MAT Exam 2022 Paper

Concept:Use the given ratio conditions four years ago to form equations, then solve with the total present age.Explanation:Let the present ages of A, B and C be $a$, $b$ and $c$ years respectively.Four years ago:A's age was $a - 4$B's age was $b - 4$C's age was $c - 4$According to the condition, A's age was thrice C's age:$$a - 4 = 3(c - 4)$$$$a - 4 = 3c - 12$$$$a = 3c - 8$$Similarly, B's age was twice C's age:$$b - 4 = 2(c - 4)$$$$b - 4 = 2c - 8$$$$b = 2c - 4$$The total of their present ages is 48:$$a + b + c = 48$$Substitute $a = 3c - 8$ and $b = 2c - 4$:$$(3c - 8) + (2c - 4) + c = 48$$$$6c - 12 = 48$$$$6c = 60$$$$c = 10$$Therefore, present age of B:$$b = 2(10) - 4 = 16$$Answer:The present age of B is 16 years, i.e. option A.