Question

Two years ago, simon was 7 times as old as his son. in 3 years time, he will be will be 4 times as old as his son, find simon's present age

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Given:}}}}$

• Two years ago, simon was 7 times as old as his son. in 3 years time, he will be 4 times as old as his son

$\large{\underline{\red{\rm{Let:}}}}$

• $\sf{The\: present\:age\: Simon=x}$
• $\sf{The\: present\:age\:his\:son=y}$

$\sf{\implies Two\: years\:ago}$

• $\sf{The\:age\:of\:Simon=x-2}$
• $\sf{The\:age\:of\:his\:son=y-2}$

$\sf{\implies x-2=7(y-2)}$

$\sf{\implies x-2=7y-14}$

$\sf{\implies x-7y=-14+2}$

$\sf\green{\implies x-7y=-12-----(i)}$

$\sf{\implies After\:3\:years}$

• $\sf{The\:age\:of\:Simon=x+3}$
• $\sf{The\:age\:of\:his\:son=y+3}$

$\small{\underline{\green{\rm{As\:per\:the\: above\: information:}}}}$

$\sf{\implies x+3=4(y+3)}$

$\sf{\implies x+3=4y+12}$

$\sf{\implies x-4y=12-3}$

$\sf{\implies x-4y=9}$

$\sf\green{\implies x-4y=9-----(ii)}$

$\sf{\implies Solving\: equation\:1\:and\:2}$

$\sf{\implies x-7y=-12}$

$\sf{\implies x-4y=9}$

$\sf{by\: solving\: equation\:we\:get}$

$\sf{\implies -3y=-21}$

$\sf\red{\implies y=7}$

$\sf{putting\:the\: value\:y=7\:in\:eq\:1}$

$\sf{\implies x-7y=-12}$

$\sf{\implies x-7*7=-12}$

$\sf{\implies x=-12+49}$

$\sf\red{\implies x=37}$

Hence,

$\sf\purple{The\: present\:age\:of\:Simon=37\: year's}$

$\sf\red{The\: present\:age\:of\:his\:son=7\: year's}$

Answer 2

Answer:

The present age of Simon is 37 years and his son is 7 years old.

Step-by-step explanation:

Given:

Two years ago, simon was 7 times as old as his son

In 3 years time, he will be will be 4 times as old as his son

To find:

Their present ages

Solution:

Let the ages 2 years back be -

• Son as y

• Simon as 7y

Present ages -

• Son = (y + 2)
• Simon = (7y + 2)

Ages after 3 years -

• Son = (y + 2) + 3
• Simon = (7y + 2) + 3

According to the question,

Simon will be 4 times the age of his son in 3 years.

⇒ 7y + 2 + 3 = 4(y + 2 + 3)

⇒ 7y + 5 =4(y + 5)

⇒ 7y + 5 = 4y + 20

⇒7y - 4y = 20 - 5

⇒ 3y = 15

⇒ y = 15/3

⇒ y = 5

Present ages -

Son's age = 5 + 2 = 7

Simon's age = 7(5) + 2 = 35 + 2 = 37

Therefore, the present age of Simon is 37 years and his son is 7 years old.