Out of the total income, a family saves 15% and the rest of the amount is spent on three types of expenditure – health, education and food in the ratio of 1:2:2. The income is Rs. 300 less than thrice the expenditure incurred on education. What is the difference between the savings and the expenditure incurred on health?

Let the total income of the family be I.
Savings = 15% of I=0.15I
Therefore, the remaining amount for expenditure = 100%−15%=85% of I=0.85I

This expenditure is divided among health, education, and food in the ratio of 1:2:2.
Total ratio parts = 1+2+2=5 parts

Expenditure on Health =
5
1
​
×0.85I=0.17I

Expenditure on Education =
5
2
​
×0.85I=0.34I

Expenditure on Food =
5
2
​
×0.85I=0.34I

According to the given condition, the total income is Rs. 300 less than thrice the expenditure on education:

I=3×(Expenditure on Education)−300
I=3×(0.34I)−300
I=1.02I−300
1.02I−I=300
0.02I=300
I=
0.02
300
​
=
2
30000
​
=Rs. 15,000
Now, calculate the values needed for the final difference:

Savings = 0.15×15000=Rs. 2,250

Expenditure on Health = 0.17×15000=Rs. 2,550

The difference between savings and expenditure on health is:

Difference=∣Savings−Expenditure on Health∣=∣2250−2550∣=Rs. 300