In Quantitative Aptitude Percentage concept helps to solving a problem of Data Interpretation, Profit and loss, SI and CI, Mixture and allegations etc.In this post i have covered introduction and the very common type of percentage problem that are frequently asked in various competitive exam.

=> To express X% as a fraction

 X%=X/100

For example: 56%

56%=56/100=14/25

=> Suppose A=120

                        B=150

(Q1)->A is a what percent(%) of B ?

Solution: X%(let) of B=A

(X/100) ×150 =120

∴ X=(120×100)/150

=80% ans

(Q2)->B is what % of A ?

solution: X% of A=B

(X/100) ×120 =150

∴ X=(150×100)/120

=125% ans.

(Q3)->B is how % more than A ?

Solution: difference=150-120=30

∴ Required percentage = (30×100)/120

=25% ans.

(Q4)->A is how % less than B ?

Solution: difference=150-120=30

∴ Required percentage = (30×100)/150

=20% ans.

Percentage Problem Concept:

* Suppose X increases by 40% means

X×(100+40)/100

=(X×140)/100 

* Suppose X decreases by 30% means

X×(100-30)/100

=(X×70)/100

(Q1)->If salary of A is 300. now 40% increases then new salary of A.

Solution:

(Q2)->If salary of A is 300. now 40% decreases then new salary of A.

Solution:

(Q3)->Salary of A is 120.now what percent of salary increases then new salary of A is 144 ?

Solution:

   % increase=(24×100)/120

                         = 20% Ans

Note: Rs 24, Rs 120 पर increase हो रहा है तो percentage हमेशा initial amount पर calculate किया जाता है न कि increased वाले amount पर .

(Q4)->If salary of A increases 40% then new salary of A is 490.find out initial salary

Solution:

 Now

                     (X×140)/100=490

                     ∴ X=(490×100)/140

                            =350Ans

Common type of percentage problem that are frequently asked in various competitive exam

(Q1)->If x% of Y% of 80 is the same as 25% of 900 then the value of xy is.

Solution: 80×(y/100)×(x/100)=900×(25/100)

                 => 4xy/500=25×9

                  ∴xy=(25×9×500)/4

                         =28125 Ans

(Q2)->If 40% of 4/5 of 3/4 of a number is 48, then what is 1% of the same number?

Solution: Let the number be x

                => x×(3/4)×(4/5)×(40/100)=48

               ∴ x=(48×4×5×100)/(3×4×40)

                    =200

Now, 1% of 200=200×(1/100)

                            =2 Ans.

(Q3)->What percent of 15 hours is 18 seconds?

Solution: x% of 15 hours = 18 seconds

                => x% of 15×60×60 seconds =18 seconds

                => 15×60×60×(x/100)=18

                ∴ x=(18×100)/(15×60×60)

                     =1/30% Ans

(Q4)->What percent of 3.5 kg is 70 gms?

Solution: x% of 3.5 kg=70 gms

                => x%×3.5×1000 gms=70 gms

                => (x/100)×3.5×1000 gms=70gms

                ∴ x=(70×100)/3.5×1000

                      =2% Ans.

(Q5)->50% of a number when added to 50 is equal to the number. The number is.

Solution:Let the number be 100x

                => 100x×(50/100)+50=100x

                => 50x+50=100x

                => 50x=50

                ∴ x=1

Number=100x

                =100×1

                 =100 Ans

(Q6)->When 75 is added to 75% of a number, the answer is the number. Find 40% of that number.

Solution: Let the number be 100x

                 =>100x×75%+75=100x

                =>100x ×(75/100)+75=100x

                =>75x+75=100x

                ∴ x=3

Number=100x

               =100×3

               =300 

Now 40% of 300=(300×40)/100

                            =120 Ans.

(Q7)->The number that is to be added to 10% of 320 to have the sum as 30% of 230 is.

Solution: Let the number to be added=x

                =>320×(10/100)+x = (230×30)100

                =>32+x = 69

                ∴ x=37 Ans

(Q8)->If 60% of A=30% of B,B=40% of c,c=x% of A,then value of x is.

Solution: A×(60/100) = B×(30/100)

                =>3A/5 = 3B/10

                =>3A/5 = (3/10)×(2C/5)

                =>3A/5 = 6C/50

                =>3A/5 = (6/50)(Ax/100)

                ∴ x=(50×100×3A)/6A×5

                      =500 Ans

Rough: B=C×(40/100)

                 =2C/5

             C =A×(x/100)

                 =Ax/100

(Q9)->51% of a whole number is 714. 25% of that number is.

Solution: Let the whole number be 100x

                =>100x×51% = 714

                =>100x ×(51/100) = 714

                ∴ x=14

whole number=100x

                          =100×14

                          =1400 Ans.

Now, 25% of 1400=(25/100)×1400

                                 =350 Ans.

(Q10)->83¹/3% of Rs 90 is equal to 60% of ?

Solution:90×83¹/3%=x×60%

                =>90 ×(250 /3×100)=x ×(60/100)

                ∴ x=(250×90×100)/(3×100×60)

                     =125 Ans.

(Q11)->If 8% of x=4% of y,then 20% of x is.

Option:(a)10% of y (b)16%of y (c)40% of y (c)80% of y

Solution: x ×(8/100)=y ×(4/100)

                =>8x=4y

                ∴ x=y/2

let,

20% of x = z% of y

(20/100)× x = y ×(z/100)

20x=yz

20×y/2 =yz      [x=y/2]

∴ z=10% Ans.

(Q12)->If 30% of A is added to 40% of B,the answer is 80% of B.what percentage of A is B ?

Solution:A×(30/100)+B×(40/100)=B×(80/100)

                =>(3A/10)+(4B/10)=8B/10

                =>3A+4B=8B

                =>3A=4B

                ∴ A/B=4/3

Now, x% of A=B

          (x/100)×A=B

           xA=B×100

           x=100B/A

             =100×3/4

             =75% Ans.