Question

present age of brahmins mother is 3 times his son's age five years hence her age will be 20 years more than that of Raman find their present age you will be grateful if you answer it pls..​

Answer 1

$\sf\large\underline{Correct\: Question:}$

• The present age of Raman's mother is 3 times of Raman's age. Five years hence her age will be 20 years more than that of Raman. Find their present.

$\sf\large\underline{Let:}$

• $\sf{The\: present\:age\:of\:mother=x\: year's}$
• $\sf{The\: present\:age\:of\:Raman=y\: year's}$

$\sf\large\underline{\:To\: Find:}$

• $\sf{The\: present\:age\:of\:mother\:and\:Raman}$

$\sf\underline{Given,\:in\:case\:1st}$

$\sf{\implies Raman's\: mother's\:age=3\: times\:of\:Raman's\:age}$

$\rm{\implies x=3y------(i)}$

$\sf\underline{Given,\:in\:case\:2nd}$

$\sf{\implies 5\: years\: hence\:her\:age\: will\:be\:20\: years\: more\:than\:of\: Rahman's\:age}$

$\rm{\implies x+5=(y+5)+20}$

$\rm{\implies x+5=y+25}$

$\rm{\implies x-y=25-5}$

$\rm{\implies x-y=20------(ii)}$

• $\sf{Putting\:the\: value\:of\:x=3y\:in\:eq\:ii}$

$\rm{\implies x-y=20}$

$\rm{\implies 3y-y=20}$

$\rm{\implies 2y=20}$

$\rm\green{\implies y=10}$

• $\sf{Putting\:the\: value\:of\:y=10\:in\:eq\:i}$

$\rm{\implies x=3y}$

$\rm{\implies x=3*10}$

$\rm\green{\implies x=30}$

Hence,

• The present age of mother is 30 year's
• The present age of Raman is 10 year's

Answer 2

Given :

• Present age of Raman's mother is 3 times of her son's age.
• 5 years hence , her age will be 20 years more than the age of Raman.

To find :

• Their present ages.

Solution :

Consider,

• Present age of mother = x years
• Present age of son = y years

According to the 1st condition :-

• Present age of Raman's mother is 3 times of her son's age.

$\implies\sf{x=3y.................eq[1]}$

According to the 2nd condition :-

• 5 years hence , her age will be 20 years more than the age of Raman.

After 5 years,

• Age of Raman's mother = (x+5) years
• Age of Raman = (y+5) years

$\implies\sf{x+5=(y+5)+20}$

$\implies\sf{x+5=y+25}$

$\implies\sf{3y+5=y+25\:[put\:x=3y\: from\:eq(1)]}$

$\implies\sf{3y-y=25-5}$

$\implies\sf{2y=20}$

$\implies\sf{y=10}$

Put y = 10 in eq(1).

$\implies\sf{x=3y}$

$\implies\sf{x=3\times\:10}$

$\implies\sf{x=30}$

• Present age of Raman = 10 years.
• Present age of Raman's mother = 30 years.

____________________

Verification :-

After 5 years,

• Raman's age = (10+5) = 15 years
• Raman's mother's age = (30+5) = 35 years.

A/Q,

Mother's age = Raman's age + 20

→ 35 = 15 + 20

→ 35 = 35

Verified _!