Percentages (increase / decrease in quantity)

Some Most Important Values

1/2 =50%                    2/5=40%

1/3 = 33.33%              3/5=60%

2/3 = 66.66%              1/6=16.66%

1/4=25%                     5/6 =83.33%

3/4 =75%                    1/5 = 20%

 Example 1:

The height of arun some times ago was 110cm. Now his height is 120cm. Find the percentage change in his height.

Solution:

120-110/110 x 100 = 9.09%

Shortcut 

10/110 = 1/11 = 9.09%

Alternatively : 12/11 = 109.09%, so increase = 9.09%

Example 2

The total expenses of a hostel were rs.8000 per month. Some students left the hostel due to which the new expenses come down by rs.1000. Find the percentage decreases in expenses of the hostel.

Solution:

1000/8000 = 1/8 = 12.5%

Example 3

Salary of raja is rs.9000 per month and salary of rani is rs. 10,000 per month.

             i) What per cent is the salary of rani to that of raja?

            ii) What per cent is the salary of raja to that of rani?

Solution:

i) 10,000/9,000 x 100 = 111.11%

Alternatively:

10/9 = 9/9 + 1/9 = 100% + 11.11% = 111.11%

ii) 9/10 = 90%                                ( 1/10 = 10%)

Hence, salary of raja is 90% to the salary of rani.