Given below is a question followed by two Statements numbered I and II, each containing some information. You have to decide which of the statements is/are sufficient to answer the question.

The sum of ages of X, Y and Z is 50 years. What is Y's age?

Statement I : Y is 10 years older than X.

Statement II: Z is 30 years old.

Question

Question

This question was previously asked in

CBSE Junior Assistant Official Paper (Held On: 20 Apr, 2025)

Both Statements I and II together are necessary to answer the question.
Statement I alone is sufficient to answer the question while Statement II alone is not sufficient.
Statement II alone is sufficient to answer the question while Statement I alone is not sufficient.
Neither Statement I alone nor Statement II alone is sufficient to answer the question.

Answer 1

Given:

The sum of ages of X, Y, and Z = 50 years

Statement I: Y is 10 years older than X

Statement II: Z is 30 years old

Calculation:

Total age: X + Y + Z = 50

From Statement I: Y = X + 10

X + Y + Z = 50

⇒ X + (X + 10) + Z = 50

⇒ 2X + Z = 40

From Statement II: Z = 30

⇒ 2X + 30 = 40

⇒ X = 5

⇒ Y = X + 10 = 5 + 10 = 15

∴ Y's age is 15 years. Both statements are required to find the answer.

∴ The correct answer is option (1).

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