Question

The present age of Sahil’s mother is three times the present age of Sahil. After 10 years their ages will add to 68 years. Find their present ages.

Answer 1

Answer:-

Let the present age of Sahil be "x" years.

Given:

Sahil's mother's present age = 3 * present age of Sahil

→ Sahil's mother's age = 3x years.

And,

The sum of their ages become 68 years after 10 years.

Sahil's age after 10 years = (x + 10) years

Sahil's mother's age after 10 years = (3x + 10) years.

Hence,

x + 10 + 3x + 10 = 68

→ 4x + 20 = 68

→ 4x = 68 - 20

→ 4x = 48

→ x = 48/4

→ x = 12

• Sahil's present age = 12 years
• Sahil's mother's present age = 3 * 12 = 36 years.

Answer 2

$\large\mathcal{\underbrace{\red{SOLUTION:-}}}$

✍️ Let,

• Present age of Sahil = ‘x’

• Present age of Sahil's mother = ‘y’

✴️ According to the question, the present age of Sahil's mother is 3times the present age of Sahil .

$\checkmark\:\rm{\boxed{\bold{y\:=\:3x}}}$------(1)

✴️ After 10 year's,

• Age of Sahil = (x + 10)
• And age of Sahil's mother = (y + 10)

✴️ Again given that, After 10 year's their ages will add to 68 year's .

$\checkmark\:\rm{\boxed{\bold{(x\:+\:10)\:+\:(y\:+\:10)\:=\:68\:}}}$

$\rm{\implies\:x\:+\:y\:+\:20\:=\:68\:}$

$\rm{\implies\:x\:+\:y\:=\:68\:-\:20\:}$

$\rm{\implies\:x\:+\:y\:=\:48\:}$

☞ Put the Value of ‘y = 3x’ is the above equation, we get

$\rm{\implies\:x\:+\:3x\:=\:48\:}$

$\rm{\implies\:4x\:=\:48\:}$

$\rm{\underline{\implies\:x\:=\:12\:}}$

$\bigstar\:\rm{\purple{\boxed{\therefore\:Present\:age\:of\:Sahil\:is\:12years\:.}}}$

✍️ Now, put the value of ‘x = 12’ in the equation (1), we get

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

$\rm{\implies\:y\:=\:3\times{12}\:}$

$\rm{\underline{\implies\:y\:=\:36\:}}$

$\bigstar\:\rm{\blue{\boxed{\therefore\:Present\:age\:of\:Sahil's\:mother\:is\:36years\:.}}}$