Rohan's Pocket Money

Rohan's pocket money is the total amount of money he receives regularly for his personal expenses. Let's assume that the pocket money Rohan receives is denoted by the variable 'P'.

Rohan's Expenditure

According to the given information, Rohan spent ½ of his pocket money on lunch and ⅓ on conveyance.

- Lunch Expenditure: Rohan spent ½ of his pocket money on lunch. This can be calculated as (1/2) * P.
- Conveyance Expenditure: Rohan spent ⅓ of his pocket money on conveyance. This can be calculated as (1/3) * P.

Remaining Money

After spending on lunch and conveyance, Rohan gave the remaining money to his sister Sweety. The amount Sweety received is given as rupees 5.

- Remaining Money: The remaining money can be calculated by subtracting the total expenditure from the pocket money. Let's denote the remaining money by the variable 'R'. Therefore, R = P - [(1/2) * P + (1/3) * P].

According to the question, Sweety received rupees 5. So, we have R = 5.

Calculating Pocket Money

To find the value of P (Rohan's pocket money), we can substitute the value of R in the equation R = P - [(1/2) * P + (1/3) * P] and solve for P.

5 = P - [(1/2) * P + (1/3) * P]

To solve this equation, we can find a common denominator for the fractions:

5 = P - [(3/6) * P + (2/6) * P]

5 = P - (5/6) * P

Combining like terms:

5 = (6/6) * P - (5/6) * P

5 = (1/6) * P

Multiplying both sides by 6 to isolate P:

30 = P

Therefore, the pocket money Rohan receives is rupees 30.

Calculating Lunch Expenditure

To find out how much Rohan spent on lunch, we can substitute the value of P in the equation for lunch expenditure: (1/2) * P.

Lunch Expenditure = (1/2) * 30 = 15.

Therefore, Rohan spent rupees 15 on lunch.

Summary:

- Rohan's pocket money is rupees 30.
- He spent rupees 15 on lunch.
- He gave the remaining money, which was rupees 5, to his sister Sweety.