1.

II. Six years from now, sum of ages of Lance and Robin will be 77 years.1). The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.2). The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.3). The data in statement I alone or in statement II alone is sufficient to answer the question.4). The data in both the statements I and II is not sufficient to answer the question.

Answer»

From statement I:

Five years back, the RATIO of ages of Lance and Robin was 6:5.

Knowing the ratio, age of Lance cannot be determined.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

Six years from now, sum of ages of Lance and Robin will be 77 years.

⇒ Present sum of their ages = 77 – 2 × 6 = 65.

But, age of Lance individually cannot be found.

∴ Statement II alone is not sufficient to answer the question.

From statements I and II together:

Five years back, the ratio of ages of Lance and Robin was 6:5. Let the ages of Lance and Robin be 6t and 5t, RESPECTIVELY, five years back.

Present age of Lance = 6t + 5

Present age of Robin = 5t + 5

Six years from now, sum of ages of Lance and Robin will be 77 years.

⇒ Present sum of their ages = 77 – 2 × 6 = 65.

We can now find VALUE of t, and hence find age of Lance.

With the present age of Lance, age of Lance three years from now can be found.

USING both the statements together, we can answer the given question.


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