The age of a Father is twice the square of the age of his son. E

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 Multiple Choice QuestionsLong Answer Type

181. 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.
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182. The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
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183. One year ago, the father was 8 times as old as his son. Now his age is the square of his son’s age. Find their present ages.
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184. Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages.
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185. The age of a Father is twice the square of the age of his son. Eight years hence the age of the father will be 4 years more than three times the age of his son. Find their present ages. 


Let the present ages of son be x years.
Then,        Age of father = 2x2
After 8 years    Age of son =  (x + 8) yrs.
And              Age of father  = (2x2+8) yrs.
According to given condition
                      2 straight x squared plus 8 space equals space 3 left parenthesis straight x plus 8 right parenthesis plus 4
rightwards double arrow                 2 straight x squared plus 8 space equals space 3 straight x plus 24 plus 4
rightwards double arrow space space space space 2 straight x squared minus 3 straight x minus 20 space equals space 0
rightwards double arrow space space space space 2 straight x squared minus 8 straight x plus 5 straight x minus 20 space equals space 0
rightwards double arrow space space space space 2 straight x left parenthesis straight x minus 4 right parenthesis plus 5 left parenthesis straight x minus 4 right parenthesis space equals space 0
rightwards double arrow space space space space space space space space left parenthesis 2 straight x plus 5 right parenthesis space left parenthesis straight x minus 4 right parenthesis space equals space 0
rightwards double arrow space space space space space space space space space space space space space space space space space space space space space 2 straight x plus 5 space equals space 0 comma space space space space space space space space space space straight x space minus space 4 space equals space 0
rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 straight x space equals space minus 5 comma space space space space space space space straight x space equals space 4
rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight x space equals space fraction numerator negative 5 over denominator 2 end fraction left parenthesis Rejected right parenthesis
Hence,  present age of son = 4 years
And, present age of father = 2(4)2 = 32 yrs.

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186. The hypotenuse of a right angled triangle is 6 metres more than twice the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle.
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187. The hypotenuse of a right triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.
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188. The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
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189. The length of the hypotenuse of a right triangle exceeds the base by 2 cm and exceeds twice the length of altitude by 1 cm. Find each side.
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