Percentage practice problems with shortcut tricks

Example 1  : Find 8 percent of Rs. 225.

8% of 225=8*225/100

2/25*225=18 Rs

Example 2:  Express 20, as a percentage of 40.

20/40 *100

=50%

Example 3: The population of town has increased from 50,000 to 60,000, find increased percentage?

Increase in population= 60,000-50,000=10,000

Percentage increase= 10,000/60,000 *100

=100/6%

Example 4: In a basket of fruits , 60% are mangoes and remaining 40 % are apples. 25 % of apples are green and rests 75% are red. In mangoes 80% are red and rests are green. What percentage of green fruits are mangoes?

If the total numbers of fruits are 100 then 60 are mangoes and 40 are apples.

Green Apples= 25% of 40= 10

Green mangoes= 20 % of 60= 12

Total number of green fruits= 10+12=22

Thus required percentage of green mangoes= 12/22 *100

=54.5%

Example 5: The tax on commodity is diminished by 20% and its consumption increased by 15%. Find effect on revenue?

Here applying concept of successive percentage change

Effect= 15-20-15*20/100

= -8%

So there is decreased of 8%.

Example 6: The length and breadth of rectangles are 10 cm and 5 cm respectively. The length is increased by 10% and breadth is increased by 5%. What is new are of rectangles?

Here applying concept of successive percentage change

=10+5+10*5/100

=15.5%

So the original area i.e 10*5=50 sq. cm. increased by 15.5% hence new area=

50 + 15.5% of 50

=57.75 sq. cm

Example 7: If the price of potato increased by 20 % and subsequently by 40%. What is final price per kg if the original price was Rs 25 per kg?

Now using the fraction methods

25 * 120/100 *140/100

=Rs 42

Example 8: A student who scored 50% of maximum marks and failed by 2 marks. If he had scored 10 % more than what he got then he would have managed to get pass. What was maximum marks in exams?

If pass max marks is M then he scored 0.5M.

If he had scored 10 5 more then he would have scored 0.5M+105 of 0.5m i.e 0.55M

Now 0.55M-0.5M=12

M=240

Example 9: 40 liter of mixture  of milk and water contain 10% water. How much water must be added to make the water 20% in new mixture?

Quantity of water= 10% of 40=> 4

Now suppose k liter of water is added

4+k=20% of (40+k)

K= 20/4=>5litre

Example 10: shyam’s expenditure and savings are in ratio of 3:2. His income increases by 10% and expenditure by 12%. What percentage does his saving increase?

Let the expenditure and saving are Rs 300 and Rs 200. So income is calculated as

300+200=Rs500

Now income increased by 10% i.e 550

Expenditure increased by 12 % i.e 336

So saving= 550-336=> Rs 214 which is 7% more than Rs 200. So our answer would be 7%.

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