A question related to work and time concept Question is,
The ratio of the efficiency of p q and r is 2:3:5. The total wages of p, q and r  working for 14,24 and 20 days respectively are 6000. Find the total wages of the three if p works for 9 days, q work for 14 days and r for 8 days.
For this question, in the solution, the ratio of efficiency is taken as the ratio of wages to be distributed per day. The solution then goes on to say thus, for their work for the respective days, we can formulate:
$2*14x + 3*24x + 5*20x = 6000$
I know that the wages will be distributed according to the total amount of work done by the person which is the amount of work done per day multiplied by total number of days. But here, we are taking the amount of work done per day as the efficiency of the person which I don't understand why. If I am doing $\frac{1}{5}$ amount of work per day then having $20%$ efficiency would mean I am doing $\frac{1}{25}$ amount of work per day. Thus efficiency is not the same as work done per day. Then why have we taken the ratios of efficiency here to be the same as the ratio of amount of work done per day?
 A: Dividing the total salary of 6000 according to the proportions $2:3:5$, p would be paid a salary of 1200, q that of 1800 and finally r that of 3000.
This on a total of 58 days of work.
But the fictitious days of work are divided as follows:
p has fictitiously worked for 11.6 days,
q for 17.4 and
r for 29 fictitious days.
But p actually worked for 14 days;
therefore the remuneration is equal to:
$\frac{1200*14}{11.6}=\frac{42000}{29}$;
while for q we have:
$\frac{1800*24}{17.4}=\frac{72000}{29}$;
finally for r we have:
$\frac{3000*20}{29}=\frac{60000}{29}$.
In fact, the sum of the three salaries is:
$=\frac{42000}{29}+\frac{72000}{29}+\frac{60000}{29}= \frac{174000}{29}=6000$.
Now by implanting three simple propositions we can obtain the actual wages of p, q and r.
If p in 14 days has earned $\frac{42000}{29}$,in 9 days he earns $\frac{27000}{29}$,
if p in 24 days has earned $\frac{72000}{29}$,in 14 days he earns $\frac{42000}{29}$,
if r in 20 days has earned $\frac{60000}{29}$,in 8 days earns $\frac{24000}{29}$.
The total salary is:
$\frac{27000}{29}+\frac{42000}{29}+\frac{24000}{29}=\frac{93000}{29}$.
