Question

A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be:

A) 23 years B) 19 years C) 20 years D) 22 years
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Answer 1

QUESTION

A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be:

ANSWER

C) 20 years

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ʟᴇᴛ ᴛʜᴇ ᴀɢᴇ ᴏꜰ ꜰᴀᴛʜᴇʀ ʙᴇ x ᴀɴᴅ ᴀɢᴇ ᴏꜰ ꜱᴏɴ ʙᴇ ʏ.

As per question, x+y=60

ꜱɪx ʏᴇᴀʀꜱ ᴀɢᴏ ᴀɢᴇ ᴏꜰ ꜰᴀᴛʜᴇʀ ᴡᴀꜱ 5 ᴛɪᴍᴇꜱ ꜱᴏɴꜱ ᴀɢᴇ ꜱᴏ ᴡᴇ ᴄᴀɴ ᴅᴇʀɪᴠᴇ ᴛʜᴇ ꜰᴏʟʟᴏᴡɪɴɢ ᴇQᴜᴀᴛɪᴏɴ.

(x−6)=5(y−6)

⇒x−5y=−30+6

⇒x−5y=−24

To eliminate y term we can multiply eq(1) with 5...thus we get.

5x+5y=300

On adding eq(1) and eq(2) we get.5x+5y=300

x−5y=−24

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6x=276

x=46

ᴘᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇ ᴏꜰ x ɪɴ ᴇQ (ɪ) ᴡᴇ ɢᴇᴛ ʏ=14

ᴀꜰᴛᴇʀ ꜱɪx ʏᴇᴀʀꜱ ꜱᴏɴ'ꜱ ᴀɢᴇ ᴡɪʟʟ ʙᴇ

( 14+6)=.

20 years.

Ｔｈａｎｋｓ ｆｏｒ

ａｓｋｉｎｇ

_________________________

ᗩᑎᔕᗯᗴᖇ ᗷƳ ᗩᖇᗰᗩᑎ

Answer 2

Given :

• The sum of the ages of father and son is 60 yrs .
• Six years ago the age of the father was five times the age of the son.

To Find :

• Age of the son after 6 years .

Solution :

$\longmapsto\tt{Let\:the\:son's\:age\:be=x}$

$\longmapsto\tt{Let\:the\:father's\:age\:be=y}$

$\longmapsto\tt{x+y=60-------(1)}$

Before 6 years :

$\longmapsto\tt{Age\:of\:son=x-6}$

$\longmapsto\tt{Age\:of\:father=y-6}$

A.T.Q :

$\longmapsto\tt{y-6=5(x-6)}$

$\longmapsto\tt{y-6=5x-30}$

$\longmapsto\tt{y=5x-30+6}$

$\longmapsto\tt\bf{y=5x-24}$

Putting the value of y in eq. (1) :

$\longmapsto\tt{x+5x-24=60}$

$\longmapsto\tt{6x-24=60}$

$\longmapsto\tt{6x=60+24}$

$\longmapsto\tt{6x=84}$

$\longmapsto\tt{x=\cancel\dfrac{84}{6}}$

$\longmapsto\tt\bf{x=14}$

Therefore :

After 6 years :

$\longmapsto\tt{Age\:of\:son=x+6}$

$\longmapsto\tt{14+6}$

$\longmapsto\tt\bf{20\:yrs}$