Question

the ages of asha and Sushma are in ratio 7 ratio 2 , 8 years hence the ratio of their ages will be 5 ratio 2 find their present ages

Answer 1

Step-by-step explanation:

Let the present age of asha be 'x'

Let the present age of sushma be 'y'

from 1st condition

x/y =7/2

x×2=y×7

2x = 7y

2x-7y =0............(1)

from 2nd condition

(x+8)/(y+8) =5/2

2(x+8) =5(y+8)

2x + 16 = 5y + 40

2x -5y = 40-16

2x - 5y = 24.............(2)

Subtract both equations 1 & 2

2x-7y=0

-2x+5y= -24

-2y = -24

y = -24/-2

y = 12

put y=12 in 1st equation

2x- 5y=0

2x - 5×12=0

2x - 60=0

2x =60

x = 30

present age of asha is 30 years

present age of sushma is 12 years

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Ratio of present ages = 7 : 2
• Ratio of ages after 5 years = 5 : 2

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Present ages = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

• let the age of asha be x
• let the age of Sushma be y

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ATQ to 1st statement :-

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$\sf: \implies\: {\bold{ \dfrac{x }{y } = \dfrac{7}{2}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ 2x = 7y}}$

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$\sf: \implies\: {\bold{ 2x - 7y = 0}}$ ---- ( i )

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ATQ:- to 2nd statement :-

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$\sf: \implies\: {\bold{ \dfrac{x + 8}{y +8} = \dfrac{5}{2}}}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ 2( x + 8) = 5 ( y + 8)}}$

⠀⠀

$\sf: \implies\: {\bold{ 2x + 16 = 5y + 40}}$

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$\sf: \implies\: {\bold{ 2x - 5y = 40 - 16}}$

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$\sf: \implies\: {\bold{ 2x - 5y = 24 }}$-----( ii )

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Subtracting eq ii from i

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$\sf: \implies\: {\bold{ 2x - 5y - 2x + 7y = 24 - 0 }}$

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$\sf: \implies\: {\bold{ 2y = 24}}$

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$\sf: \implies\: {\bold{ y = \dfrac{24}{2}}}$

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$\sf: \implies\: {\bold{ y = 12 }}$

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• Putting value of y in eq ( i )

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$\sf: \implies\: {\bold{ 2x - 7y = 0 }}$

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$\sf: \implies\: {\bold{ 2x - 7 \times 12 = 0 }}$

⠀⠀

$\sf: \implies\: {\bold{ 2x - 84 = 0 }}$

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$\sf: \implies\: {\bold{ 2x = 84 }}$

⠀⠀⠀⠀

$\sf: \implies\: {\bold{ x = 42 }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Asha's age = x = 42 years
• Sushma's age = y = 12 years