Home / Aptitude / Percentage / Comparision of numbers
Many questions are asked in competitive exams on comparison of numbers.
Usually, students take X as the base to solve these kinds of questions.
Instead, you can take the base as 100 or any number to solve questions easily.
Example: Two numbers are 20% and 50% more than a third number.
i) What percent is the first of the second number?
ii) What percent is the first less than the second number?
iii) What percent is the second more than the first number?
Solution: Let us take the third number = 100
Hence the first number = 120 & Second number = 150
i) ^{ 120 }/ _{150} x 100 = 80%
ii) ^{30} /_{150} x 100 = 20%
iii) ^{30} / _{120} x 100 = 25%
Q1. 
Two numbers are respectively 20% and 25% of a third number. What percentage is the second of the first? 
A. 25% 

B. 20% 

C. 80% 

D. 125% 
Let the third number = 100
The first number = 20 (20% of 100 =20)
The second number = 25 (25% of 100 = 25)
^{25} / 20 × 100 = 125%
Q2. 
Two numbers are respectively 20% and 40% less than a third number. What percentage is the first number more than the second? 
A. 20% 

B. 33.33% 

C. 70% 

D. 80% 
Let the third number = 100
The first number = 80
The second number = 60
^{20 }/ _{60} × 100 = 33.33 %
Q3. 
Two numbers are respectively 32% and 20% less than a third number. What percentage is the first less than the second? 
A. 85% 

B. 25% 

C. 15% 

D. 75% 
Let the third number = 100
The first number = 68
The second number = 80
^{12 }/ _{80} × 100 = 15%
Q4. 
Two numbers are respectively 28% and 25% less than a third number. What percentage is the first of the second? 
A. 80% 

B. 90% 

C. 95% 

D. 96% 
Let the third number = 100
The first number = 72%
The second number = 75%
72 /_{75} × 100 = 96%
Q5. 
Two numbers are respectively 25% and 30% less than a third number. What percentage is the second of the first? 
A. 90% 

B. 95% 

C. 93 ^{1} / _{3}% 

D. 44% 
Let the third number = 100
The first number = 75
The second number = 70
^{70}/_{75}
× 100 = 93 ^{1}/_{3}
%
Q6. 
Two numbers are respectively 48% and 11% more than a third number. What percentage is the second of the first? 
A. 133.33% 

B. 60% 

C. 144% 

D. 75% 
Let the third number = 100
The first number = 148
The second number = 111
^{111} /_{148} × 100 = 75%
Q7. 
Two numbers are respectively 20% and 60% more than a third number. What percentage is the first of the second? 
A. 60% 

B. 75% 

C. 80% 

D. 30% 
Let the third number = 100
The first number = 120
The second number = 160
^{120}/_{160} × 100 = 75%
Q1. 
There are 4 positive integers P, Q & R and S. P is 60% of R. Q is 20% more than P. If S is 33.33 % less than Q, then what percentage is S of P? 
A. 80% 

B. 60% 

C. 72% 

D. 40% 
There are 4 positive integers P, Q & R and S. P is 60% of R. Q is 20% more than P. If S is 33.33 % less than Q, then what percentage is S of P?
Let R = 100
Then P = 60, Q =72
S = 48
^{48} / _{60} × 100 = 80%
Q2. 
There are 3 positive integers X, Y & Z. X is 60% of Y. Z is 20% more than X. If the value of Z is 216, then what is the value of Y. 
A. 330 

B. 180 

C. 300 

D. 230 
Let Y = 100
Then X = 60, Z = 72
If 72 = 216
100 = 300
Q3. 
A number is 80% of the second number. The third number is 50% more than the first number. What percentage is the second number more/less than the third number? 
A. 66.67% 

B. 116.66% 

C. 33.33% 

D. 16.67% 
Let the second number = 100
The first number = 80
The third number = 120
^{20} /_{120} × 100 = 16.66%
Q4. 
A number is 20% less than the second number. The third number is 50% more than the first number. What percentage is the third number of the second number? 
A. 80% 

B. 120% 

C. 20% 

D. 40% 
Let the second number = 100
The first number = 80
The third number = 120
^{120} /_{100} × 100 = 120%
Q5. 
A number is 20 % more than a second number. The third number is 50 % of the first number. What percent is the second number more than the third number? 
A. 33.33% 

B. 66.67% 

C. 60% 

D. 80% 
Let the second number = 100
The first number = 120
The third number = 60
^{40} / 60 × 100 = 66.67 %
Q1. 
A sells his good 20% cheaper than B and 20% dearer than C. Instead of purchasing goods from B, a customer decides to purchase goods from C. What percent does the save? 
A. 25% 

B. 66.67% 

C. 33.33% 

D. 50% 
A sells his good 20% cheaper than B and 20% dearer than C. Instead of purchasing goods from B, a customer decides to purchase goods from C. What percent does the save?
When B's price = 100, A's price = 80
When C's price = 100, A 's price = 120
A's price = 120, C's price = 80
When A's price is 80, C's price =^{ 80} /_{120 }× 100 = 66.67
Hence, when B sells his good at 100, A sells at 80 and C sells at 66.67.
When the customer shifts from B to C, he saves 10066.67= 33.33
33.33 /_{100 }× 100 = 33.33%
Q2. 
An examination was conducted for 1200 marks. A scored 25% more than B and B scored 20% more than C. C scored 20% less than D. If A secured 720 marks, what percentage of full marks did D get? 
A. 66.67% 

B. 33.33% 

C. 40% 

D. 50% 
An examination was conducted for 1200 marks. A scored 25% more than B and B scored 20% more than C. C scored 20% less than D. If A secured 720 marks, what percentage of full marks did D get?
Let the mark scored by D = 100
Hence, marks scored by C =80, B = 96, A = 120
If 120 = 720
then 100 = 600
Percentage score of D = ^{600}/_{1200} × 100 = 50%
Q3. 
There are 4 positive integers P, Q & R and S. P is 60% more than R. S is 25% less than Q. If Q is 40 % less than R, then what percentage is S of P? 
A. 45% 

B. 33.33% 

C. 71.875% 

D. 28.125% 
There are 4 positive integers P, Q & R and S. P is 60% more than R. S is 25% less than Q. If Q is 40 % less than R, then what percentage is S of P?
Let R = 100
Then P = 160, Q =60
S = 45
45 /_{160} × 100 = 300