Out of the 144 persons working in an office, 56 are men and the remaining are women. Find the ratio of number of women to number of men.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the total number of persons and the number of men.
- Total persons in the office = 144
- Number of men = 56

### Step 2: Calculate the number of women.
- To find the number of women, subtract the number of men from the total number of persons:
\[ \text{Number of women} = \text{Total persons} - \text{Number of men} = 144 - 56 = 88 \]

### Step 3: Write the ratio of the number of women to the number of men.
- The ratio of the number of women to the number of men can be expressed as:
\[ \text{Ratio of women to men} = \frac{\text{Number of women}}{\text{Number of men}} = \frac{88}{56} \]

### Step 4: Simplify the ratio.
- To simplify the ratio \(\frac{88}{56}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 88 and 56 is 8.
\[ \frac{88 \div 8}{56 \div 8} = \frac{11}{7} \]

### Step 5: State the final ratio.
- Therefore, the ratio of the number of women to the number of men is:
\[ \text{Ratio of women to men} = 11 : 7 \]

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