The ratio of the age of Ishu 8 years hence and that of Ahana 6 years hence will be 5:6. The age of Ishu 10 years hence will be equal to the age of Ahana 6 years hence. Find the present age of Ishu.

Options

A. 1.5 years
B. 2 years
C. 3 years
D. 4 years

Answer

To find the present age of Ishu, we will follow these steps:

### Step 1: Define Variables
Let the present age of Ishu be \( X \) years and the present age of Ahana be \( Y \) years.

### Step 2: Set Up the First Equation
According to the problem, the ratio of Ishu's age 8 years hence to Ahana's age 6 years hence is given as 5:6. This can be expressed mathematically as:
\[ \frac{X + 8}{Y + 6} = \frac{5}{6} \]
Cross-multiplying gives us:
\[ 6(X + 8) = 5(Y + 6) \]
Expanding this, we get:
\[ 6X + 48 = 5Y + 30 \]
Rearranging the equation leads to:
\[ 6X - 5Y = -18 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
The problem also states that Ishu's age 10 years hence will be equal to Ahana's age 6 years hence. This can be expressed as:
\[ X + 10 = Y + 6 \]
Rearranging gives us:
\[ X - Y = -4 \quad \text{(Equation 2)} \]

### Step 4: Substitute Equation 2 into Equation 1
From Equation 2, we can express \( X \) in terms of \( Y \):
\[ X = Y - 4 \]
Now, substitute this expression for \( X \) into Equation 1:
\[ 6(Y - 4) - 5Y = -18 \]
Expanding this gives:
\[ 6Y - 24 - 5Y = -18 \]
Simplifying leads to:
\[ Y - 24 = -18 \]
Thus,
\[ Y = 6 \]

### Step 5: Find Ishu's Present Age
Now that we have \( Y \), we can find \( X \) using Equation 2:
\[ X = Y - 4 = 6 - 4 = 2 \]

### Conclusion
The present age of Ishu is \( 2 \) years.

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