Q. The ratio of present ages of Virat and Sachin is 5 : 9. Three years hence ratio of their ages will be 3 : 5. Find Virat's present age?
Answers
Step-by-step explanation:
Given :
Present Ages of Virat and Sachin are in the ratio 5:9 .
After 3 years their ages will be in the ratio 3:5 .
To Find :
Present Age of Virat .
Solution :
\longmapsto\tt{Let\:Present\:Age\:of\:Virat\:be=5x}⟼LetPresentAgeofViratbe=5x
\longmapsto\tt{Let\:Present\:Age\:of\:Sachin\:be=9x}⟼LetPresentAgeofSachinbe=9x
After 3 years :
\longmapsto\tt{Present\:Age\:of\:Virat=5x+3}⟼PresentAgeofVirat=5x+3
\longmapsto\tt{Present\:Age\:of\:Sachin=9x+3}⟼PresentAgeofSachin=9x+3
A.T.Q :
\longmapsto\tt{\dfrac{5x+3}{9x+3}=\dfrac{3}{5}}⟼
9x+3
5x+3
=
5
3
\longmapsto\tt{5(5x+3)=3(9x+3)}⟼5(5x+3)=3(9x+3)
\longmapsto\tt{25x+15=27x+9}⟼25x+15=27x+9
\longmapsto\tt{25x-27x=9-15}⟼25x−27x=9−15
\longmapsto\tt{-2x=-6}⟼−2x=−6
\longmapsto\tt{x=\cancel\dfrac{-6}{-2}}⟼x=
−2
−6
\longmapsto\tt\bf{x=3}⟼x=3
Therefore :
\longmapsto\tt{Present\:Age\:of\:Virat=5(3)}⟼PresentAgeofVirat=5(3)
\longmapsto\tt\bf{15\:yrs}⟼15yrs
\longmapsto\tt{Present\:Age\:of\:Sachin=9(3)}⟼PresentAgeofSachin=9(3)
\longmapsto\tt\bf{27\:yrs}⟼27yrs
Answer:
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