Each question is followed by three statements I, II and
III. You have to decide whether the data given in the statements are sufficient to answer the question. What is the present age of A?
I. The present ages of A and B are in the ratio 5 : 3. Four years from now, the sum of their ages will be 64 years.
II. B is 8 years younger than
A.
III. Six years ago, the ratio of the ages of A and B was 7 : 5.

ATQ, Let present ages be A and B. Statement I: A : B = 5 : 3 ⇒ A = 5k, B = 3k Four years from now: A + 4 + B + 4 = 64 ⇒ (5k + 4) + (3k + 4) = 64 ⇒ 8k + 8 = 64 ⇒ 8k = 56 ⇒ k = 7 So A = 5k = 35, B = 21. A is uniquely determined. I alone is sufficient. Statement II: A = B + 8 Infinitely many (A, B) pairs ⇒ A not unique. II alone is not sufficient. Statement III: Six years ago: (A − 6) : (B − 6) = 7 : 5 ⇒ 5(A − 6) = 7(B − 6) ⇒ 5A − 30 = 7B − 42 ⇒ 5A − 7B = −12 Single linear equation in two variables ⇒ many solutions ⇒ A not unique. III alone is not sufficient. Thus, only statement I alone is sufficient.