Alice can complete a certain work in 24 days. Bob is twice as efficient as Alice. Both of them worked together for x days and stopped. The remaining work was completed by Carol working alone for (x+1) days. If Carol is 25 % less efficient than Bob, then the total number of days it took to complete the whole work was

Given that Alice completes a certain work in 24 days.

Fraction of work done by her in 1 day = $$\dfrac{1}{24}$$

Also, it is given that Bob is twice as efficient as Alice.

Fraction of work done by him in 1 day = $$\dfrac{2}{24}$$ = $$\dfrac{1}{12}$$

Fraction of work done by both in 1 day = $$\dfrac{1}{12}+\dfrac{1}{24}\ =\ \dfrac{1}{8}$$

Fraction of work done by both in $$x$$ days = $$\dfrac{x}{8}$$

Carol is 25 % less efficient than Bob. So Carol completes the work in $$\dfrac{4}{3}\times\ 12=16  days$$ working alone from scratch.

She works for $$x+1$$ days. Fraction of work done = $$\dfrac{x+1}{16}$$

So,

$$\dfrac{x}{8}$$ + $$\dfrac{x+1}{16}$$ = 1 (entire fraction of the work is done by the trio)

$$\dfrac{3x+1}{16}=1$$

$$x=5$$. Alice and Bob work for 5 days.

$$x+1=6$$. Carol works for 6 days.

The entire work is finished in 11 days.