All quantitative aptitude examinations will have questions based on percentage system. Most of the questions from this category are related to
change of percentages or
successive change of percentages, for example “
In a shop price of Laptop which is marked at $1000 was discounted 20% for Christmas eve and further 30% discounted for New Year eve. What is the price of Laptop now?”
Here we have provided a set of basic concepts, tips and shortcuts on how to solve percentage problems easily and quickly. The following is a list of important formulas for Percentage:
- Percent implies “for every hundred”.
% is read as percentage and x % is read as x per cent.
- To calculate p % of y
(p/100) x y = (p x y)/100
p % of y = y % of p
- To find what percentage of x is y: y/x × 100
- To calculate percentage change in value
Percentage change = {change/(initial value)} x 100
- Percentage point change = Difference of two percentage figures
- Increase N by S % = N( 1+ S/100 )
- Decrease N by S % = N (1 – S/100)
- If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original point is 100x/ (100 + x) %.
- If A is x% more /less than B, then B is 100x/(100 + x) % less/more than A.
- If the price of an item goes up/down by x %, then the quantity consumed should be reduced by 100x/ (100 + x)% so that the total expenditure remains the same.
- Successive Percentage Change
If there are successive percentage increases of a % and b%, the effective percentage increase is:
{(a + b + (ab/100)}%
- Percentage – Ratio Equivalence:
1/2*100 = 50%
1/3*100 = 33.33%
1/4*100 = 25%
1/5*100 = 20%
1/6*100 = 16.66%
1/7*100 = 14.28%
1/8*100 = 12.5%
1/9*100 = 11.11%
1/10*100 = 10%
1/11*100 = 9.09%
1/12*100 = 8.33%
1/13*100 = 7.69%
1/14*100 = 7.14%
1/15*100 = 6.66%
1/16*100 = 6.25%
13.
Converting fractions – decimals to percents:
- Percent to Decimal:move the decimal point two places to the left. For example, 42% = 0.42.
- Percent to Fraction:place the percent number in the numerator and 100 in the denominator; simplify. For example, 42% = 42/100 = 21/50.
- Decimal to Percent:move decimal point two places to the right, For example, 1.6 = 160%.
- Fraction to Percent:first convert fraction to decimal, then follow the directions to convert from decimal to percent. For example, 5/6 = 0.833 repeating = 83 and 1/3 %.
14. If the price of a commodity increases by p%, then the reduction in consumption so as not to increase the expenditure is:
(P/100 + P*100)%
15. If the price of a commodity decreases by p%, then the increase in consumption so as not to decrease the expenditure is:
(P/100 – P*100)%
Percentage is a favourite topic of examiners across competitive examinations. Most students skip statement based questions on Percentages and fractions because they appear to be lengthy and time consuming. However, a good hold on decimals, fractions and percentages provide you an extra edge over other candidates.
