Question

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

Answer 1

Given :

• Shobo's mother's present age is 6 times Shobo's present age.
• Shobo's age 5 years from now will be 1/3 of his mother's present age.

To find :

• Their present ages.

Solution :

Consider,

• Present age of Shobo's Mother= x years
• Present age of Shobo's = y years

According to the 1st condition :-

• Shobo's mother's present age is 6 times Shobo's present age.

$\to\sf{x=6y..............(1)}$

According to the 2nd condition :-

• Shobo's age 5 years from now will be 1/3 of his mother's present age.

$\to\sf{(y+5)=\dfrac{1}{3}\times\:x}$

$\to\sf{y+5=\dfrac{x}{3}}$

$\to\sf{y+5=\dfrac{6y}{3}\:[Put\:x=6y\: from\:eq(1)]}$

$\to\sf{y+5=2y}$

$\to\sf{y-2y=-5}$

$\to\sf{y=5}$

• Present age of Shobo = 5 years

Now , put y = 5 in eq(1) for getting the value of x.

$\to\sf{x=6y}$

$\to\sf{x=6\times\:5}$

$\to\sf{x=30}$

• Present age of Shobo's Mother = 30 years.

Therefore , the present age of Shobo is 5 years & present age of Shobo's Mother is 30 years.

Answer 2

Given :

• Shobo's mother's present age is six times Shobo's present age.

• Shobo's age five years from now will be one third of his mother's present age.

To find :

• Their present ages =?

Step-by-step explanation :

Let, the Shodo's present age be, x.

Then, the present age of Shobo's mother be 6x.

Five years from now Shobo's age will be, x + 5.

Five years from now Shobo's age will be 1/3rd of Shobo's mother age. [Given]

According to the question :

➮ x + 5 = 1/3 × 6x

➮ x + 5 = 6x/3

➮ 6x = 3(x + 5)

➮ 6x = 3x + 15

➮ 6x - 3x = 15

➮ 3x = 15

➮ x = 15/3

➮ x = 5.

Therefore, We got the value of, x = 5.

Hence,

The Shodo's present age, x = 5 years

Then, the present age of Shobo's mother, 6x = 6 × 5 = 30 years