If the amount of A is 45% more than B, C is 60% less than A and B together and D is 20% less than C and the amount difference between B and D is Rs. 21,600 then find the amount of C.

Options

A. Rs. 82,000
B. Rs. 98,000
C. Rs. 96,000
D. Rs. 84,000

Answer

To solve the problem step by step, let's define the amounts of A, B, C, and D based on the information provided in the question.

### Step 1: Define the amount of B
Let the amount of B be Rs. 100 (this is an arbitrary choice to simplify calculations).

### Step 2: Calculate the amount of A
Since A is 45% more than B, we can calculate A as follows:
\[ A = B + 0.45 \times B = 100 + 45 = 145 \]

### Step 3: Calculate the total amount of A and B
Now, we find the total amount of A and B:
\[ A + B = 145 + 100 = 245 \]

### Step 4: Calculate the amount of C
C is 60% less than the total of A and B. To find C, we calculate:
\[ C = (A + B) - 0.60 \times (A + B) = 245 - 0.60 \times 245 \]
Calculating 60% of 245:
\[ 0.60 \times 245 = 147 \]
Thus,
\[ C = 245 - 147 = 98 \]

### Step 5: Calculate the amount of D
D is 20% less than C. Therefore, we calculate D as follows:
\[ D = C - 0.20 \times C = 98 - 0.20 \times 98 \]
Calculating 20% of 98:
\[ 0.20 \times 98 = 19.6 \]
Thus,
\[ D = 98 - 19.6 = 78.4 \]

### Step 6: Calculate the difference between B and D
We know that the difference between B and D is given as Rs. 21,600:
\[ B - D = 100 - 78.4 = 21.6 \]

### Step 7: Set up the proportion to find the actual amounts
Since we assumed B = 100 corresponds to a difference of Rs. 21.6, we can find the scaling factor:
\[ \text{Scaling Factor} = \frac{21600}{21.6} = 1000 \]

### Step 8: Calculate the actual amount of C
Now we can find the actual amount of C:
\[ \text{Actual amount of C} = C \times \text{Scaling Factor} = 98 \times 1000 = 98000 \]

### Final Answer
Thus, the amount of C is Rs. 98,000.

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