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Mathematics

Consider the following two statements:

Statement 1: A husband is 2 years older than his wife, and sum of their ages is 52 years. Then the wife is 25 years old.

Statement 2: A father is twice as old as his daughter, and difference of their ages is 26 years. Then the father is 50 years old.

Which of the following is valid?

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and Statement 2 is false.

  4. Statement 1 is false, and Statement 2 is true.

Linear Equations

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Answer

Let x years be the husband's age and y years be the wife's age.

Given,

Husband is 2 years older than his wife.

⇒ x = y + 2 ………………(1)

Sum of husband's age and wife's age = 52 years

⇒ x + y = 52 ………………(2)

Substituting the value of x from equation (1) in equation (2), we get

⇒ (y + 2) + y = 52

⇒ 2y + 2 = 52

⇒ 2y = 52 - 2

⇒ 2y = 50

⇒ y = 502\dfrac{50}{2}

⇒ y = 25 years.

∴ Statement 1 is true.

Let the age of daughter be a years.

Given,

Father's age is twice that of daughter's age.

Father's age = 2a years

Difference of father's age and daughter's age = 26 years

⇒ 2a - a = 26

⇒ a = 26

Father's age = 2a = 2 x 26 = 52 years.

∴ Statement 2 is true.

∴ Both the statements are true.

Hence, option 1 is the correct option.

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