The ratio of ages of Suraj and Mohan 4 years ago was `7 : 8` and after 5 years from now, their ratio will become 10 : 11 . Find the present age of Suraj

Options

A. A)24 years
B. B)25 years
C. C)28years
D. D)21 years

Answer

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let Suraj's present age be \( S \) and Mohan's present age be \( M \).

### Step 2: Set Up the Equations from Given Ratios
According to the problem:
1. Four years ago, the ratio of their ages was \( 7:8 \).
- This can be expressed as:
\[ \frac{S - 4}{M - 4} = \frac{7}{8} \]
Cross-multiplying gives:
\[ 8(S - 4) = 7(M - 4) \]
Expanding this, we have:
\[ 8S - 32 = 7M - 28 \]
Rearranging gives us:
\[ 8S - 7M = 4 \quad \text{(Equation 1)} \]

2. Five years from now, the ratio of their ages will be \( 10:11 \).
- This can be expressed as:
\[ \frac{S + 5}{M + 5} = \frac{10}{11} \]
Cross-multiplying gives:
\[ 11(S + 5) = 10(M + 5) \]
Expanding this, we have:
\[ 11S + 55 = 10M + 50 \]
Rearranging gives us:
\[ 11S - 10M = -5 \quad \text{(Equation 2)} \]

### Step 3: Solve the System of Equations
Now we have a system of two equations:
1. \( 8S - 7M = 4 \) (Equation 1)
2. \( 11S - 10M = -5 \) (Equation 2)

We can solve these equations using substitution or elimination. Let's use elimination.

First, we will multiply Equation 1 by 10 and Equation 2 by 7 to align the coefficients of \( M \):
- \( 10(8S - 7M) = 10(4) \) gives:
\[ 80S - 70M = 40 \quad \text{(Equation 3)} \]
- \( 7(11S - 10M) = 7(-5) \) gives:
\[ 77S - 70M = -35 \quad \text{(Equation 4)} \]

Now, we can subtract Equation 4 from Equation 3:
\[ (80S - 70M) - (77S - 70M) = 40 - (-35) \]
This simplifies to:
\[ 3S = 75 \]
Thus,
\[ S = 25 \]

### Step 4: Find Mohan's Age
Now we can substitute \( S = 25 \) back into Equation 1 to find \( M \):
\[ 8(25) - 7M = 4 \]
This simplifies to:
\[ 200 - 7M = 4 \]
Rearranging gives:
\[ 7M = 196 \quad \Rightarrow \quad M = 28 \]

### Conclusion
The present age of Suraj is \( \boxed{25} \).