Dear Readers, Here we have given the TOP 10 Shortcuts for Percentage Problems for IBPS PO/Clerk , candidates those who are preparing for the upcoming Bank PO/Clerk and all other competitive exams can make use of it.
Fraction and Percentage Equivalents:
Fraction |
%age | Fraction |
%age |
1/2 | 50% | 1/9 | 11.11% |
1/3 | 33.33% | 1/10 | 10% |
1/4 | 25% | 1/11 | 9.09% |
1/5 | 20% | 1/12 | 8.33% |
1/6 | 16.66% | 1/13 | 7.69% |
1/7 | 14.28% | 1/14 | 7.14% |
1/8 | 12.5% | 1/15 | 6.66% |
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Type 1:
Two number are in the ratio x:y if the first number is increased by a% and the second number is increased by b%, then
- Percentage increase in the sum of the number = (ax+by/x+y)ร100
- Percentage change in difference of the numbers = (ax-by/x-y) ร 100
Sum original numbers = x+y.ย –>ย sum of new numbers = x + ax/100 + y + by/100
Increase in sum = ax/100 + by/100 = ax+by/100ย –>ย increase = ax+by/x+yร100
Example:
1) Sukumarโs expenditure and savings are in the ratio 5:3. If his income increases by 12% and expenditure by 15%, then how much percent do his savings increase?
- a) 3%ย ย ย ย ย ย b) 5%ย ย ย ย ย ย ย ย ย c) 7%ย ย ย ย ย ย ย ย d) 27%
Solution:
Savings = Income โ Expenditure
Increase in savings = (18ร12-5ร15) / 8-5
= 21/3=7%
Type 2:
Assume that there are two persons A and B and Aโs salary is X%ย moreย than Bโs salary.
Then Bโs salary isย lesserย than Aโs salary byย X/(100+X) x 100%
Variant of the above formula:
If Aโs salary is X%ย lesserย than Bโs salary,
then Bโs salary will beย moreย than Aโs salary byย X/(100-X) x 100%
Example:
1) Ramโs salary is 30% more than Renuโs salary, by how much percent is Renuโs salary less than Ram?
Solution:
From the question you know that Ramโs salary is 30% more than that of Renu.
Therefore our value of X (to use in formula) = 30
Now, Renuโs formula is lesser than that of Renu by X/(100+X) x 100%
= 30/(100 + 30) x 100%
= 30/130 x 100%
= 23.07%
Type 3:
1) Raman`s salary was decreased by 50% and subsequently increased by 50%. How much percent does he lose?
- a) 45%ย ย ย ย ย b) 50%ย ย ย ย c) 75%ย ย ย ย d) 25%
Solution:
Let the original salary = Rs.100
( x^{2}/100 ) % or 100 ร โ50/100 ร 50/100 = -25 % or Decrease = 25%
Type 4:
1) The salary of a person was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
- a) 12.1%ย ย ย ย b) 10%ย ย ย ย c) 5%ย ย 6) 11.11%
Solution:
Let the original salary be Rs.100. New salary = Rs.90.
Percentage increase in salary = ( (Old โ New/New) ร 100) %
= ( (100 โ 90/90) ร 100) % = ( 100/ 9 ) %
=11.11%
Type 5:
1)Shabaโs mathematics test had 75 problems i.e.10 arithmetic, 30 algebra and 35 geometry problems. Although she had answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly. She did not pass the test because she got less than 60% of the problems right. How many more questions she would have to answer correctly to earn 60% of the passing grade?
a)2ย ย ย ย ย b) 6ย ย ย ย ย c) 5ย ย ย ย d) 7
Solution:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
70 /100 ร 10 + 40/ 100 ร 30 + 60 /100 ร 35 = 7 + 12+21= 40
questions to be answered correctly for 60% grade=60% of 75 = 45
therefore required number of questions= (45 – 40) = 5.
Type 6:
1) The population of a town is 1, 76,400. If it increases at the rate of 5% per annum, what will be its population 2 years hence? What was it 2 years ago
a) 170000ย ย ย b) 160000ย ย ย c) 180000ย ย e) None of this
Solution:
Population Increase for n year = p ร (1 + R/100)^{n}
=176400 ร (100 + 5)^{2}/100
= 176400 ร ( 105/100)^{2}
= 176400 ร ( (21/ 20) ร (21 /20)) = 194481.
Population 2 years ago = (174600/ (1+ 5/100)^{2} ) = ( 174600/ (105 /100)^{2}) = 160000.
Type 7:
If Aโs salary is 20% less then B`s salary, by how much percent is B’s salary more than A`s ?
a) 25%ย ย ย ย b) 30%ย ย ย c) 45%ย ย ย d) None of this
Solution:
Required percentage = (x/(100 โ x)) ร 100
= (20/100 โ20) ร 100 = 25%.
Type 8:
In a box of fruits, there are 25% of apples, 40% of orange and the rest are mangoes. If there are 2000 fruits in the box. How many mangoes are there in the box?
a) 600ย ย ย b) 700ย ย ย c) 500ย ย ย ย d) 300
Solution:
Total fruits = 100% = 2000
Mangoes = total fruits โ (apples + oranges) = 100%-(25%+40%)
= 100-65 = 35%
Given 100% = 2000
35% = ?
–>(35 *2000)/100 = 700.
Type 9:
1) When a discount of 20% offered by a trader, his sales increased by 80%. What was the effect on his receipts?
a) 55%ย ย ย ย b) 44%ย ย ย c) 45%ย ย ย d) None
Solution:
Shortcut formula,
-a + b โab/100
Net percentage = – discount % + Increment% – (discount%) (increment%) /100
=20 +80-1600/100 = -20 +80-16 = 44% increased
Type 10:
If the present population of a city is P and there is a incrementย of R1%, R2% ,R3% in first, second and third year respectively, then
Population of city after 3 yr=P(1+R1/100)(1+R2/100)(1+R3/100)
1) Population of a city in 2004 was 1000000. If in 2005 there is an increment of 15 % , in 2006 there is a decrement of 35 % and in 2007 there is an increment of 45 %, then find the population of city at the end of the year 2007.
a)1083875ย ย ย ย b) 1125685ย ย c) 8546945ย ย d) None
Solution :
Required population = P (1 + R1/100)(1 – R2/100)(1 + R3/100)
=ย P (1 + 15/100)(1 – 35/100)(1 + 45/100)
= 1083875
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