The largest sum of money which is contained in both Rs. 49.56 and Rs. 38.94 an exact number of times is :

Options

A. 2.7
B. 3.54
C. 4.28
D. none

Answer

To find the largest sum of money that is contained in both Rs. 49.56 and Rs. 38.94 an exact number of times, we need to determine the greatest common divisor (GCD) of the two amounts. Here’s how to do it step by step:

### Step 1: Convert the amounts into a more manageable form
First, we will convert the amounts into whole numbers by eliminating the decimal points. We can do this by multiplying both amounts by 100.

- Rs. 49.56 becomes 4956
- Rs. 38.94 becomes 3894

### Step 2: Find the GCD of the two whole numbers
Now we need to find the GCD of 4956 and 3894. We can use the Euclidean algorithm for this.

1. Divide 4956 by 3894 and find the remainder:
- 4956 ÷ 3894 = 1 (quotient)
- Remainder = 4956 - (1 × 3894) = 4956 - 3894 = 1062

2. Now, take the previous divisor (3894) and divide it by the remainder (1062):
- 3894 ÷ 1062 = 3 (quotient)
- Remainder = 3894 - (3 × 1062) = 3894 - 3186 = 708

3. Next, take 1062 and divide it by 708:
- 1062 ÷ 708 = 1 (quotient)
- Remainder = 1062 - (1 × 708) = 1062 - 708 = 354

4. Now, take 708 and divide it by 354:
- 708 ÷ 354 = 2 (quotient)
- Remainder = 708 - (2 × 354) = 708 - 708 = 0

Since the remainder is now 0, the last non-zero remainder is the GCD. Thus, GCD(4956, 3894) = 354.

### Step 3: Convert the GCD back to the original currency
Now that we have the GCD in whole numbers, we need to convert it back to the original currency format by dividing by 100.

- GCD = 354 ÷ 100 = Rs. 3.54

### Conclusion
The largest sum of money which is contained in both Rs. 49.56 and Rs. 38.94 an exact number of times is Rs. 3.54.

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