A, B and C together can do a work in 4 days, while B alone can do the same work in 24 days. If efficiency of C is 300% more than that of B, then find the difference between number of days taken by A and C to complete the work alone?

The correct option is 18.

Let's break down the problem step-by-step to find the difference between the number of days taken by A and C to complete the work alone.

Step 1: Understand the given data

Let total work be calculated based on the rate of work done by each person.

B alone can complete the work in 24 days.

Let the work efficiency of B be x units/day.

Therefore, Total Work = Efficiency of B × Time taken by B

Total Work = 24x units

Step 2: Determine the efficiency of C

The efficiency of C is 300% more than that of B.

Efficiency of C = x + 300% of x

$\text{Efficiency of C}=x+3x=4x\text{units/day}$

Step 3: Determine the efficiency of A

A, B, and C together can finish the work in 4 days.

$\text{Combined efficiency of (A + B + C)}=\frac{\text{Total Work}}{\text{Time taken together}}=\frac{24x}{4}=6x\text{units/day}$

Now, substituting the efficiencies of B and C into the combined efficiency equation:

$\text{Efficiency of A}+\text{Efficiency of B}+\text{Efficiency of C}=6x$

$\text{Efficiency of A}+x+4x=6x$

$\text{Efficiency of A}+5x=6x$

$\text{Efficiency of A}=6x-5x=x\text{units/day}$

Step 4: Calculate the days taken by A and C to finish the work alone

Time taken by A alone =

$\frac{\text{Total Work}}{\text{Efficiency of A}}=\frac{24x}{x}=24\text{days}$

Time taken by C alone =

$\frac{\text{Total Work}}{\text{Efficiency of C}}=\frac{24x}{4x}=6\text{days}$

Step 5: Find the difference between the number of days taken by A and C

$\text{Difference}=24-6=18\text{days}$

Thus, the difference between the number of days taken by A and C to complete the work alone is 18 days.