The daily pocket expenses of A and B are `"Rs. 60"` and `"Rs. 75"'` respectively. What is the ration of their expenses in simplest form?

Options

A. `4 : 9`
B. `4 : 5`
C. `4 : 7`
D. `5 : 7`

Answer

To find the ratio of the daily pocket expenses of A and B, we will follow these steps:

### Step 1: Identify the expenses of A and B
- A's daily pocket expense = Rs. 60
- B's daily pocket expense = Rs. 75

### Step 2: Write the ratio of their expenses
- The ratio of A's expenses to B's expenses can be written as:
\[ \text{Ratio} = \frac{A's \, expense}{B's \, expense} = \frac{60}{75} \]

### Step 3: Simplify the ratio
To simplify the ratio, we need to find the greatest common divisor (GCD) of 60 and 75.

- The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- The factors of 75 are: 1, 3, 5, 15, 25, 75
- The common factors are: 1, 3, 5, 15
- The greatest common factor is 15.

Now, we will divide both the numerator and the denominator by their GCD (15):
\[ \frac{60 \div 15}{75 \div 15} = \frac{4}{5} \]

### Step 4: Write the ratio in simplest form
The simplified ratio of A's expenses to B's expenses is:
\[ 4 : 5 \]

### Final Answer
The ratio of the daily pocket expenses of A and B in simplest form is **4 : 5**.

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