MAT Exam 2023 Paper

Concept:When ages are given in the ratio $3:1$, represent them as $3x$ and $x$.The average of two values is half of their sum.So, first find the total of their ages from the given average.Explanation:Let the daughter's age be $x$ years.Since the ratio of the woman's age to the daughter's age is $3:1$, the woman's age is $3x$ years.The average age of the woman and her daughter is $44$ years.So, their total age is $44 \times 2 = 88$ years.Hence, $3x + x = 88$.This gives $4x = 88$.Therefore, $x = \frac{88}{4} = 22$ years.So, the daughter's age is $22$ years.This matches option A.Answer:The daughter's age is $22$ years, which is option A.