An easy one !!!
Algebra
Level
1
A fraction becomes 6/5 if 1 is added to each of the numerator and the denominator. However, if we subtract 5 from each, the fraction becomes 3/2. find the fraction.write them in the form of their sum i.e. - x+y
The answer is 20.
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1 solution
let the required fraction be x/y
acc. to cond. 1 , x+1 / y+1 = 6 / 5
5(x+1) = 6(y+1)
5x + 5 = 6y + 6
5x - 6y = 1 .........................................(1)
acc. to cond. 2 , x - 5 / y - 5 = 3 / 2
2(x - 5) = 3(y - 5)
2x - 10 = 3y - 15
2x - 3y = -5
4x - 6y = -10 .............................................(2)
subtracting (2) from (1) ,
x = 11
substituting x = 11 in (1) ,
5(11) - 6y = 1
6y = 55 - 1
6y = 54
y = 9
so, x + y = 11 + 9 = 20
x +y = 20 :)