1. Concept of Percentage:

By a certain percent, we mean that many hundredths.

Thus, x percent means x hundredths, written as x%

To express x% as a fraction: We have, x% = x/100

Thus, 20% =20/100 = 1/5.

To express a/b as a percent: We have a/b=(a/b)*100%

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

[(R/(100+R))*100]%

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

[(R/(100-R))*100]%

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/100)]^n

2. Population n years ago =P/[1+(R/100)]^n

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/100)]^n

2. Value of the machine n years ago = P/[1-(R/100)]^n

3. If A is R% more than B, then B is less than A by {[R/(100+R)]*100}%

4. If A is R% less than B, then B is more than A by {[R/(100-R)]*100}%

When any value increases by

10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)

20%, it becomes 1.2 times of itself.

36%, it becomes 1.36 times of itself.

4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases.

When any value decreases by

10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)

20%, it becomes 0.8 times of itself

36%, it becomes 0.64 times of itself

4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases.

NOTE:

1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and so on.

- 1. Problems on Train
- 2. Time and Work
- 3. Percentage
- 4. Time and Distance
- 5. Problems on ages
- 6. Profit and Loss
- 7. Average
- 8. Permutation and Combination
- 9. Problems on H.C.F and L.C.M
- 10. Square Root and Cube Root
- 11. Chain Rule
- 12. Alligation or Mixture
- 13. Stocks and Shares
- 14. Banker's Discount
- 15. Simple Interest
- 16. Compound Interest
- 17. Partnership
- 18. Height and Distance
- 19.Calendar

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