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The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. What is the present age of Priyanka? Statement I: When Himani was 10 years old, Priyanka’s age was half than Himani’s age Statement II: Four years ago, Sakshi’s age was three times than Priyanka’s age. Statement III: At present, Sakshi’s age is double than Himani’s age.

The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. What is the present age of Priyanka? Statement I: When Himani was 10 years old, Priyanka’s age was half than Himani’s age Statement II: Four years ago, Sakshi’s age was three times than Priyanka’s age. Statement III: At present, Sakshi’s age is double than Himani’s age. Correct Answer All I, II and III together

From Statement I,

When Himani was 10 years old, Priyanka’s age was half than Himani’s age

It means that Priyanka is 5 years younger than Himani

Hence, this statement is not enough to get the answer

From Statement III,

At present, Sakshi’s age is double than Himani’s age

Let the current age of Himani be x years

Then, the current age of Sakshi will be 2x years

But, this statement alone is not enough to get the answer

From Statement II,

Four years ago, Sakshi’s age was three times than Priyanka’s age

Current age of Sakshi is 2x years

Then, four years ago her age was 2x - 4 years

Four years ago Priyanka’s age will be (2x - 4)/3 years

This statement alone is also not enough to get the answer

Considering I, II and III together,

From II, the current age of Himani is x years

From III, four years ago Priyanka’s age was (2x - 4)/3 years      ----(1)

Four years ago Himani age will be x - 4 years

From I, Four years ago Priyanka’s age will be = x - 4 - 5

years = x - 9 years      ----(2)

From (1) and (2),

(2x - 4)/3 = x - 9

⇒ 2x - 4 = 3x - 27

⇒ 27 - 4 = 3x - 2x

⇒ x = 23

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