# TOP 10 Shortcuts for Percentage Problems

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%

Â

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

1. Percentage increase in the sum of the number = (ax+by/x+y)Ã—100
2. Percentage change in difference of the numbers = (ax-by/x-y) Ã— 100

Sum original numbers = x+y.Â –>Â sum of new numbers = x + ax/100 + y + by/100

Increase in sum = ax/100 + by/100 = ax+by/100Â –>Â increase = ax+by/x+yÃ—100

Example:

1) Sukumarâ€™s 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?

1. a) 3%Â Â Â Â Â Â  b) 5%Â Â Â Â Â Â Â Â Â  c) 7%Â Â Â Â Â Â Â Â  d) 27%

Solution:

Savings = Income â€“ Expenditure

Increase in savings = (18Ã—12-5Ã—15) / 8-5

= 21/3=7%

Type 2:

Assume that there are two persons A and B and Aâ€™s salary is X%Â moreÂ than Bâ€™s salary.
Then Bâ€™s salary isÂ lesserÂ than Aâ€™s salary byÂ X/(100+X) x 100%

Variant of the above formula:
If Aâ€™s salary is X%Â lesserÂ than Bâ€™s salary,
then Bâ€™s salary will beÂ moreÂ than Aâ€™s salary byÂ X/(100-X) x 100%

Example:

1) Ramâ€™s salary is 30% more than Renuâ€™s salary, by how much percent is Renuâ€™s salary less than Ram?

Solution:

From the question you know that Ramâ€™s salary is 30% more than that of Renu.

Therefore our value of X (to use in formula) = 30

Now, Renuâ€™s 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?

1. a) 45%Â Â Â Â Â  b) 50%Â Â Â Â  c) 75%Â Â Â Â  d) 25%

Solution:

Let the original salary = Rs.100

( x2/100 ) % or 100 Ã— âˆ’50/100 Ã— 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?

1. a) 12.1%Â Â Â Â  b) 10%Â Â Â Â  c) 5%Â Â  6) 11.11%

Solution:

Let the original salary be Rs.100. New salary = Rs.90.

Percentage increase in salary = ( (Old â€“ New/New) Ã— 100) %

= ( (100 â€“ 90/90) Ã— 100) % = ( 100/ 9 ) %

=11.11%

Type 5:

1)Shabaâ€™s 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)2Â Â Â Â Â  b) 6Â Â Â Â Â  c) 5Â Â Â Â  d) 7

Solution:

Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)

70 /100 Ã— 10 + 40/ 100 Ã— 30 + 60 /100 Ã— 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) 170000Â Â Â  b) 160000Â Â Â  c) 180000Â Â  e) None of this

Solution:

Population Increase for n year = p Ã— (1 + R/100)n

=176400 Ã— (100 + 5)2/100

= 176400 Ã— ( 105/100)2

= 176400 Ã— ( (21/ 20) Ã— (21 /20)) = 194481.

Population 2 years ago = (174600/ (1+ 5/100)2 ) = ( 174600/ (105 /100)2) = 160000.

Type 7:

If Aâ€™s salary is 20% less then B`s salary, by how much percent is B’s salary more than A`s ?

a) 25%Â Â Â Â  b) 30%Â Â Â  c) 45%Â Â Â  d) None of this

Solution:

Required percentage = (x/(100 â€“ x)) Ã— 100

= (20/100 âˆ’20) Ã— 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) 600Â Â Â b) 700Â Â Â  c) 500Â Â Â Â  d) 300

Solution:

Total fruits = 100% = 2000

Mangoes = total fruits â€“ (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%Â Â Â Â  b) 44%Â Â Â  c) 45%Â Â Â  d) None

Solution:

Shortcut formula,

-a + b â€“ab/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 incrementÂ 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)1083875Â Â Â Â  b) 1125685Â Â  c) 8546945Â Â  d) None
Solution :

Required population = P (1 + R1/100)(1 – R2/100)(1 + R3/100)

=Â P (1 + 15/100)(1 – 35/100)(1 + 45/100)
= 1083875