Question

A man's age is there times the sum of ages of his two sons. After 5 years , his age will be twice the sum of the ages of his two sons. Find the age of the man.​

Answer 1

✬ Man's Age = 45 Years ✬

Step-by-step explanation:

Given:

• Man's age is three times the sum of ages of his two sons.
• After 5 years , man's age will be twice the sum of ages of his two sons.

To Find:

• What is the age of man ?

Solution: Let the present age of man be x years and sum of present ages of his sons be y years.

➙ Three times of man's age = y

➙ 3y = xㅤㅤㅤㅤㅤ(eqⁿ i)

[ After 5 years their ages will be ]

• Man's age = (x + 5) years

• His two son's ages = (y + 5 + 5) years

$\implies{\rm }$ (x + 5) = 2(y + 10)

$\implies{\rm }$ x + 5 = 2y + 20

$\implies{\rm }$ 3y – 2y = 20 – 5

$\implies{\rm }$ y = 15

So the sum of ages of his son is 15 years. Now put the value of y in eqⁿ i.

➥ 3 × 15 = x

➥ 45 = x

Hence, the present age of man is 45 years.

Answer 2

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Question :

• A man's age is there times the sum of ages of his two sons. After 5 years , His age will be twice the sum of the ages of his two sons. Find the age of the man.

Required Answer :

• Present age of man is 45 years.

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

Step by step explanation :

• Let age of two sons = m years , n years.
• So, age of man = 3(m + n) years.
• Sum of ages of two sons after 5 years = (m + 5) + (n + 5) = (m + n + 10) years.
• Age of man 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 two sons = 15 years

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

Now,

➡ㅤㅤㅤAge of man = 3(m + n)

➡ㅤㅤㅤAge of man = 3(15)

➡ㅤㅤㅤAge of man = 3 × 15

➡ㅤㅤㅤAge of man = 45 years

∴ Present age of man is 45 years

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