Hope you all have practiced problems on trains. Now let us discuss problems on percentage. percentage is a way of expressing a quantity in 100.
The fundamental concept to remember when performing calculations with percentages is that the percent symbol can be treated as being equivalent to the pure number constant 1 / 100 = 0.01 , for example 35% of 300 can be written as (35/100) × 300 = 105
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:
- (50/100) × (40/100) = 0.50 × 0.40 = 0.20 = 20/100 = 20%.
It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = 25/100 = 0.25, not 25% / 100, which actually is (25/100) / 100 = 0.0025.)
The easy way to calculate addition in percentage (discount 10% + 5%):
- y = [(x1+x2) - (x1*x2)/100%]
For example, in a department store promotion "discount 10%+5%", the total discount is not 15%, but:
- y = [(10% + 5%) − (10% * 5%) / 100%] = [15% − 0.5%] = 14.5%
- SOME SAMPLE PROBLEMS:
- What is 200% of 30?
- What is 13% of 98?
- 60% of all university students are female. There are 2400 female students. How many students are in the university?
- Answer: , therefore
- There are 300 cats in the village, and 75 of them are black. What is the percentage of black cats in that village?
- Answer: , so and therefore n% = 25%.
- The number of students at the university increased to 4620, compared to last year's 4125, an absolute increase of 495 students. What is the percentual increase?
- Answer: , so , and therefore n% = 12%.
- SOME IMPORTANT CONCEPTS:
- An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 200% of initial); in other words, the quantity has doubled.
- An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
- A decrease of 60% means the final amount is 40% of the original (100% − 60% = 40%).
- A decrease of 100% means the final amount is zero (100% − 100% = 0%).
CONVERTING A FRACTION INTO PERCENTAGE:
- Divide the numerator of the fraction by the denominator (e.g. 4 ÷ 5=0.80)
- Multiply by 100 (Move the decimal point two places to the right) (e.g. 0.80*100 = 80)
- Round the answer to the desired precision.
- Follow the answer with the % sign (e.g. 80%)
CONVERTING PERCENTAGE TO FRACTION:
- Remove the Percent sign
- Make a fraction with the percent as the numerator and 100 as the denominator (e.g. 83/100)
- Reduce the fraction if needed
Percentage Increase/Decrease:If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
R x 100 % (100 + R)
If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
R x 100 % (100 - R)
Results on Population:Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
1. Population after n years = P 1 + R n 100
2. Population n years ago = P 1 + R n 100
Results on Depreciation:Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
1. Value of the machine after n years = P 1 - R n 100
2. Value of the machine n years ago = P 1 - R n 100
3. If A is R% more than B, then B is less than A by R x 100 %. (100 + R)
4. If A is R% less than B, then B is more than A by R x 100 %. (100 - R)
Will discuss further topics in upcoming blogs.please do comment on the blog and give suggestion to improvise it.