The present age of Ram is 25 years and Mohan is 10 years younger than Ram. Find after how many years the ratio between their ages will become 16 : 11.

Options

A. 5 years
B. 8 years
C. 7 years
D. 6 years

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the present ages of Ram and Mohan.
- Ram's present age = 25 years.
- Mohan is 10 years younger than Ram, so:
\[ \text{Mohan's age} = 25 - 10 = 15 \text{ years} \]

### Step 2: Let \( x \) be the number of years after which the ratio of their ages will be 16:11.
- After \( x \) years, Ram's age will be:
\[ \text{Ram's age after } x \text{ years} = 25 + x \]
- After \( x \) years, Mohan's age will be:
\[ \text{Mohan's age after } x \text{ years} = 15 + x \]

### Step 3: Set up the equation based on the given ratio.
- According to the problem, the ratio of their ages after \( x \) years will be:
\[ \frac{25 + x}{15 + x} = \frac{16}{11} \]

### Step 4: Cross-multiply to eliminate the fraction.
- Cross-multiplying gives:
\[ 11(25 + x) = 16(15 + x) \]

### Step 5: Expand both sides of the equation.
- Expanding both sides:
\[ 275 + 11x = 240 + 16x \]

### Step 6: Rearrange the equation to isolate \( x \).
- Rearranging gives:
\[ 275 - 240 = 16x - 11x \]
\[ 35 = 5x \]

### Step 7: Solve for \( x \).
- Dividing both sides by 5:
\[ x = \frac{35}{5} = 7 \]

### Conclusion
- Therefore, after 7 years, the ratio of their ages will be 16:11.