Question

6. Rani is 6 years older than her younger sister. After 10 years, the sum of their ages will be 50 years. Find their present ages.​

Answer 1

Given :

• Rani is 6 years older than her younger sister.
• After 10 years, the sum of their ages will be 50 years.

To Find :

• Present age of Rani and her sister .

Solution :

$\longmapsto\tt{Let\:age\:of\:sister\:be=x}$

As Given that Rani is 6 years older than her younger sister. So ,

$\longmapsto\tt{Age\:of\:Rani=x+6}$

After 10 years :

$\longmapsto\tt{Age\:of\:Sister=x+10}$

$\longmapsto\tt{Age\:of\:Rani=x+6+10}$

A.T.Q :

$\longmapsto\tt{x+10+x+6+10=50}$

$\longmapsto\tt{2x+26=50}$

$\longmapsto\tt{2x=50-26}$

$\longmapsto\tt{2x=24}$

$\longmapsto\tt{x=\cancel\dfrac{24}{2}}$

$\longmapsto\tt\bf{x=12}$

Value of x is 12 .

Therefore :

$\longmapsto\tt{Age\:of\:Sister=x}$

$\longmapsto\tt\bf{12\:yrs}$

$\longmapsto\tt{Age\:of\:Rani=12+6}$

$\longmapsto\tt\bf{18\:yrs}$

Answer 2

Answer:

Step-by-step explanation:

Given,

Rani is 6 years older than her younger sister.

After 10 years, the sum of their ages will be 50 years.

To Find,

Their present ages.

Solution,

Let the present age of Rani's younger sister be x years.

And the present age of Rene be (x + 6) years.

Now, According to the Question,

⇒ (x + 6) + 10 + x + 10  = 50

⇒ (x + 16) + (x + 10) = 50

⇒ 2x + 26 = 50

⇒ 2(x + 13) = 50

⇒ x + 13 = 50/2

⇒ x + 13 = 25

⇒ x = 25 - 13

⇒ x = 12

Hence, the present age of Rani's younger sister is 12 years.

Now, Rani's age = x + 6

= 12 + 6 = 18 years.

Hence, the present age of Rani is 18 years.