Aptitude - Time and Work - Discussion

I think it is 100:30 ans is wrong please explain how it is 100:130?

It is given that A is 30% efficient than B,it means that A can do better WORK than B, so the time time taken by A will obviously be less than by B.

So, their ratio of times taken by A and B will get reversed. (As from the problem).The ratio of A and B work is 130:100, but the time taken by them to complete will get reversed that is 100:130.

Thank you!
CORRECT ME IF I AM WRONG PLEASE!

Why we consider 10:13::23:x ?

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.

In the problem while adding A+B why they have written 10/299 instead of writting 299/10 ?

@nayana
A can complete the work in 23 days.
A's 1 day work is 1/23
in similar manner
B can complete the work in 299/10 days
then B's 1 day work is 10/299
now they considered (A+B) 1 days work
therefore,(1/23)+(10/229)=1/13

I can explain why ratio 100:130 comes, as in problem it is given that A is 30% more effificient than B. That is A can do work in Less time so ratio By time will be A:B = 100:130 that is Time taken by A is 100 and B by 130 .......

A s 30% more eff...
i.e
A -> x(1+30/100) = 1/23
=> x(13/10) = 1/23
therefore
B -> x =10/299
add A+B u ll get 1/13
hence ans is 13

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

Here why dont we use shortcut formula (K*X)/{(k^2)-1}???.

Can any one clear my doubt??