Question

Suraj is now half as old as his father. 20 years ago, Suraj's father was six times Suraj's age. What are their ages now?​

Answer 1

✯ Father's age = 50 years✯

✯ Suraj's age = 25 years✯

Step-by-step explanation:

Given:

• Suraj is now half as old as his father.
• 20 years ago, Suraj's father was 6 times of Suraj's age.

To find:

• Their present ages.

Solution:

Let the present age of Suraj's father be x years.

✯ Suraj is now half as old as his father.

Then,

• Present age of Suraj = x/2 years

★ ${\underline{\sf{According\:to\:the\: question,}}}$

• 20 years ago, Suraj's father was 6 times of Suraj's age.

20 years ago,

• Suraj's age = (x/2 - 20) years
• Suraj's father's age = (x-20) years

$\implies\sf{x-20=6(\dfrac{x}{2}-20)}$

$\implies\sf{x-20=6(\dfrac{x-40}{2})}$

$\implies\sf{x-20=3(x-40)}$

$\implies\sf{x-20=3x-120}$

$\implies\sf{x-3x=-120+20}$

$\implies\sf{-2x=-100}$

$\implies\sf{x=50}$

† Father's present age = 50 years

† Suraj's present age = 50/2 = 25 years

_________________

[ Verification ]

• Suraj's present age = 25 years
• Father's present age = 50 years

20 years ago,

• Suraj's age = (25-20) = 5 years
• Father's age = (50-20) = 30 years

A/Q,

Father's age = 6× Suraj's age

→ 30 = 6×5

→ 30 = 30

Hence Verified !

Answer 2

Answer:

ʟᴇᴛ ᴀʀᴜɴꜱ ᴀɢᴇ ʙᴇ x yᴇᴀʀꜱ ɴᴏᴡ.

ᴛʜᴇɴ ʜɪꜱ ꜰᴀᴛʜᴇʀꜱ ᴀɢᴇ =2x yᴇᴀʀꜱ

12 yᴇᴀʀꜱ ᴀɢᴏ, ᴀʀᴜɴꜱ ᴀɢᴇ ᴡᴀꜱ (x−12) yᴇᴀʀꜱ ᴀɴᴅ ʜɪꜱ ꜰᴀᴛʜᴇʀꜱ ᴀɢᴇ ᴡᴀꜱ (2x−12) yᴇᴀʀꜱ.

ɢɪᴠᴇɴ ᴛʜᴀᴛ, (2x−12)=3(x−12)

2x−12=3x−36

36−12=3x−2x

x=24

ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴀʀᴜɴ'ꜱ ᴩʀᴇꜱᴇɴᴛ ᴀɢᴇ =24 yᴇᴀʀꜱ.

ʜɪꜱ ꜰᴀᴛʜᴇʀ'ꜱ ᴩʀᴇꜱᴇɴᴛ ᴀɢᴇ 2(24)=48 yᴇᴀʀꜱ.

ᴠᴇʀɪꜰɪᴄᴀᴛɪᴏɴ:

ᴀʀᴜɴ'ꜱ ᴀɢᴇꜰᴀᴛʜᴇʀ'ᴀ ᴀɢᴇɴᴏᴡ : 244812 yᴇᴀʀꜱ ᴀɢᴏ

24−12=1248−12=36

36=3 (ᴀʀᴜɴ'ꜱ ᴀɢᴇ)

=3(12)=36