Question

1 in 4 families now owes money on a
personal loan, a rise of a quarter from
last year. What is the fraction of
families that owes money a year ago ?

Answer 1

"a rise of a quarter from  last year" means the percentage went up by 25%

x = old value

x + 25% of x = x + 0.25x = 1.25x = new value = 0.25 since "1 in 4" means 1/4 = 0.25

So,

1.25x = 0.25

x = 0.25/1.25

x = 0.2

x = 2/10

x = 1/5

Answer:  The fraction of families that owed money is 1/5, or 1 in 5.