Question

A father's age is three times the sum of the ages of his two children.
After 5 years, his age will be two times the sum of their ages. Find the present age of the father.
CLASS 10 MATHEMATICS QUESTION
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Answer 1

Answer:

Step-by-step explanation:

Given,

A father's age is three times the sum of the ages of his two children.

After 5 years, his age will be two times the sum of their ages. Find the present age of the father.

To Find,

Present age of the father.

Solution,

Let us assume the ages of two children be x years and y years.

And the father age be 3(x + y) years.

After 5 years,

Age of two children = (x + 5) + (y + 5) years

= (x + y + 10) years.

And, the age of father,

= 3(x + y) + 5

= 3x + 3y + 5 years.

Now, According to the question,

⇒ 3x + 3y + 5 = 2(x + y + 10)

⇒ 3x + 3y + 5 = 2x + 2y + 20

⇒ 3x - 2x + 3y - 2y = 20 - 5

⇒ x + y = 15 years.

Here, the age of two children is 15 years.

Now, the age of father,

= 3(x + y)

= 3 × 15

= 45 years.

Hence, the age of father is 45 years.

Answer 2

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★ Correct Question :

• A father's age is three times the sum of the ages of his two children. After 5 years, his age will be two times the sum of their ages. Find the present age of the father.

★ Required answer :

• Present age of father is 45 years.

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★ Step by step explanation :

• Let age of two children = m years ,n years
• So, Age of father = 3(m + n) years
• Sum of Age of two children after 5 years = (m + 5) + (n + 5) = (m + n + 10) years
• Age of father after 5 years = 3(m + n) + 5 = (3m + 3n + 5) years

Atq,

➢ㅤㅤㅤ3m + 3n + 5 = 2(m + n + 10)

➢ㅤㅤㅤ3m + 3n + 5 = 2m + 2n + 20

➢ㅤㅤㅤ3m - 2m + 3n - 2n = 20 - 5

➢ㅤㅤㅤm + n = 15

∴ Sum of ages of 2 children = 15 years

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Now,

➢ㅤㅤㅤAge of father = 3(m + n)

➢ㅤㅤㅤAge of father = 3(15)

➢ㅤㅤㅤAge of father = 3 × 15

➢ㅤㅤㅤAge of father = 45 years

∴ Present age of father = 45 years

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