Out of 120 applications for a post, 70 are males and 80 have a driver's license. What is the ratio between the minimum to maximum number of males having driver's license ?

Options

A. `1 : 2`
B. `2 :3`
C. `3 : 7`
D. `5 : 7`

Answer

To solve the problem, we need to find the minimum and maximum number of males who have a driver's license among the 120 applicants.

### Step 1: Understand the given data
We have:
- Total applications = 120
- Males = 70
- Applicants with a driver's license = 80

### Step 2: Calculate the maximum number of males with a driver's license
To find the maximum number of males who could have a driver's license, we assume that all males have a driver's license. Thus, the maximum number of males with a driver's license is:
- Maximum males with driver's license = 70 (since there are only 70 males)

### Step 3: Calculate the minimum number of males with a driver's license
To find the minimum number of males who could have a driver's license, we assume that all females have a driver's license. Since there are 120 total applicants and 70 are males, the number of females is:
- Females = Total applicants - Males = 120 - 70 = 50

If all 50 females have a driver's license, then the remaining applicants with a driver's license must be males. Since there are 80 applicants with a driver's license, the minimum number of males with a driver's license is:
- Minimum males with driver's license = Total with driver's license - Females with driver's license = 80 - 50 = 30

### Step 4: Find the ratio of minimum to maximum number of males with a driver's license
Now we can find the ratio of the minimum to the maximum number of males having a driver's license:
- Ratio = Minimum males with driver's license : Maximum males with driver's license = 30 : 70

### Step 5: Simplify the ratio
To simplify the ratio, we can divide both sides by 10:
- Simplified ratio = 3 : 7

### Final Answer
The ratio between the minimum to maximum number of males having a driver's license is **3 : 7**.

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