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+1 vote
55.2k views
in Quadratic Equations by (44.5k points)
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Seven years ago Varun's age was five times the square of Swati's age. Three years hence, Swati's age will be two–fifth of Varun's age. Find their present ages.

3 Answers

+2 votes
by (55.4k points)
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Best answer

Let seven years, age of Swati was x years and age of Varun was 5xyears.

Present age of Swati = (x + 7) years

Present age of Varun = (5x2 + 7) years

Given, after 3 years swati's age will be 2/5th of Varun's age.

Age of Swati after 3 years = (x + 7 + 3) years = (x + 10) years

Age of Varun after 3 years = (5x2 + 7 + 3) years = (5x2 + 10) years

Given, age of Swati after 3 years = Two–fifths age of varun after 3 years

(x + 10) = 2(x2 + 2)

x + 10 = 2x2 + 4

2x2 – x + 4 – 10 = 0

2x2 – x – 6 = 0

2x2 – 4x + 3x – 6 = 0

2x(x – 2) + 3(x – 2) = 0

x = 2 [ Age can't be negative ]

Therefore, the present age of Swati = (2 + 7) = 9 year and the present age of Varun = 5(2)2+7=27 years.

+1 vote
by (15.0k points)

Seven years ago. let Swati's age be x years. Then, seven years ago Varun's age was 5x2 years.

Swati's present age = (x + 7) years, Varun's present age = (5x2 + 7) years

Three years hence, we have

Swati's age (x + 7 + 3) years = (x + 10) years

Varun's age = (5x2 + 7 + 3) = (5x2 + 10)

It is given that three years hence Swati's age will be 52​ of Varun's age

∴ x + 10 = 52​(5x2 + 10)

⇒ x + 10 = 2x2 + 4

⇒ 2x2 − x − 6 = 0

⇒ 2x2 − 4x + 3x − 6 = 0

⇒ (2x + 3)(x − 2) = 0

⇒ x − 2 = 0

⇒ x = 2

Hence Swati's present age = (2 + 7) years = 9 years

Varun's present age = (5(2)2 + 7) years = 27 years

+1 vote
by (155 points)
Seven years ago. let Swati's age be x years.

Then, 7 years ago Varun's age was 5x² years.

Swati's present age =(x+7) years,

Varun's present age=(5x²+7) years

3 years hence, we have

Swati's age (x+7+3) years =(x+10) years

Varun's age =(5x²+7+3)=(5x²+10)

It is given that 3 years hence Swati's age will be 2/5​ of Varun's age

∴x+10=2/5​(5x²+10)

 x+10=2x²+4

2x²−x−6=0

2x²−4x+3x−6=0

(2x+3)(x−2)=0

x−2=0

x=2

Swati's present age =(2+7) years =9 years

Varun's present age =(5×x2+7) years =27 years

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