How to solve this work and time problem?

Question

A can complete a work in 20 days. B is 66.67% as efficient as A. A and B work together. A leaves after working for some days. The remaining work is done by B in 10 days. After
how many days did A leave the work?

I am a little confused as it says that B is 66.67% as efficient as A. I want to know whether B is 66.67 % more efficient than A or the other way around.

The answer to the above question is 8 days.

It means that B's efficiency is $\frac23$ of A's. In a given time, B can do $\frac23$ of the work that A can do. — saulspatz, Aug 09 '21 at 16:32
are you wanting confirmation whether its right or wrong or what? — AYUSHROCKS123, Aug 09 '21 at 17:30
Steven, My bad, I corrected the question. It is a instead of Ramesh. — Dark Devil, Aug 09 '21 at 17:56
@AYUSHROCK123 I want to know what does "B is 66.67 % as efficient as A means. Suppose A does a work in 100 days, B being 66.67% as efficient as, A how long it would take for B to complete the same work ? — Dark Devil, Aug 09 '21 at 18:00
We are given that A's rate of work is $\frac{1}{20}\frac{\text{work}}{\text{day}}$ (i.e. $1$ work per $20$ days), and the meaning is that B's rate of work is $\frac{2}{3} \cdot \left(\frac{1}{20}\frac{\text{work}}{\text{day}}\right) = \frac{1}{30}\frac{\text{work}}{\text{day}}$ (assuming $66.67%$ is an approximation for $\frac{2}{3}).$ In case it could help, about 1.5 years ago I gave a very elaborately detailed answer to a question similar to your question. — Dave L. Renfro, Aug 09 '21 at 18:11

score 1 · Accepted Answer · answered Aug 10 '21 at 06:57

We define a unit of work $L$ equal to the product of unit efficiency for one day: $L=e g$.

If the work were to be done only A in 20 days, with an efficiency of $100%$, the work units would be equal to:

$L_{A}=100.20=2000$ (work units);

if only B were to do the job, with an efficiency of $66.67%$, it would take $30$ days. But in $10$ days B runs $666.67$ work units.

Ultimately, in the first part the work is performed by both A and B, namely:

$100x+66.67x$,

(where $x$ are the days),to which must be added the work done by B in the remaining $10$ days:

$100x+66.67x+666.67=2000$,

from which

$x=8$ days.

How to solve this work and time problem?

1 Answers1