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Twelve years ago, the age of Reena's mother was three times the age of Reena. Two years hence, the mother's age will be 2 times the age of Reena. Find the ratio of the present ages of Reena and her mother.
5 : 9
27 : 13
13 : 27
9 : 11
13 : 27
Assign variables for ages 12 years ago. Let Reena be x and Mother be 3x. Then add 12 to find present ages (x+12, 3x+12) and equate with the +2 condition.
Assign variables for ages 12 years ago. Let Reena be x and Mother be 3x. Then add 12 to find present ages (x+12, 3x+12) and equate with the +2 condition.
Set Variables (12 years ago)
Let Reena's age 12 years ago be x and Mother's age be 3x. Thus, present ages are: Reena = x + 12, Mother = 3x + 12.
Apply Future Condition
Two years hence, Reena will be (x + 12 + 2) = x + 14 and Mother will be (3x + 12 + 2) = 3x + 14. Given Mother = 2 * Reena, we write 3x + 14 = 2(x + 14).
Solve for x
3x + 14 = 2x + 28 results in x = 14. Present ages: Reena = 14 + 12 = 26; Mother = 3(14) + 12 = 42 + 12 = 54.
Calculate Ratio
Ratio of Reena to Mother = 26 : 54. Dividing by 2, we get 13 : 27.
A: 5:9 does not simplify to 26:54. B: 27:13 is the inverse of the required ratio. D: 9:11 is mathematically incorrect based on the age equation.
C is correct because the derived present ages of 26 and 54 result in a simplified ratio of 13:27.
Always verify the order of the ratio; the question asks for Reena to Mother, so ensure Reena's age comes first in the final fraction.
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