Latest general Aptitude Question SOLUTION: If the difference of squares of two numbers is 88 and if the larger number is 5 less than twice the smaller number, Find the two numbers.

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(#M40009616) GENERAL question Keep an EYE

If the difference of squares of two numbers is 88 and if the larger number is 5 less than twice the smaller number, Find the two numbers.

Asked In general Devendra Marghade (12 years ago)

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Vignesh  (12 years ago)

9 and 13 are the two numbers.

Let X = Larger number
And Y = Smallest number

So,
X^2 - Y^2 = 88-------->(i)
X = 2Y - 5 ---------->(ii)

Substitute equation (ii) in (i)

(2Y-5)^2 - Y^2 = 88
4Y^2 - 20Y + 25 - Y^2 = 88
3Y^2 - 20Y - 63 = 0

Equation can be written as
3Y^2 - 27y + 7y - 63 = 0
3Y(Y-9) + 7(Y-9) = 0
(3Y+7) (Y-9) = 0
3Y+7=0 (or) Y-9=0
Y = -7/3 (or) Y=9
Y = 9
So,
X = 2Y-5
X = 2(9)-5
X = 13.

X = 13 = Larger number
Y = 9 = Smallest number

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