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Answers
Answer:
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}⟼Letageofsisterbe=x
As Given that Rani is 6 years older than her younger sister. So ,
\longmapsto\tt{Age\:of\:Rani=x+6}⟼AgeofRani=x+6
After 10 years :
\longmapsto\tt{Age\:of\:Sister=x+10}⟼AgeofSister=x+10
\longmapsto\tt{Age\:of\:Rani=x+6+10}⟼AgeofRani=x+6+10
A.T.Q :
\longmapsto\tt{x+10+x+6+10=50}⟼x+10+x+6+10=50
\longmapsto\tt{2x+26=50}⟼2x+26=50
\longmapsto\tt{2x=50-26}⟼2x=50−26
\longmapsto\tt{2x=24}⟼2x=24
\longmapsto\tt{x=\cancel\dfrac{24}{2}}⟼x=
2
24
\longmapsto\tt\bf{x=12}⟼x=12
Value of x is 12 .
Therefore :
\longmapsto\tt{Age\:of\:Sister=x}⟼AgeofSister=x
\longmapsto\tt\bf{12\:yrs}⟼12yrs
\longmapsto\tt{Age\:of\:Rani=12+6}⟼AgeofRani=12+6
\longmapsto\tt\bf{18\:yrs}⟼18yrs