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The following question has three statements. Study the question and the statements and decide which of the statement (s) is/are necessary to answer the question. What is the current age of Sonam? I) When Shreya was 10 years old, Sonam’s age was half than Shreya’s age II) Four years ago, Preeti’s age was three times than Sonam’s age III) At present, Preeti’s age is double than Shreya’s age

The following question has three statements. Study the question and the statements and decide which of the statement (s) is/are necessary to answer the question. What is the current age of Sonam? I) When Shreya was 10 years old, Sonam’s age was half than Shreya’s age II) Four years ago, Preeti’s age was three times than Sonam’s age III) At present, Preeti’s age is double than Shreya’s age Correct Answer All statements are required

Considering Statement I,

When Shreya was 10 years old, Sonam’s age was half than Shreya’s age

It means that Sonam is 5 years younger than Shreya

Hence, this statement is not enough to get the answer

Considering Statement III,

At present, Preeti’s age is double than Shreya’s age

Let the current age of Shreya be x years

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

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

Considering Statement II,

Four years ago, Preeti’s age was three times than Sonam’s age

Current age of Preeti is 2x years

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

Four years ago Sonam’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 Shreya is x years

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

Four years ago Shreya age will be x - 4 years

From I, Four years ago Sonam’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

Current age of Shreya is 23 years

∴ So, current age of Sonam is 23 - 5 i.e. 18 years

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