The average of the daily income of A,B,C is ₹60 if B earns ₹20 more than C and A earns double of what C earns what is the daily income of C?

Options

A. ₹75
B. ₹60
C. ₹40
D. none of these

Answer

To solve the problem step by step, let's denote the daily incomes of A, B, and C as follows:

- Let C's income be \( C \).
- Since B earns ₹20 more than C, B's income can be expressed as \( B = C + 20 \).
- A earns double what C earns, so A's income can be expressed as \( A = 2C \).

### Step 1: Set up the equation for the average income
The average income of A, B, and C is given as ₹60. The formula for average is:

\[ \text{Average} = \frac{A + B + C}{3} \]

Substituting the known values into the equation:

\[ \frac{A + B + C}{3} = 60 \]

Multiplying both sides by 3 gives:

\[ A + B + C = 180 \]

### Step 2: Substitute the expressions for A and B
Now, substitute \( A = 2C \) and \( B = C + 20 \) into the equation:

\[ 2C + (C + 20) + C = 180 \]

### Step 3: Simplify the equation
Combine like terms:

\[ 2C + C + 20 + C = 180 \]
\[ 4C + 20 = 180 \]

### Step 4: Solve for C
Now, isolate \( C \) by subtracting 20 from both sides:

\[ 4C = 180 - 20 \]
\[ 4C = 160 \]

Now, divide both sides by 4:

\[ C = \frac{160}{4} = 40 \]

### Conclusion
The daily income of C is ₹40.

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