# 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%

ย

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)ร100
2. 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+yร100

Example:

1) Sukumarโ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%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 = (18ร12-5ร15) / 8-5

= 21/3=7%

Type 2:

Assume that there are two persons A and B and Aโs salary is X%ย moreย than Bโs salary.
Then Bโs salary isย lesserย than Aโs salary byย X/(100+X) x 100%

Variant of the above formula:
If Aโs salary is X%ย lesserย than Bโs salary,
then Bโs salary will beย moreย than Aโs salary byย X/(100-X) x 100%

Example:

1) Ramโs salary is 30% more than Renuโs salary, by how much percent is Renuโs salary less than Ram?

Solution:

From the question you know that Ramโs salary is 30% more than that of Renu.

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

Now, Renuโ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%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

( x2/100 ) % or 100 ร โ50/100 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?

1. 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)Shabaโ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)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 Aโs 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 โ20) 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 โ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 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