The average age of A, B & C is 48 years. Ratio of present ages of A to C is 3:5 and present age of B is 33.33% more than that of A. find the difference between age of A after 5 years to age of B two years ago.

Correct Answer: 5 years

Step-by-Step Explanation:

Step 1: Calculate the total sum of the present ages of A, B, and C

We are given that the average age of A, B, and C is 48 years.

$\text{Total sum of present ages}=\text{Average age}\times \text{Number of persons}$

$A+B+C=48\times 3=144\text{years}$

Step 2: Express the ages in terms of a variable

The ratio of the present ages of A to C is 3 : 5.

Let the present age of A be 3x years and the present age of C be 5x years.

We are also given that the present age of B is 33.33% more than that of A.

Since 33.33% is equivalent to the fraction 1/3, the age of B can be written as:

$B=A+\frac{1}{3}\times A=\frac{4}{3}\times A$

Substituting A = 3x into the equation for B:

$B=\frac{4}{3}\times 3x=4x\text{years}$

Step 3: Solve for x and find the present ages

Now, substitute the values of A, B, and C in terms of x into the total sum equation:

$3x+4x+5x=144$

$12x=144$

$x=\frac{144}{12}=12$

Therefore, the present ages are:

Present age of A = 3x = 3 × 12 = 36 years

Present age of B = 4x = 4 × 12 = 48 years

Step 4: Find the required difference

Age of A after 5 years = 36 + 5 = 41 years

Age of B two years ago = 48 - 2 = 46 years

Difference between age of B two years ago and age of A after 5 years:

$\text{Difference}=46-41=5\text{years}$