Multiple choice

Directions: The problem consists of a question and three statements numbered I, II and III given below it. You have to decide which of the given statements is/are sufficient to answer the question. Read all the statements and give answer accordingly. What is the present age of Raja? I. 3 years ago, the ratio of the ages of Raka and Raja was 4 : 5. II. 2 years hence, the ratio of the ages of Rana and Raja will be 4 : 5. III. 2 years ago, the ratio of the ages of Rana and Raka was 12 : 13.

  1. I and II only

  2. II and III only

  3. I and III only

  4. All I, II and III together

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We have three variables (Raja, Raka, Rana) and three linear equations from the ratios. Solving this system of equations allows us to determine the present ages.

AI explanation

The question requires forming a system of linear equations using the ratios provided across different time periods. Statements I, II and III individually relate Raja to Raka and Raja to Rana without linking all three people, making any two statements insufficient to find Raja's exact age. Using all three statements together establishes the complete chain of ratios between Raka, Rana and Raja, allowing you to solve for the single unknown variable multiplier and find Raja's present age.

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