Question

Two years ago, Raju was thrice as old as his daughter and six
years later, he will be four years older than twice her age.
How old are they now?

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Answer 1

Answer:

• Present age of Raju = 38 yrs
• Present age of his daughter = 14 yrs.

Explanation:

Let, present age of Raju = x

and present age of his Daughter = y

Now as given,

Two years ago, Raju was thrice as old as her daughter. so,

→ Raju's age two years ago = 3 ( Daughter's age two years ago )

→ x - 2 = 3 ( y - 2 )

→ x - 2 = 3 y - 6

→ x = 3 y - 4    ____equation (1)

Now, Also given that

Six years later Raju will be four years older than twice her daughter, hence

→ Raju's age 6 years later = 4 + 2 ( Daughter's age 6 yrs later )

→ x + 6 = 4 + 2 ( y + 6 )

→ x + 6 = 4 + 2 y + 12

[Using equation (1)]

→ 3 y - 4 + 6 = 2 y + 16

→ 3 y + 2 = 2 y + 16

→ 3 y - 2 y = 14

→ y = 14

[Putting value of y in equation (1)]

→ x = 3 y - 4

→ x = 3 ( 14 ) - 4

→ x = 42 - 4

→ x = 38

Therefore,

• Present age of Raju = 38 yrs and
• Present age of his daughter = 14 yrs.

Answer 2

$\huge \mathbb{\underbrace{\red{Question\:}}}$

Two years ago, Raju was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

$\huge{\boxed{\sf Solution}}$

Let the age of Raju be ‘ x ’ and the age of daughter = ‘ y ’ both in year

Then 2 years back their ages are x - 2 and y - 2

∴ By the given condition

️ ➭ x - 2 = 3(y - 2)

️ ➭ x - 3y = -4 ………(i)

️ Again six years later their age will be x + 6 and y + 6 respectively.

∴ By the given condition

️ ➭ x + 6 = 2(y + 6) + 4

➭ x - 2y = 10 ………(ii)

Subtraction from (ii) from (i) , we get

➭ -y = -14

➭ y = 14

Put y = 14 in equation (i) , we get

️➭ x - 3 × 14 = -4

️➭ x = 38

∴ x = 38 ; y = 14

So, Raju's present age = 38 years

Raju's daughter age = 14 years

Hence Verified