Question

sujatha is 30 yrs younger than her father. The product of their ages after 10 yrs will be 600 yrs more than the product of their present ages. What is the ages of sujatha today
a) 15 yrs
b) 10 yrs
c) 18 yrs
d) 16 yrs
e) 12 yrs ​

Answer 1

Given : Sujatha is 30 yrs younger than her father & the product of their ages after 10 yrs will be 600 yrs more than the product of their present ages.

Exigency To Find : The Present age of Sujatha .

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❍ Let's Consider Present age of Sujatha be x yrs .

⠀⠀⠀⠀⠀Given that ,

⠀》 Sujatha is 30 yrs younger than her father .

• Present age of Father will be ( x + 30 ) yrs .

⠀⠀⠀⠀⠀☆ After 10 years their ages :

• Sujatha's age will be ( x + 10 ) yrs .
• Sujatha Father's age will be ( x + 30 + 10 ) = ( x + 40 ) yrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: to \: the \: Question \::}}$

⠀⠀━━━⠀The product of their ages after 10 yrs will be 600 yrs more than the product of their present ages.

$\qquad \dashrightarrow \sf Sujatha \:Father's\:age_{(After \:10\:yrs)} \:\times Sujatha's\:age_{(After \:10\:yrs)} = \sf Sujatha \:Father's\:age_{(Present\:age)} \:\times Sujatha's \: age_{(Present \:age)} + 600$

$\qquad \dashrightarrow \sf (x + 40 ) \:\times ( x + 10 ) = (x + 30) \:\times x + 600 \\\\ \qquad \dashrightarrow \sf (x + 40 ) \:\times ( x + 10 ) = x^2 + 30x \: + 600 \\\\ \qquad \dashrightarrow \sf x(x + 40 ) + 10( x + 40) \: = x^2 + 30x \: + 600 \\\\ \qquad \dashrightarrow \sf x^2 + 40x + 10x + 400\: = x^2 + 30x \: + 600 \\\\ \qquad \dashrightarrow \sf x^2 + 50x + 400\: = x^2 + 30x \: + 600 \\\\ \qquad \dashrightarrow \sf \cancel {x^2} + 50x + 400\: = \cancel {x^2} + 30x \: + 600 \\\\ \qquad \dashrightarrow \sf 50x + 400\: = 30x \: + 600 \\\\ \qquad \dashrightarrow \sf 50x\: = 30x \: + 600 - 400 \\\\ \qquad \dashrightarrow \sf 50x\: = 30x \: + 200 \\\\ \qquad \dashrightarrow \sf 50x- 30x \: = \: 200 \\\\ \qquad \dashrightarrow \sf 20x \: = \: 200 \\\\ \qquad \dashrightarrow \sf x \: = \: \cancel {\dfrac{200}{20}} \\\\ \qquad \dashrightarrow \sf x \: = \: 10 \\\\ \qquad \therefore \pmb{\underline{\purple{\bf \:x = 10 \:yrs }} }\:\:\bigstar$

Therefore,

• Present Age of Sujatha is x = 10 yrs .
• Present Sujatha's Father is ( x + 30 ) = ( 10 + 30 ) = 40 yrs

$\therefore \underline { \sf Hence,\:Present \: ages \:of \:Sujatha \:and \: Sujatha's \:father \:are \bf \:\:10 \:yrs \:\& \:40 \:yrs \:\sf , \:respectively. }$

Answer 2

$\bigstar\;\underline{\boxed{ \frak{\pmb{ \: Given : sujatha \: age \: = 30yrs \:}}}}$

$\bigstar\;\underline{\boxed{ \frak{\pmb{ \: Given : after \: 10 \: yrs \: will \: be \: 600 \: yrs\:}}}}$

To Find : The Present age of Sujatha.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider Present age of Sujatha be x yrs.

⠀⠀⠀⠀⠀Given that ,

⠀◆ Sujatha is 30 yrs younger than her father.

Present age of Father will be ( x + 30 ) yrs.

⠀⠀⠀⠀⠀◆ After 10 years their ages :

Sujatha's age will be ( x + 10 ) yrs.

◆ Sujatha Father's age will be ( x + 30 + 10 ) = ( x + 40 ) yrs.

⠀⠀⠀⠀⠀⠀

$❍ \: \underline{\boxed{\rm \: According \: to \: the \: Question : - }}$

⠀⠀━━━⠀The product of their ages after 10 yrs will be 600 yrs more than the product of their present ages.

Calculation :

$\rightarrow \rm(x + 40) \times (x + 10) = (x + 30) \times x + 600 \\ \\ \rightarrow \rm(x + 40) \times (x + 10) = {x }^{2} + 30x + 600 \\ \\ \rightarrow \rm \: x(x + 40) + 10(x + 40) = {x}^{2} + 30x + 600 \\ \\ \rightarrow \rm \: {x}^{2} + 50x + 10x + 400 = {x}^{2} + 30x + 600 \\ \\ \rightarrow \rm \cancel{{x}^{2} } + 50x + 400 = \cancel{ {x}^{2} } + 30x + 600 \\ \\ \rightarrow \rm50x + 400 = 30x + 600 \\ \\ \rightarrow \rm50x = 30x + 600 - 400 \\ \\ \rightarrow \rm50x = 30x + 200 \\ \\ \rightarrow \rm50x - 30x = 200 \\ \\ \rightarrow \rm20 \times = 200 \\ \\ \rightarrow \rm \: x = \cancel\dfrac{200}{20} \\ \\ \rightarrow \rm \: x = 10$

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★ Therefore,

• Present Age of Sujatha is x = 10 yrs.

• Present Sujatha's Father is ( x + 30 ) = ( 10 + 30 ) = 40 yrs.

$\begin{gathered}\therefore \underline { \sf Hence,\:Present \: ages \:of \:Sujatha \:and \: Sujatha's \:father \:are\:\:10 \:yrs \:\& \:40 \:yrs \:\sf , \:respectively. }\end{gathered}$