Question

the sum of numerator and denominator of a fraction is 16.if the numerator is decreased by 3 and the denominator by 4 the result is 4\5.then the sum of square of a numerator and denomimator is??​

Answer 1

Answer:

130

Step-by-step explanation:

Let the numerator be 'x' and denominator be 'y'

x+y=16

=>y=16-x                                     ................eqn1

ATQ,

$\frac{x-3}{y-4} =\frac{4}{5}$

=>5(x-3)=4(y-4)

=>5x-15=4y-16

=>5x-4y= -16+15

=>5x-4y= -1                                   ....................eqn2

Putting eqn1 in eqn2,

5x-4(16-x)=-1

=>5x-64+4x=-1

=>9x=63

=>x=7

=>y = 16-x = 16-7 = 9

$x^{2} =49\\y^{2} = 81$

$x^{2} +y^{2} = 130$