On Calculating we get answer = 23/299 = 1/13.
So, They Took 13 days to Complete the Work.

Say B does a piece of work in 100 days.
Then as A is 30% more efficient has to complete the work in

100-(30/100)*100=70 days

A's 70 days work = B's 100 days work
so A's 1 day work = B's 100/70 days work

Therefore A's 23 days work = B's 2300/70 days Work

Which implies that 1 work is completed by B in 230/7 days

From this total work done by A & B in 1 day = (1/23)+(7/230)
=(10+7)/230
=17/230
So time taken to complete a work = 230/17=13.529 days


LET ME KNOW IF THIS IS WRONG OR EVEN RIGHT.

Hello its very easy ....
see
A is 30% more efficient than B
that means A=130% speed B=100% speed assume, then convert into ratio format because 13:10 it's work, now we can convert to days 10:13 (this ratio for separate man work days)

we must now ratio formula then only we understand
this method
A:B=A:B
also we write A:B::A:B

now apply
10:13::23:X ( Formula A:B::c:d =>A*d=B*c )

now we can solve that
10X=13*23
X=(13*23)/10
now we got X value X =299/10 days for B
B 1 day work is 299/10
then as usually go next steps

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.

A is 30% more efficient than B.

That means A=130% speed B=100% speed assume, then convert into ratio format because 13:10 it's work, now we can convert to days 10:13 (this ratio for separate man work days)

We must now ratio formula then only we understand,
This method.
A:B=A:B.
Also we write A:B::A:B.

Now apply
10:13::23:X ( Formula A:B::c:d =>A*d=B*c ).

Now we can solve that,
10X=13*23.
X=(13*23)/10.
NNow we got X value X =299/10 days for B.
B 1 day work is 299/10.
Then as usually go next steps.

When A is 30% more efficient than B then,
B's efficiency = 100%.
A's efficiency =130%.

Now,
A takes 23 days to complete 1 or whole job.
A takes 1 day to complete 1/23 job.
According to the question,
130% = 1/23,
1% = 1/23 * 130,
100% = 1*100/23 * 130,
= 10/299 = B's 1-day work.

So, A + B together can do the work in 1 day = (1/23+10/299)
= 23/299 = 1/13.
They can do 1/13 part of the work in 1 day.
So, they can do 1 or whole part of the work in 13 * 1 = 13 days.
Ans: 13 days.

A can do a work in 100 days
B can do a work in 130 days, since A is 30% more efficient than B.
Take LCM of 100 & 130.i.e 1300
A's per day capacity = 1300/100 = 13
B's per day capacity = 1300/130 = 10

Given that A alone can do the given work in 23 days.
Therefore ,work completed by A alone in 23 days = 13 x 23 = 299
if they work together, their per day capacity = 13 + 10 = 23
both together will complete the given work in 299/23 = 13 days

Ans : 13 days

A can do a work in 23 days.

So,
B can do a work in [ 23 + (30/100)*23] = 29.9 days or ~30 days.

Now,
A------------> 23 days.
B------------> 30 days.

LCM(23,30)= 690 (consider it as whole work).

Hence,
A can do 30 part of a work in 1 day.
B can do 23 part of a work in 1 day.

Therefore,
Both A+B can do 53 part of work in 1 day.
Hence, to finish whole work (i.e., 690) (A + B) will take (690/53) = 13.01 days or ~13 days

Here, A's efficiency : B's efficiency = 130:100.
So , A time: B time=100:130 or 10:13.

Now we calculate this,
If A takes 10 days B takes = 13 dyas.
If A takes 1 days B takes = 13/10 days.
If A takes 23 days B takes = (13*23)/10 days =299/10.
So B's 1 day work=10/299 and A's 1 day work=1/23.

So A and B work together = 1/23+299/10 = 1/13.
So total time required to finish this job together = 13 days.

So, answer is 13.