Akash is younger than Vineet by 5 years. If their ages are in the respective ratio of `3 : 4`, then how old is Akash ?

Options

A. 25 years
B. 15 years
C. 20 years
D. 23 years

Answer

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

### Step 1: Define the Variables
Let the age of Akash be \( A \) and the age of Vineet be \( V \).

### Step 2: Set Up the Equations
According to the problem, we know two things:
1. Akash is younger than Vineet by 5 years:
\[ A = V - 5 \]
2. The ratio of their ages is \( 3:4 \):
\[ \frac{A}{V} = \frac{3}{4} \]

### Step 3: Express Akash's Age in Terms of Vineet's Age
From the ratio equation, we can express Akash's age in terms of Vineet's age:
\[ A = \frac{3}{4}V \]

### Step 4: Substitute the Expression into the First Equation
Now, we can substitute the expression for \( A \) from the ratio into the first equation:
\[ \frac{3}{4}V = V - 5 \]

### Step 5: Clear the Fraction
To eliminate the fraction, multiply every term by 4:
\[ 3V = 4V - 20 \]

### Step 6: Solve for Vineet's Age
Now, rearranging the equation gives:
\[ 3V - 4V = -20 \]
\[ -V = -20 \]
\[ V = 20 \]

### Step 7: Find Akash's Age
Now that we have Vineet's age, we can find Akash's age using the first equation:
\[ A = V - 5 = 20 - 5 = 15 \]

### Conclusion
Thus, Akash is **15 years old**.

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