Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below: Find the age of the son if I. 5 years ago his father’s age was five times his age. II. 5 years later he would be half as old as his father’s present age.

Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

Find the age of the son if

I. 5 years ago his father’s age was five times his age.

II. 5 years later he would be half as old as his father’s present age.

A Statement I alone is sufficient to answer the question.

B Statement II alone is sufficient to answer the question.

C Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D Either Statement I or Statement I alone is sufficient to answer the question

E Neither Statement I nor Statement II is sufficient to answer the question.

Solution

Correct Answer: Option C

Let the age of son and father be x and y respectively.

From statement 1,

5 years ago his father’s age was five times his age.

y – 5 = 5(x – 5)

⇒ y = 5x – 20

We have two variables and one equation.

∴ Statement 1 alone is not sufficient to answer the question.

From statement 2,

5 years later he would be half as old as his father’s present age.

x + 5 = y/2

2x + 10 = y

Again, we have two variables and one equation.

∴ Statement 2 alone is not sufficient to answer the question.

From statement 1 and 2:

Solving the two equations simultaneously, we get x = 10 and y = 30.

Thus both statements are required to answer the question.

Solution

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