Percentages Tricks - Application with Examples

Few weeks back I shared how to make application of Percentages concept. Today I am sharing examples to illustrate the usage of this concept.

Question 1.

Salary of A is 75% of B’s salary. Salary of A is increased by 40% but salary of B is increased by only 10%. Whose salary is more and by what percent?

     Solution:

     

     Salary of A = 75% of Salary of B 

Question 2.

The price of a commodity increases by 25% and therefore a house wife reduces the quantity purchased by certain percentage in order to maintain expenditure. By what percentage should she reduce the quantity purchased ?

The short cut could be made on the basis that 

Price ∝  1/Quantity

Which means if you reduce the price , the quantity will increase and vice-versa, so our formula would be :

Question 3.

The price of a commodity increases by 25%. Find out the reduction in quantity such that the expenditure is allowed to increase by 20%?

Now again let the price = 100, Quantity =100

Expenditure =100 X 100= 10000

New Price =125, New Quantity =?

New Expenditure =10000+20%of 10000=12000

New Expenditure= New Price X New Quantity

            

12000 =   125 X New Quantity

New Quantity = 12000/125= 96

Required reduction% in the quantity = (100-96)/100 X 100 =4%

Question 4.

The price of a commodity increases by 20% and expenditure is allowed to increase by 15%. What changes would occur in the quantity ?

Question 5.

The price of an apple reduce by 10% and thus enables a person to buy 10 more apples for Rs. 50. Find out :

1. New price
2. Old Price
3. New Quantity
4. Old Quantity

Solution:

Let us say, initially he is able to buy m apples for Rs.50.

Initially

Rs.50    = m apples

Now

Rs. 50 = (m+10) apples

Now we can see that

⇒ Earlier in Rs. 50 , 90 apples could be bought

Now in Rs. 50, 90+10=100 apples could be bought. which clearly shows that the price has dropped

New price = Rs. 50/100

Old price = Rs. 50/90

Now let us learn a quick way

The person has got = Rs 50

The price reduces by 10 % that means he could save 10% of what he has in his pocket.

He could buy the apples in Rs 45 and can save Rs 5,  but instead of saving, he is buying 10 apples for Rs 5

⇒ Rs. 5  = 10 apples

Rs. 1  = 2 apples which means Rs 50 = 100 apples

The new price of one apple = Rs.0.5

Earlier Rs 50 = 100-10 = 90 apples

The old price per apple = 50/90= Rs. 0.55

So this was another method to deal with such questions.

Question 6.

A container has got 130 liters of water which has 15% salt. From this container some of the water has got evaporated and after evaporation, the salt strength in the container is now 20%. Find out how much water evaporated from the container.

Solution - Let the water evaporated= m liter