In a village the ratio of males to females is 2:1 - OCR - GCSE Maths - Question 22 - 2018 - Paper 4
Question 22
In a village the ratio of males to females is 2:1.
40% of the people in the village are right-handed males.
25% of the people in the village are right-handed female... show full transcript
Worked Solution & Example Answer:In a village the ratio of males to females is 2:1 - OCR - GCSE Maths - Question 22 - 2018 - Paper 4
Step 1
Calculate total population and gender distribution
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Answer
Let the total population of the village be 100 (for simplicity).
Given the ratio of males to females is 2:1, we have:
Males = 2 parts
Females = 1 part
Thus,
Number of males = (2/3) * 100 = 66.67 ~ 67
Number of females = (1/3) * 100 = 33.33 ~ 33
Step 2
Find the number of right-handed males
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Answer
According to the problem, 40% of the population are right-handed males.
Number of right-handed males = 40% of 100 = 40.
Step 3
Find the number of right-handed females
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Answer
According to the problem, 25% of the population are right-handed females.
Number of right-handed females = 25% of 100 = 25.
Step 4
Calculate the proportion of males who are right-handed
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Answer
The proportion of males who are right-handed = ( \frac{\text{Number of right-handed males}}{\text{Total number of males}} = \frac{40}{67} \approx 0.597 ) or 59.7%.
Step 5
Calculate the proportion of females who are right-handed
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Answer
The proportion of females who are right-handed = ( \frac{\text{Number of right-handed females}}{\text{Total number of females}} = \frac{25}{33} \approx 0.758 ) or 75.8%.
Step 6
Compare the proportions
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Answer
As observed, 75.8% (the proportion of right-handed females) is greater than 59.7% (the proportion of right-handed males). Thus, we have shown that the proportion of females who are right-handed is indeed greater than that of males who are right-handed.
