Father reduced the quantity of food bought for the family by 10% when he found that the cost of living had increased 15%. Thus the fractional increase in the family food bill is now
A
\(\frac{1}{12}\)
B
\(\frac{6}{35}\)
C
\(\frac{19}{300}\)
D
\(\frac{7}{200}\)
E
\(\frac{5}{100}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Let the cost of living = y.
The new cost of living = \(y + \frac{15y}{100} = 1.15y\)
The food bill now = \((1 - \frac{90}{100})(1.15y)\)
= \(1.035y\)
The fractional increase in food bill = \((1.035 - 1) \times 100% = 3.5%\)
= \(\frac{35}{1000} = \frac{7}{200}\)
Source: Myschool Past Questions Archive (Record #32696)