Percentage: Important concepts with examples

Today I am sharing important Percentage concepts with solved examples :-

Rule 1

If two values are respectively x%  and y%  more  than a third value,

Ques 1.

Two numbers are respectively 20% and 50% more than a third number, What percentage is the first of the second?

Solution :-

Ques 2.

Two numbers are respectively 30% and 40% less than the a third number .What percent is the second of the first?

Solution :-

Her our formulas would change , we will put a – sign instead of +sign.

Ques 3.

A positive number is divided by 5 instead of being multiplied by 5. What percent is the result of the required correct value?

Solution :-

      Let the number be 1

     Then the correct answer = 5

     The incorrect answer that was obtained = 1/5

Ques 4.

A positive number is by mistake multiplied by 5 instead of being divided by 5. By what percent more or less than the correct answer is the result obtained?

Solution :-

      Let the number be 1

       

      Then the correct answer= 1/5

      

       The incorrect answer that was obtained = 5

       

       The result is more than the correct answer= 5-1/5=24/5

Ques 5.

A man loses 12.5% of his money and, after spending 70% of the remainder, he is left with Rs 210. How much had he at first?

Solution :-

It is very easy and fast calculating method. The only thing is to remember the formula well.

Note: As his initial money is definitely more than the left money, Ther should not be any confusion in putting the larger value (100) in the numerator and the smaller value (100-12.5) in the denominator.

Ques 6.

3.5% of income is taken as tax and 12.5% of the remaining is saved .This leaves Rs. 4,053 to spend .What is the income?

Solution :-

Quicker method 

Rule 2

If x% of a quantity is taken by the first , y% of the remaining is taken by the second and the Z% of the remaining is taken by third person. Now if A is left in the fund, then there was

Rule 3

If x% of a quantity is taken by the first , y% of the increased is added. Again z% of the increased quantity is added. Now it becomes A, Then the initial amount is given by

Ques 7.

After deducting 10% from a certain sum , and 20% from the remainder, there is 3600 left. Find the original sum

Solution :-

      The original sum is naturally more than Rs. 3600.

Ques 8.

A man had Rs 4800 in his locker two years ago. In the first year, he deposited 20% of the amount in his locker. In the second year, he deposited 25% of the increased amount in his locker. Find the amount at present in his locker.

Solution :-

The amount is certainly more than Rs 4800. And in each year, the new amount is added. So, the sum should be multiplied by 

(100+20)/100 and (100+25)/100

Rule 4

Population formula 

If the original population of a town is P, and the annual increase is r%. What will be the population in n years?

Ques 9. 

If the annual increase in the population of a town is 4% and the present number of people is 15,625. What will be the population in 3 years?

Solution :-

Rule 5

The population of a town is P. It increases by x% during the first year, increases by y% during the second year and again increases by z% during the third year. The population after 3 years will be

Ques 10.

The population of a town is 8000.It increases by 10% during the first year and by 20% during the second year. What is the population after two years?

Solution :-

Rule 6

When the population of a town decreases by y% during the second year, while for the first and third year, it follows the same ( means it increases x% and z% respectively), the population after 3 years will be 

Ques 11.

The population of a town is 10,000, It increases by 10% during the first year . During the second year, it decreases by 20% and increases by 30% during the third year. What is the population after 3 years?

Solution :-

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