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Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answerWhat is the sum of the ages of Rakesh and Rama after 15 years.Statement I. 7 years ago, Rakesh's age was 8 years more than that of Rama.Statement II. The ratio of present age of Rama and Rakesh is 5 : 11.1. The statement I alone is sufficient to answer the question but, statement II alone is not sufficient. 2. The statement II alone is sufficient to answer the question but, statement I alone is not sufficient.3. Both the statements I and II together are needed to answer the question.4. Either statement I alone or statement II alone is sufficient to answer the question.5. Neither statement I nor statement II is sufficient to answer the question.

Answer» Correct Answer - Option 3 : Both the statements I and II together are needed to answer the question.

Concept Used:

If present age is x yrs., then

Age a years ago = (x – a)

Age a years hence = (x + a)

Statement I.

7 years ago, Rakesh's age was 8 years more than that of Rama.

Let the present age of Rakesh and Rama be x and y respectively.

⇒ (x – 7) = (y – 7) + 8

⇒ x – y = 8  

So, Statement I alone is not sufficient

Statement II.

The ratio of present age of Rama and Rakesh is 5 : 11

⇒ x : y = 11 : 5

Again we get a relation between their ages but not the exact values

So, Statement II alone is not sufficient

Combining Statement I and Statement II

x – y = 8

⇒ (11a – 7a) = 8

⇒ a = 2

Now, x = 11 × 2 = 22 yrs.

y = 5 × 2 = 10 yrs.

Sum of the ages of Rakesh and Rama after 15 years = (22 + 15) + (10 + 15)

⇒ Sum of the ages of Rakesh and Rama after 15 years = 62 yrs.

∴ Both statements together are needed to answer the question.


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