A has thrice as much amount as that of B and B has 40% more amount than C. If the average of the amount of all three of them is Rs 1320, then what amount (in Rs) A has?

Options

A. 2410
B. 2520
C. 2250
D. 3240

Answer

To solve the problem step by step, we will define the amounts that A, B, and C have in terms of a variable and then use the information given in the question to find the amount A has.

### Step 1: Define the amounts
Let the amount C has be \( x \).

### Step 2: Find the amount B has
According to the question, B has 40% more than C. Therefore, the amount B has can be expressed as:
\[ B = x + 0.4x = 1.4x = \frac{7x}{5} \]

### Step 3: Find the amount A has
The question states that A has thrice as much as B. Thus, the amount A has is:
\[ A = 3B = 3 \times \frac{7x}{5} = \frac{21x}{5} \]

### Step 4: Set up the equation for the average
The average amount of A, B, and C is given as Rs 1320. Therefore, we can set up the equation:
\[ \text{Average} = \frac{A + B + C}{3} = 1320 \]
Substituting the values of A, B, and C into the equation gives:
\[ \frac{\frac{21x}{5} + \frac{7x}{5} + x}{3} = 1320 \]

### Step 5: Combine the amounts
Combine the amounts in the numerator:
\[ \frac{\frac{21x + 7x + 5x}{5}}{3} = 1320 \]
This simplifies to:
\[ \frac{\frac{33x}{5}}{3} = 1320 \]

### Step 6: Simplify the equation
Multiply both sides by 3:
\[ \frac{33x}{5} = 3960 \]

### Step 7: Solve for x
Multiply both sides by 5:
\[ 33x = 19800 \]
Now divide by 33:
\[ x = \frac{19800}{33} = 600 \]

### Step 8: Find the amount A has
Now that we have the value of \( x \), we can find the amount A has:
\[ A = \frac{21x}{5} = \frac{21 \times 600}{5} = 2520 \]

### Conclusion
Thus, the amount A has is Rs 2520.

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