Question

The ratio of Mona's age to the age of het
mother is 3 : 11. The difference of their
ages
is 24 yrs. The ratio of their ages after 3 years
will be:
A. 1:3
B. 2 : 3
C. 3: 5
D. None of these​

Answer 1

Answer:

A. 1 : 3

Step-by-step explanation:

Question says that, The age ratio of Mona and her mother is 3 : 11. The difference between there age is 24 years. Find the ratio of their age after 3 years.

Step 1 : Let's assume the ages of :

➪ Mona = $3x$ years.

➪ Mona's mother = $11x$ years.

Step 2 : Calculate the value of ${\underline{\boldsymbol{x}}}$ :

Given,

$\implies 11x - 3x = 24 \bf years.$

${ \underline{ \boldsymbol{Solving \: for \: x :}}}$

$\implies 11x - 3x = 24$

$\implies \: 8x = 24$

$\implies x = \dfrac{24}{8}$

$\implies x = 3$

${ \blue{ \therefore{ \boldsymbol{x = 3 \: years}}}}$

Step 3 : Calculate the actual age :

➪ Mona's age : $3x = \bf 3(3) = 9 years.$

➪ Mona's mother's age : $11x = \bf 11(3) = 33 years.$

Step 4 : Find the age after 3 years :

➪ Mona's age = 9 + 3 = 12 years.

➪ Her mother's age = 33 + 3 = 36 years.

Step 5 : Forming in ratio :

→ Mona's age : Her mother's age

→ 12 : 36

→ 1 : 3 ${\boxed{\green{\checkmark{}}}}$