The average pocket money of 3 friends A ,B,C is Rs 80 in a particular month. If B spends double and C spends triple of what A spends during that month and if the average of their unspent pocket money is Rs 60, then A spends (in Rs)

Options

A. Rs 10
B. Rs 20
C. Rs 30
D. Rs 40

Answer

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

### Step 1: Determine the total pocket money of A, B, and C.
Given that the average pocket money of A, B, and C is Rs 80, we can calculate their total pocket money.

\[ \text{Total Pocket Money} = \text{Average} \times \text{Number of Friends} = 80 \times 3 = 240 \text{ Rs} \]

### Step 2: Assign variables for the pocket money of A, B, and C.
Let:
- A's pocket money = \( A \)
- B's pocket money = \( B \)
- C's pocket money = \( C \)

From the total pocket money calculated, we have:
\[ A + B + C = 240 \]

### Step 3: Express B and C in terms of A.
According to the problem, B spends double what A spends, and C spends triple what A spends. If we let A spend \( X \), then:
- B spends \( 2X \)
- C spends \( 3X \)

### Step 4: Calculate the unspent pocket money for each friend.
The unspent pocket money for each friend can be expressed as:
- A's unspent money = \( A - X \)
- B's unspent money = \( B - 2X \)
- C's unspent money = \( C - 3X \)

### Step 5: Write the equation for the average unspent pocket money.
We know the average of their unspent pocket money is Rs 60. Therefore:
\[ \frac{(A - X) + (B - 2X) + (C - 3X)}{3} = 60 \]

### Step 6: Substitute the total pocket money into the equation.
Substituting \( A + B + C = 240 \) into the equation gives:
\[ \frac{240 - (X + 2X + 3X)}{3} = 60 \]
This simplifies to:
\[ \frac{240 - 6X}{3} = 60 \]

### Step 7: Multiply both sides by 3 to eliminate the fraction.
\[ 240 - 6X = 180 \]

### Step 8: Solve for \( X \).
Rearranging the equation gives:
\[ 240 - 180 = 6X \\ 60 = 6X \\ X = 10 \]

### Step 9: Determine how much A spends.
Since \( X \) represents the amount A spends, we find that:
\[ \text{A spends} = X = 10 \text{ Rs} \]

### Final Answer:
A spends Rs 10.

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