Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively.
Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y)
Now, 6x – 5y = 1/4(6x)
24x – 20y = 6x
18x = 20y
x/y = 20/18 = 10 / 9
Savings of P / Savings of Q = 6x – 5y / 8x – 8y
= [6(x/y) – 5] / [8(x/y) – 8]
= [(6 × 10/9) – 5] / [(8 × 10/9) – 8]
= 15/8
Savings of Q / Savings of R = 8x – 8y / 11x – 12y
= [8(x/y) – 8] / [11(x/y) – 12]
= (8 × 10/9) – 8 / (11 × 10/9) – 12
= 8/2
Ratio of savings of P : Q : R = 15 : 8 : 2