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Ratio of Sumati's age and Sudha's age is 3:5. After 10 years the ratio of their ages becomes2:3. Find Sudha's present agea. 55b. 60​

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Answer:

\large\underline{\frak{\qquad Given :\qquad}} \\\\

  • Ratio of Sumati's age and Sudha's age is 3:5. After 10 years the ratio of their ages becomes 2:3.

\large\underline{\frak{\qquad To\:Find :\qquad}} \\\\

  • Sudha's present age = ?

\large\underline{\frak{\qquad Solution :\qquad}} \\\\

\sf Present\:Age \:\:\xrightarrow{After\:10\:Years} \:\:Future\:Age\\{\sf Sumati : Sudha \qquad \qquad\:\:\:Sumati : Sudha} \\{\qquad\sf 3 \::\:5 \qquad \qquad \qquad\qquad\:\: 2 : 3} \\\\

Let present age of Sumati be be 3x and present age of Sudha be 5x.

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\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\\

\dashrightarrow\:\: \sf \dfrac{Sumati's \:age + 10}{Sudha's\: age + 10} = \dfrac{2}{3} \\\\\\

\dashrightarrow\:\: \sf \dfrac{3x + 10}{5x+ 10} = \dfrac{2}{3} \\\\\\

Cross multiplying both the sides we get :

\dashrightarrow\:\: \sf 3(3x + 10) = 2(5x + 10) \\\\\\

\dashrightarrow\:\: \sf 9x + 30 = 10x + 20 \\\\\\

Transferring the constant to LHS and variable based expression to RHS.

\dashrightarrow\:\: \sf 30 - 20 = 10x - 9x \\\\\\

\dashrightarrow\:\: \underline{ \boxed{ \textsf { \textbf{x = 10 years }}}}\\\\\\

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\large\bigstar \: \underline{\textsf{Present Age of Sudha }} \\\\

:\implies \textsf{ Present Age of Sudha = 5x} \\\\\\

:\implies \textsf{ Present Age of Sudha = 5(10)} \\\\\\

:\implies \underline{ \boxed{ \textsf{ Present Age of Sudha = 50 years} }}\\ \\\\

\therefore\:\underline{\textsf{Present age of Sudha is \textbf{50 years}}}. \\\\

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