I got it,

A saving= 4x -5y --> = (1/4)*A

from that we get 4x-5y=x --> 3x=5y

saving ratios as mention are:

A: 4x-5y B:5x-6y

now we take the 3x=5y

A: 4x-3x(5y=3x)B:5x-6(3/5)X

so we got x:5x-(18/5)x --> let double both side with 5 to eliminate the fruction (1/5)


5x=25x-18x --> the answer is 5:7

Income A:B = 4:5
A's income = 4*x
B's income = 5*x
Expenditure A:B = 5:6
A's saving = 1/4 of his income = (1/4)*4*x = x
so,
A's Expenditure = 3/4 of his income = (3/4)*4*x = 3*x
Expenditure 3*x:B's expenditure = 5:6
B's expenditure = (6/5)*3*x = 18*x/5
B's saving = 5*x - 18*x/5 = 7*x/5
Saving Ratio A:B = x:7*x/5 = 5:7

The incomes of A and B are in the ratio 4:5 and their expenditures are in the ratio of 5:6. If A saves 1/4th of his income find the ratio of their savings.

Income:
A= 4x
B= 5x
expenditure:
A=5y
B=6y
saving:
A = 4x-5y = x => 3x=5y
B = 5x-6y = 5x- 18x/5 = 7x/5
required ratio = x/(7x/5) = 5/7

Hope this helps..!!