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
b. 60​

Answer 1

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

• 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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Answer 2

Question :

To find present age of Sudha.

Answer :

Given :

• Ratio of Sumathi's and Sudha's age is 3:5

• After 10 years, ratio of ages become 2:3

Let's find ::

• let , present ages be 3x and 5x (3x : 5x)

• Ratio of ages after 10 years is ,

• 3x + 10 : 5x + 10 = 2 : 3

$\sf⇢3x + 10 : 5x + 10 = 2 : 3 \\ \\ \: ⇢ \sf\frac{3x + 10}{5x + 10} = \frac{2}{3} \\ \\ ⇢\sf \: 3(3x + 10) = 2(5x + 10) \\ \\ ⇢\sf \: 3 \times 3x + 3 \times 10 = 2 \times 5x + 2 \times 10 \\ \\ \sf⇢ \: 9x + 30 = 10x + 20 \\ \\ \sf⇢ \: 10x - 9x = 30 - 20 \\ \\ \sf⇢1x = 10 \\ \\ \bf⇢x = 10$

So, x = 10.

Then, (3:5)

$\sf \bullet \: present \: age \: of \: sudha \: = 5x \\ \\ =\sf 5 \times 10 \: \\ \\ = \sf \: 50\: years$

ie, Sudha 's age is 50 years