Joshna and Vijay have some chocolates, The num-ber of chocolates with Joshna is two -third of the number of chocolates with Vijay. If Vijay gives five chocolates to Joshna, then both will have equal number of chocolates. How many chocolates does Joshna have ?

Explanation

To solve the problem step by step, let's break it down.

### Step 1: Define the Variables
Let the number of chocolates Vijay has be represented by \( X \). According to the problem, Joshna has two-thirds of the chocolates that Vijay has. Therefore, we can express the number of chocolates Joshna has as:
\[ \text{Joshna's chocolates} = \frac{2}{3}X \]

### Step 2: Set Up the Equation
The problem states that if Vijay gives 5 chocolates to Joshna, they will have an equal number of chocolates. After Vijay gives 5 chocolates to Joshna, the number of chocolates each will have can be expressed as:
- Vijay's chocolates after giving away 5: \( X - 5 \)
- Joshna's chocolates after receiving 5: \( \frac{2}{3}X + 5 \)

Since they will have equal chocolates after this transaction, we can set up the equation:
\[ X - 5 = \frac{2}{3}X + 5 \]

### Step 3: Solve the Equation
Now, we will solve the equation for \( X \).

1. First, isolate \( X \) on one side:
\[ X - \frac{2}{3}X = 5 + 5 \]

2. Simplify the left side:
\[ \frac{1}{3}X = 10 \]

3. Multiply both sides by 3 to solve for \( X \):
\[ X = 30 \]

### Step 4: Find the Number of Chocolates Joshna Has
Now that we know the number of chocolates Vijay has, we can find out how many chocolates Joshna has:
\[ \text{Joshna's chocolates} = \frac{2}{3}X = \frac{2}{3} \times 30 = 20 \]

### Conclusion
Thus, the number of chocolates Joshna has is:
\[ \text{Joshna has } 20 \text{ chocolates.} \]

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