A boy is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
Quadratic Equations
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Question

A boy is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

KnowledgeBoat · Accepted Answer

Let the age of sister be x years. It is given in question that the boy is twice as old as her sister. ⇒ Boy's age = 2x Four years hence, the product of their ages = 160 ⇒ (Sister's age + 4) x (Boy's age + 4) = 160 ⇒ (x + 4) (2x + 4) = 160 ⇒ x (2x + 4) + 4 (2x + 4) = 160 ⇒ 2x2 + 4x + 8x + 16 = 160 ⇒ 2x2 + 12x + 16 - 160 = 0 ⇒ 2x2 + 12x - 144 = 0 ⇒ x2 + 6x - 72 = 0 ⇒ x2 + 12x - 6x - 72 = 0 ⇒ x(x + 12) - 6(x + 12) = 0 ⇒ (x + 12)(x - 6) = 0 ⇒ (x + 12) = 0 or (x - 6) = 0 ⇒ x = -12 or x = 6 Since age cannot be negative, ∴ Present age of sister = 6 years Boy's age = 2 x 6 = 12 years Thus, the present age of boy = 12 years and sister = 6 years.

Mathematics

A boy is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

Quadratic Equations

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Mathematics

A boy is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

Quadratic Equations

Related Questions

The speed of a boat is 32 km/h. If the speed of stream is 8 km/h, the speed of the boat upstream is :36km/h40 km/h16 km/h24 km/h

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The speed of a boat is 32 km/h. If the speed of stream is 8 km/h, the speed of the boat upstream is :
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40 km/h
16 km/h
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