Question

the denominator of a common fraction exceeds the numerator by 10 if 8 is added to the numerator and denominator the new fraction obtained is 5/6 find out original number

Answer 1

Let the numerator be x

So, the dinominator be x + 10

Original Fraction = x / x + 10

If 8 is Added to both -

Numerator = x + 8

Dinominator = x + 10 + 8 = x + 18

According to Question,

x + 8 / x + 18 = 5 / 6

=> 6(x + 8) = 5(x + 18)

=> 6x + 48 = 5x + 90

=> 6x - 5x = 90 - 48

=> x = 42

Required Fraction -

Numerator = x = 42

Dinominator = x + 10 = 42 + 10 = 52

Hence, the original Fraction is 42/52

Answer 2

Let the fraction be a/(a+10)

8 is added

i.e., (a+8)/(a+10+8) = 5/6

(a+8)/(a+18) = 5/6

6a+48=5a+90

a=42=Numerator

a+10 = 52 = Denominator

the original number is = 42/52