Question

four years ago the ratio of the ages of a mother and her daughter was 3:1.The sum o their present ages is 56 years.Find the present age of the daughter.​

Answer 1

Solutions :-

Given :
Four years ago the ratio of the ages of a mother and her daughter was 3 : 1

Let the present ages a mother and her daughter be x and y respectively.

According to the question,


(x - 4) / (y - 4) = 3/1
=> (x - 4) = 3 (y - 4)
=> x - 4 = 3y - 12
=> x - 3y = - 12 + 4
=> x - 3y = - 8 _____(i)

x + y = 56
=> x = 56 - y _____(ii)


Putting the value of x in equation (i) we get,

=> 56 - y - 3y = - 8
=> - 4y = - 8 - 56
=> - 4y = - 64
=> y = - 64/-4 = 16


Hence,
The present age of the daughter = 16 years

Answer 2

According to the Question

4 years ago the ratio of the ages of a mother and her daughter  

= 3 : 1

Suppose the ages a mother and her daughter be p and y

By the Information

$\bf\huge\frac{p - 4}{y - 4} = \frac{3}{1}$

⇒ (p - 4) = 3 (y - 4)

⇒ p - 4 = 3y - 12

⇒ p - 3y = - 12 + 4

⇒ p - 3y = - 8 ... (Eqn i)

⇒ p + y = 56

⇒ p = 56 - y ...... (Eqn ii)

Substitute value of p in equation (i)

⇒ 56 - y - 3y = - 8

⇒ - 4y = - 8 - 56

⇒ - 4y = - 64

$\bf\huge y = \frac{-64}{(-4)}$

= 16

Therefore

Present age of the daughter = 16 years