Multiple choice

What is the ratio of the ages of Ram and Ravi? I. 6 years ago their ages were in the ratio 3 : 4. II. After 2 years the younger one's age will be 85% that of the older. III. The sum of their ages is three less than twice the age of the older.

  1. Only II and III are sufficient

  2. Any two of them is sufficient

  3. Only I and II are sufficient

  4. All are not sufficient

  5. None
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives a ratio 6 years ago. Statement II relates their ages in 2 years. Statement III relates the sum of ages to the older one's age. With three variables (Ram's age, Ravi's age, and who is older), these statements provide sufficient linear equations to solve for the ratio.

AI explanation

Testing the three statements pairwise shows that any two equations form a solvable system. Statements one and two provide two linear equations in two variables, as do statements one and three, and statements two and three. Because each pair uniquely determines both ages, any two of the three statements are sufficient to find the ratio.

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