14. Presentages of Anu and are on the rate 4:5. Eight years from now the ratio of the ages will be 5:6. Find their presentare age
Answers
Answer:
Let the present age of Anu is 4x. Then, the present age of Raj will be 5x. so, Present age of Anu is 32 years and present age of Raj is 40 years.
CORRECT QUESTION :
Present ages of Anu and Raj are in the ratio 4:5 . Eight years from now the ratio of the ages will be 5:6. Find their present ages .
Given :
Present ages of Anu and Raj are in the ratio 4:5 .
Eight years from now the ratio of the ages will be 5:6.
To Find :
Present Age of Anu and Raj .
Solution :
\longmapsto\tt{Let\:Present\:age\:of\:Anu\:be=4x}⟼LetPresentageofAnube=4x
\longmapsto\tt{Let\:Present\:age\:of\:Raj\:be=5x}⟼LetPresentageofRajbe=5x
After 8 years :
\longmapsto\tt{Age\:of\:Anu=4x+8}⟼AgeofAnu=4x+8
\longmapsto\tt{Age\:of\:Raj=5x+8}⟼AgeofRaj=5x+8
A.T.Q :
\longmapsto\tt{\dfrac{4x+8}{5x+8}=\dfrac{5}{6}}⟼5x+84x+8=65
\longmapsto\tt{6(4x+8)=5(5x+8)}⟼6(4x+8)=5(5x+8)
\longmapsto\tt{24x+48=25x+40}⟼24x+48=25x+40
\longmapsto\tt{24x-25x=40-48}⟼24x−25x=40−48
\longmapsto\tt{-1x=-8}⟼−1x=−8
\longmapsto\tt\bf{x=8}⟼x=8
Value of x is 8 .
Therefore :
\longmapsto\tt{Present\:age\:of\:Anu=4(8)}⟼PresentageofAnu=4(8)
\longmapsto\tt\bf{32\:yrs}⟼32yrs
\longmapsto\tt{Present\:age\:of\:Raj=5(8)}⟼PresentageofRaj=5(8)
\longmapsto\tt\bf{40\:yrs}⟼40yrs