Ratio of present age of A to that of B is 2:5, ratio of present age of B to that of C is 25: 18 and, ratio of present age of C to that of D is 12:13. If D is 11 years younger than B, then find present age of A.

Options

A. A)24 years
B. B)20 years
C. C)28 years
D. D)30 years

Answer

To solve the problem step by step, we will first express the ages of A, B, C, and D in terms of a common variable based on the given ratios.

### Step 1: Express the ages in terms of a variable
Given the ratios:
- The ratio of the present age of A to B is 2:5.
Let A's age = 2x and B's age = 5x.

- The ratio of the present age of B to C is 25:18.
Since we already have B's age as 5x, we can express C's age in terms of x:
\[ \frac{B}{C} = \frac{25}{18} \implies \frac{5x}{C} = \frac{25}{18} \implies C = \frac{5x \cdot 18}{25} = \frac{90x}{25} = \frac{18x}{5}. \]

- The ratio of the present age of C to D is 12:13.
We can express D's age in terms of C's age:
\[ \frac{C}{D} = \frac{12}{13} \implies \frac{\frac{18x}{5}}{D} = \frac{12}{13} \implies D = \frac{\frac{18x}{5} \cdot 13}{12} = \frac{234x}{60} = \frac{39x}{10}. \]

### Step 2: Set up the equation based on the relationship between B and D
We know from the problem that D is 11 years younger than B:
\[ D = B - 11. \]
Substituting the expressions we found:
\[ \frac{39x}{10} = 5x - 11. \]

### Step 3: Solve for x
To eliminate the fraction, multiply the entire equation by 10:
\[ 39x = 50x - 110. \]
Rearranging gives:
\[ 110 = 50x - 39x \implies 110 = 11x \implies x = 10. \]

### Step 4: Find the present age of A
Now that we have x, we can find A's age:
\[ A = 2x = 2 \cdot 10 = 20. \]

### Conclusion
The present age of A is **20 years**.

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