Question

1. Arjun's mother's present age is six times Arjun's present age. Arjun's age five years
from now will be one-third of his mother's present age. What are their present ages?​

Answer 1

Answer:-

Let the present age of Arjun be x years and his mother be y years.

Given:-

Arjun's mother's age is 6 times the present age of Arjun.

⟹ y = 6x -- equation (1).

Also given that,

After 5 years, Arjun's age will be 1/3 times his mother's age.

• Arjun's age after 5 years = (x + 5) years.

According to the above condition,

⟹ x + 5 = (1/3)(y)

⟹ 3(x + 5) = y

Substitute the value of y from equation (1).

⟹ 3x + 15 = 6x

⟹ 15 = 6x - 3x

⟹ 15/3 = x

⟹ 5 years = x

Substitute the value of x in equation (1).

⟹ y = 6x

⟹ y = 6(5)

⟹ y = 30 years.

∴

• Arjun's present age = 5 years.

• Arjun's mother's present age = 30 years.

Answer 2

Answer:

Given :-

• Arjun's mother present age is six times Arjun's present age. Arjun's age five years from now will be one-third of his mother's present age.

To Find :-

• What is their present age.

Solution :-

Let, the present age of Arjun's be x years

And, the present age of Arjun's mother will be 6x years

$\bigstar \: \boxed{\sf{According\: to\: the\: question\: :-}}$

⇒ $\sf x + 5 =\: 6x \times \dfrac{1}{3}$

⇒ $\sf x + 5 =\: \dfrac{6x}{3}$

By doing cross multiplication we get,

⇒ $\sf 6x =\: 3(x + 5)$

⇒ $\sf 6x =\: 3x + 15$

⇒ $\sf 6x - 3x =\: 15$

⇒ $\sf 3x =\: 15$

⇒ $\sf x =\: \dfrac{\cancel{15}}{\cancel{3}}$

➠ $\sf\bold{\green{x =\: 5\: years}}$

Hence, the required present ages are :

$\longmapsto$ Present age of Arjun :

$\implies$ $\sf x\: years$

$\implies$ $\sf\bold{\red{5\: years}}$

And,

$\longmapsto$ Present age of Arjun's mother :

$\implies$ $\sf 6x\: years$

$\implies$ $\sf 6 \times 5\: years$

$\implies$ $\sf\bold{\red{30\: years}}$

$\therefore$ The present age of Arjun is 5 years and the present age of Arjun's mother is 30 years.

${\underline{\boxed{\mathcal{\pmb{\quad VERIFICATION\: :-\quad}}}}}$

↦ $\sf x + 5 =\: 6x \times \dfrac{1}{3}$

By putting x = 5 we get,

↦ $\sf 5 + 5 =\: 6(5) \times \dfrac{1}{3}$

↦ $\sf 10 =\: 30 \times \dfrac{1}{3}$

↦ $\sf 10 =\: \dfrac{30}{3}$

By doing cross multiplication we get,

↦ $\sf 30 =\: 3(10)$

↦ $\sf 30 =\: 3 \times 10$

↦ $\sf\bold{30 =\: 30}$

➦ LHS= RHS

Hence, Verified .