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In a group of workers, the ratio of men to women is 7:5. If there are 12 more men than women, what is the total number of people in the group?
60
72
84
96
72
Calculate the unit value directly: The difference in parts is 7тИТ5=2 units. Since 2 units correspond to 12, then 1 unit = 6. Total units = 7+5=12, so total people = 12├Ч6=72.
Ratio of men to women is 7:5. The difference between the number of men and women is 12.
Total=(Ratio1тАЛ+Ratio2тАЛ)├ЧRatio1тАЛтИТRatio2тАЛDifferenceтАЛ
Calculate the unit value directly: The difference in parts is 7тИТ5=2 units. Since 2 units correspond to 12, then 1 unit = 6. Total units = 7+5=12, so total people = 12├Ч6=72.
Students often calculate the number of men (7├Ч6=42) or women (5├Ч6=30) individually and forget to sum them to find the total number of people.
Define units based on ratio
Let the number of men be 7x and the number of women be 5x.
Men=7x,Women=5x
Formulate equation based on difference
The problem states there are 12 more men than women, so the difference is 7xтИТ5x=12.
2x=12
Solve for the variable x
Dividing both sides by 2, we get x=6.
x=6
Calculate the total number of people
The total number of people is the sum of men and women: 7x+5x=12x. Substituting x=6, we get 12├Ч6=72.
12x=12├Ч6=72
B is correct because the calculated total of men and women is 72.
This ratio-based logic is essential for Mixture and Alligation problems where you need to distribute a total quantity based on proportional parts.