Mohit and Rohit each have certain number of oranges. Mohit says to Rohit, ''if you give me 10 of your oranges, I will have twice the number of oranges left with you''. Rohit replies, ''if you give me 10 of your oranges, I will have the same number of oranges as left with you.'' Find the number of oranges with Mohit and Rohit respectively.

Options

A. 50, 70
B. 70, 50
C. 60, 60
D. 80, 40

Answer

To solve the problem, we will set up equations based on the statements made by Mohit and Rohit.

Let:
- \( M \) = number of oranges Mohit has
- \( R \) = number of oranges Rohit has

### Step 1: Create the first equation based on Mohit's statement
Mohit says, "If you give me 10 of your oranges, I will have twice the number of oranges left with you."

If Rohit gives Mohit 10 oranges:
- Mohit's new count = \( M + 10 \)
- Rohit's new count = \( R - 10 \)

According to Mohit's statement:
\[ M + 10 = 2(R - 10) \]

### Step 2: Simplify the first equation
Expanding the equation:
\[ M + 10 = 2R - 20 \]
Rearranging gives:
\[ M = 2R - 30 \quad \text{(Equation 1)} \]

### Step 3: Create the second equation based on Rohit's statement
Rohit replies, "If you give me 10 of your oranges, I will have the same number of oranges as left with you."

If Mohit gives Rohit 10 oranges:
- Mohit's new count = \( M - 10 \)
- Rohit's new count = \( R + 10 \)

According to Rohit's statement:
\[ R + 10 = M - 10 \]

### Step 4: Simplify the second equation
Rearranging gives:
\[ M = R + 20 \quad \text{(Equation 2)} \]

### Step 5: Solve the equations simultaneously
Now we have two equations:
1. \( M = 2R - 30 \)
2. \( M = R + 20 \)

We can set these equations equal to each other:
\[ 2R - 30 = R + 20 \]

### Step 6: Solve for \( R \)
Subtract \( R \) from both sides:
\[ 2R - R - 30 = 20 \]
This simplifies to:
\[ R - 30 = 20 \]
Adding 30 to both sides gives:
\[ R = 50 \]

### Step 7: Find \( M \) using \( R \)
Now substitute \( R = 50 \) back into Equation 2:
\[ M = R + 20 = 50 + 20 = 70 \]

### Final Answer
Thus, the number of oranges with Mohit and Rohit are:
- Mohit: \( 70 \)
- Rohit: \( 50 \)