Question

Ratio of Sumati's age and Sudha's age is 3:5. After 10 years the ratio of their ages becomes
2:3. Find Sudha's present age
a. 55 and b. 60​
​

Answer 1

$\large\underline{\tt{\qquad Given :\qquad}}$

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

$\large\underline{\tt{\qquad To\:Find :\qquad}}$

Sudha's present age = ?

$\large\underline{\tt{\qquad Solution :\qquad}}$

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

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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${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$

$\red{\tt{sωєєтcнαям♡~}}$

Answer 2

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

2:3. Find Sudha's present age

a. 55 and b. 60

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

2:3. Find Sudha's present age

a. 55 and b. 60

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

2:3. Find Sudha's present age

a. 55 and b. 60