Question

The denominator of a rational number is greater than its numerator by 3. If numerator and denominator is increased by 1 and 4 , the number obtained is 1/2 , find the number​

Answer 1

Heya user

here is your answer

let the numerator = x

so denominator = x+3

so the rational number = x/x+3

if the numerator decreased by 1 = x-1

if the denominator decreased by 4

= (x+3)-4

= x+3-4

= x-1

so the number formed = (x-1)/(x-1)

so according to the question

(x-1)/(x-1) = 1/2

=> x-1 = 1/2 × (x-1)

=> x-1 = (x-1)/2

=> x = (x-1)/2 + 1

=> x = [(x-1) + 2]/2

=> x = [ x-1+2 ] /2

=> x = (x+1)/2

=> x = x/2 + 1/2

=> x - x/2 = 1/2

=> (2x - x)/2 =1/2

=> x/2 = 1/2

=> x = 1/2 × 2

=> x = 1

So numerator = x = 1

denominator = x+3 = 1+3 = 4

Hence the rational number is 1/4

HOPE THIS HELPS

any further doubt ask me frankly

always present for help

thanks