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At a vaccination center on Sunday, 60% of the registered candidates are men and 80% of the men are aged 45 or 45+. If 80% of the registered candidates are 45 or 45+, what fraction of the women registered are aged less than 45? 
1. 4/5
2. 1/5
3. 2/25
4. 23/25
5.

1 Answer

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Correct Answer - Option 2 : 1/5

Calculation:

Let the total candidates registered at the vaccination center on Sunday be 'x';

Given 60% of registered candidates are men ⇒ Total men registered = 0.6x;

⇒ Total women registered = 0.4x;

Now, 80% of the men are aged 45 or 45+

Total men with age 45 or 45+ = 80% of 0.6x = 0.48x;

Given 80% of the registered candidates are 45 or 45+ 

Total registered candidates with age 45 or 45+ = 0.8x;

Now,

The total women with age 45 or 45+ = Total registered candidates with age 45 or 45+ - Total men with age 45 or 45+

total women with age 45 or 45+ = 0.8x - 0.48x = 0.32x;

Now,

The total women with age less than 45 = Total women - Total women with age 45 or 45+ 

⇒ total women with age less than 45 = 0.4x - 0.32x = 0.08x;

Now,

Fraction of woman registered aged less than 45 = \(\rm \dfrac {Total \; women \; with \; age \; < \; 45}{Total \; registered \; women}\)

Fraction of woman registered aged less than 45 = 0.08x/0.4x = 1/5;

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