QUESTION

CSAT

Easy

Maths

Prelims 2013

Out of 120 applications for a post, 70 are male, and 80 have a driver’s license.

What is the ratio between the minimum to maximum number of males having a driver’s license?

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Explanation

Let's denote the following:

Total number of applicants: $120$
Number of males: $70$
Number of applicants with a driver's license: $80$
Number of females: $120 - 70 = 50$
Number of females with a driver's license: $80$ - (number of males with a driver's license)

Now, we need to find the ratio of the minimum to maximum number of males who have a driver's license.

Maximum number of males with a driver's license: For the maximum number of males with a driver's license, we assume that all the females do not have a driver's license. So, all 80 applicants with a driver's license must be male. Therefore, the maximum number of males with a driver's license is 70 (since there are only 70 males).

Minimum number of males with a driver's license: For the minimum number of males with a driver's license, we assume that as many females as possible have a driver's license. Since there are 50 females, the maximum number of females with a driver's license is 50. Therefore, the remaining number of applicants with a driver's license must be male, which is:

$80 - 50 = 30$ .

Ratio of the minimum to maximum number of males with a driver's license: The minimum number of males with a driver's license is 30, and the maximum number is 70. The ratio is:

$30 / 70 = 3 / 7$ .