Question

The numerator of a rational number is 3 less than the denominator. If the
numerator is increased by 8 and the denominator increased by 14, we get the
same number. Find the number.
​

Answer 1

Answer:

32/47

Step-by-step explanation:

Let numerator be x

then denominator is x+3

therefore the fraction is x/x+3

next, numerator increased by 8, i.e, x+8

and denominator increases by 14, i.e, x+17

also, (x/x+4) = (x+8)/(x+17)

=> (x) × ( x+17 ) = (x+4) × (x+8)

=> x^2 + 17x = x^2 + 12x + 32

=> 5x = 32

=> x= 32/5

therefore fraction is (32/5) / {(32/5) + 3}

i.e, 32/47