Q.No : 28. If one number is 80% of the other and 4 times the sum of their squares is 656, then the number are4,58,1016,20none of these
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Let the number be x
The other number = 80/100 of x
= 4x/5
4 [x^2 + (4x/5) ^2] = 656
x^2 + 16x^2/25 = 164
(25x^2 + 16x^2) = 164 x 25
41x^2 = 164 x 25
x^2 = 164/41 x 25
x^2 = 4 x 25
x^2 = 100
Taking square root on either side
Therefore,
x = +/- 10
The other number = 80/100 of x
= 4x/5
4 [x^2 + (4x/5) ^2] = 656
x^2 + 16x^2/25 = 164
(25x^2 + 16x^2) = 164 x 25
41x^2 = 164 x 25
x^2 = 164/41 x 25
x^2 = 4 x 25
x^2 = 100
Taking square root on either side
Therefore,
x = +/- 10
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