Question

The age of a man is twice the sum of the ages of his two children . After 20 years his age will be equal to the sum of the ages of his children at that time . Find the present age of the man​

Answer 1

ᴄᴏʀʀᴇᴄᴛ ǫᴜᴇsᴛɪᴏɴ :-

The age of a man is twice the sum of the ages of his two children . After 20 years his age will be 20 years more than the sum of the ages of his children at that time .

ᴛᴏ ғɪɴᴅ :-

• Sum of ages of two children
• Man's age

sᴏʟᴜᴛɪᴏɴ :-

Let the sum of ages of two children be x years and man's age be y years

then,

✞ According to 1st condition :-

• Man's age = 2 × (Sum of ages of two children )

• y = 2x. --(1)

✞ According to 2nd condition :-

➤ After 20 years :-

• Sum of Children's age = (x + 20) years
• Man's age = (y + 20) years

• Man's age = Sum of Children's age

➭ ( y + 20) = (x + 20) + 20

➭ y = x + 20 ---(2)

Put value of y = x + 20 in (1) , we get,

➭ y = 2x

➭ x + 20 = 2x

➭ 2x - x = 20

➭ x = 20 years

Put x = 20 years in (1) , we get,

➭ y = 2x

➭ y = 2×20

➭ y = 40 years

Hence,

• Sum of children's age = x = 20 years
• Man's age = y = 40 years

Answer 2

Given

The age of a man is twice the sum of the ages of his two children . After 20 years his age will be equal to the sum of the ages of his children at that time.

To Find

Find the present age of the man

Solution

★ Let the sum of the ages of two children be y and man's age be x

• x = 2y ---(i)

**According to the given condition**

• After 20 years

→ x + 20 = y + 20 + 20

→ x + 20 = y + 40

→ x - y = 40 - 20

Putting the value of x from (i)

→ 2y - y = 20

→ y = 20 yrs

Put the value of y in eqⁿ (i)

→ x = 2y

→ x = 2*20 = 40 yrs

Hence,

Man's present age = x = 40yrs