Question

The sum of the numeratar and demaminator of a fraction is 10. If both are increased by 1, the fraction becomes equal to 1/2. Find the original fraction

Answer 1

If fraction is a/b then
a + b = 10 ——(1)

(a + 1) / (b + 1) = 1/2
b + 1 = 2a + 2
b - 2a = 1 —-(2)

Subtract equation (1) from (2)
b - 2a - a - b = 1 - 10
-3a = -9
a = 3

Substitute a = 3 in equation (1)
a + b = 10
3 + b = 10
b = 7

Fraction is a/b = 3/7

Answer 2

let x be the numerator and y be the denominator .
so according to the given condition
x+y=10........(1)

now second condition is given that ,
(x+1) ÷ (y+1) =1/2
2x+2=y+1
2x-y+1=0.....(2)

adding equation (1) & (2) we get ,

3x=9
x=3

so,
y=7

so , original fraction is ,

3/7..........answer