Question

the denominator of a rational number is greater than the numerator by 3 if the numerator is increased by 14 denominator is decreased by 3 the new number will be formed 3 upon 4 what will be the original number​

Answer 1

N=x

D=x+D

x+14/×+3-3=3/4

×+14/×=3/4

3×=4×+56

3×-4×=56

-×=56

×=-56

Answer 2

Let

N = x

D = y

it is given that

y=x+3.....(1)

now according to the question

if N =x + 14 then D=y - 3

and the new number is 3/4

x + 14/ y - 3 = 3/4

3(y - 3) = 4(x + 14)

3y - 9 = 4x + 56

3y - 4x = 56 + 9

3y -4x = 65......(2)

it is given y = x + 3

put the value of y in (2)

3(x+3) - 4x = 65

3x +9 - 4x = 65

3x - 4x = 65 - 9

-x = 56

x = - 56

put the value of x in (2)

y = x + 3

y = -56 + 3 = -53

original number is = -56/-53 or 56/53