The ratio between the present age of Tarun and Varun is 3 :7 respectively. After 4 yr, Varun's age will be 39 yr. What was Tarun's age 4 yr ago?

Options

A. 12 yr
B. 13 yr
C. 19 yr
D. none to these

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Understand the ratio of ages
The ratio of the present ages of Tarun and Varun is given as 3:7. This means if we let Tarun's present age be 3x years, then Varun's present age will be 7x years.

### Step 2: Determine Varun's present age
We know that after 4 years, Varun's age will be 39 years. Therefore, we can set up the equation:
\[ \text{Varun's present age} + 4 = 39 \]
This simplifies to:
\[ \text{Varun's present age} = 39 - 4 = 35 \text{ years} \]

### Step 3: Relate Varun's present age to the ratio
From the ratio, we have:
\[ 7x = 35 \]
To find the value of x, we divide both sides by 7:
\[ x = \frac{35}{7} = 5 \]

### Step 4: Calculate Tarun's present age
Now that we have the value of x, we can find Tarun's present age:
\[ \text{Tarun's present age} = 3x = 3 \times 5 = 15 \text{ years} \]

### Step 5: Calculate Tarun's age 4 years ago
To find Tarun's age 4 years ago, we subtract 4 from his present age:
\[ \text{Tarun's age 4 years ago} = 15 - 4 = 11 \text{ years} \]

### Final Answer
Tarun's age 4 years ago was **11 years**.

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