Rahul and Rohit are `10^(th)` standard student. Both of them have certain number of fruit with them. Rahul says to, Rohit "If you give me your 10 fruits, I will have twice the number of fruits left with you." Rohit replies that you give me 10 of your fruits, I will have the same number of fruits as left with you."
Signify the number of fruits that Rahul and Rohit has by 'x' and 'y' respectively.

What are the number of fruits that Rahul had?

Options

A. 50
B. 60
C. 55
D. 70

Answer

To solve the problem step by step, let's denote the number of fruits that Rahul has as \( x \) and the number of fruits that Rohit has as \( y \).

### Step 1: Set up the equations based on the statements given.

1. **From Rahul's statement:**
- If Rohit gives 10 fruits to Rahul, then Rahul will have \( x + 10 \) fruits, and Rohit will have \( y - 10 \) fruits left.
- Rahul states that he will have twice the number of fruits left with Rohit:
\[ x + 10 = 2(y - 10) \]

2. **From Rohit's statement:**
- If Rahul gives 10 fruits to Rohit, then Rahul will have \( x - 10 \) fruits, and Rohit will have \( y + 10 \) fruits.
- Rohit states that he will have the same number of fruits as Rahul will have left:
\[ y + 10 = x - 10 \]

### Step 2: Simplify the equations.

1. **From Rahul's equation:**
\[ x + 10 = 2y - 20 \]
Rearranging gives:
\[ x - 2y = -30 \quad \text{(Equation 1)} \]

2. **From Rohit's equation:**
\[ y + 10 = x - 10 \]
Rearranging gives:
\[ x - y = 20 \quad \text{(Equation 2)} \]

### Step 3: Solve the system of equations.

Now we have the following two equations:
1. \( x - 2y = -30 \) (Equation 1)
2. \( x - y = 20 \) (Equation 2)

We can solve these equations using the elimination method.

### Step 4: Eliminate one variable.

From Equation 2, we can express \( x \) in terms of \( y \):
\[ x = y + 20 \]

Now substitute \( x \) in Equation 1:
\[ (y + 20) - 2y = -30 \]
This simplifies to:
\[ 20 - y = -30 \]
Rearranging gives:
\[ -y = -30 - 20 \]
\[ -y = -50 \]
\[ y = 50 \]

### Step 5: Find \( x \).

Now substitute \( y = 50 \) back into Equation 2:
\[ x - 50 = 20 \]
\[ x = 20 + 50 \]
\[ x = 70 \]

### Conclusion:

Thus, the number of fruits that Rahul had is \( \boxed{70} \).