Practice Questions
The population of a town increases by 12% in one year and decreases by 10% the next year. Find the net percentage change.
Using $x + y + (xy/100)$: $12 - 10 + (12 \times -10)/100 = 2 - 1.2 = 0.8\%$ increase.
A number is increased by 25% and then decreased by 20%. Find the overall percentage change.
$25 - 20 + (25 \times -20)/100 = 5 - 5 = 0\%$.
If the price of petrol increases by 15%, by what percentage should consumption be reduced so that expenditure remains the same?
Reduction = $(r / (100+r)) \times 100 = (15 / 115) \times 100 \approx 13.04\%$.
A student scored 72 marks which is 28% less than the maximum marks. Find the maximum marks.
If score is 28% less, then $72\%$ of Max = 72. So Max = 100.
If the ratio of two numbers is 5:8, the first number is what percentage of the second?
$(5/8) \times 100 = 62.5\%$.
If A’s salary is 20% more than B’s, by what percent is B’s salary less than A’s?
Difference is 20 if B is 100. Percentage less than A (120) = $(20/120) \times 100 = 16.67\%$.
A's salary is first increased by 10% and then decreased by 10%. Find the net percentage change.
$10 - 10 + (10 \times -10)/100 = 0 - 1 = -1\%$ (1% decrease).
In an election, a candidate got 60% of the votes and won by 2000 votes. Find the total number of votes.
Winning margin $=60\%-40\%=20\%$. $20\%$ of total $=2000 \Rightarrow$ Total $=2000/0.2 = 10000$.
The price of sugar increases by 25%. By what percentage must consumption be reduced to keep expenditure the same?
Reduction $= r/(100+r) \times 100 = 25/125 \times 100 = 20\%$.
A shopkeeper marks goods 25% above cost price and gives a 10% discount. Find profit percentage.
Let $CP=100 \Rightarrow MP=125$. $SP = 125 \times 0.9 = 112.5$. Profit $=12.5\%$.
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