Bipin is 6 times old as Alok. Bipin's age will be twice of chandan's age after 10 years. If chandan's `7^(th)` birthday was celebrated 3 years ago, what is Alok's present age?

Options

A. 15 years
B. 12 years
C. 5 years
D. none of these

Answer

To solve the problem, we need to find Alok's present age based on the information given. Let's break it down step by step.

### Step 1: Define the variables
Let:
- Alok's present age = A
- Bipin's present age = B
- Chandan's present age = C

### Step 2: Set up the equations based on the problem statement
From the problem, we have the following information:
1. Bipin is 6 times as old as Alok:
\[ B = 6A \]

2. Chandan's 7th birthday was celebrated 3 years ago, which means Chandan is currently:
\[ C = 7 + 3 = 10 \text{ years old} \]

3. After 10 years, Bipin's age will be twice Chandan's age:
\[ B + 10 = 2(C + 10) \]

### Step 3: Substitute Chandan's age into the equation
Now we substitute C = 10 into the equation from step 2:
\[ B + 10 = 2(10 + 10) \]
\[ B + 10 = 2 \times 20 \]
\[ B + 10 = 40 \]
\[ B = 40 - 10 \]
\[ B = 30 \]

### Step 4: Substitute Bipin's age into the first equation
Now we substitute B = 30 into the first equation:
\[ 30 = 6A \]
To find A, divide both sides by 6:
\[ A = \frac{30}{6} \]
\[ A = 5 \]

### Conclusion
Alok's present age is 5 years.