Question

10 years ago the age was 2/5 of her mother age while 10 years hence her age will be 3/5 of her mother age find the differnce of age of two

Answer 1

Answer:

Age difference is 30.

Step-by-step explanation:

Let mother's age be x.

10 years ago:

Age of girl = 2/5 * x

10 years later:

(2/5 * x) + 10 = 3/5 * x

(2/5 * x) + 10 = 3/5 * x

(3/5 * x) - (2/5 * x) = 10

(3x - 2x/5) = 10

x/5 = 10

x = 50

Hence,

Mother's age = 50

Therefore, girl's age = 2/5*x = 2/5 * 50 = 20

Age difference = 50 - 20 = 30

Answer 2

Answer: The difference in their age is 24 years.

Step-by-step explanation:

Concept : Ratio

Given : 10 years ago,  the age was 2/5 of her mother age while 10 years  

            hence her age will be 3/5 of her mother age

To Find : The difference in the age of mother and daughter

Solution :

Let the present age of daughter be x and the present age of mother be y.

10 years ago :

⇒ $x - 10 = \frac{2}{5} (y - 10)$  

⇒ $5(x - 10) = 2y - 20$

⇒ $5x - 50 = 2y - 20$

⇒ $5x - 2y = 30$   ...(i)

10 years hence :

⇒ $x + 10 = \frac{3}{5} (y + 10 )$  

⇒ $5(x + 10) = 3y + 30$

⇒ $5x + 50 = 3y + 30$

⇒ $5x - 3y = - 20$   ...(ii)

Subtracting equation (i) from (ii) :

⇒ $5x - 3y - 5x + 2y = - 20 - 30$

⇒ $- y = - 50$

∴ y = 50 years

∴ $5x - 2(50) = 30$

⇒ $5x = 130$

∴ x = 26 years

∴ The difference in their age = 50 - 26 = 24 years

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