Question

the income of a person is H.his expenditure and savings are in the ratio 3:5.if income is raised by 10 but his expenditure remains the same what is the new ratio of the expenditure to the savings

Answer 1

I suppose in the question, the Income is raised by 10 AND NOT by 10%

Income = H  units

As expenditure : Savings = 3:5  or  3 / (3+5)  :  5 / (3+5)    =  3/8  :  5/8

Expenditure = H * [ 3 / (3+5)  ]  =  3 H / 8  units
Savings = 5 H / 8  units

Now, Income is raised by 10 and NOT 10%, So  New income is = H + 10 units
Expenditure =  same = 3 H / 8 units
Savings = H+10 - 3H/8 = 5H/8 + 10

New ratio of expenditure to savings

[ 3H/8 ]  /  [ 5H/8 + 10 ]         multiply numerator & denominator by 8

3 H / [ 5H + 80 ]