Home / Aptitude / Percentage / Finding the Base
Instead of taking the base as 'x' one can take 100 as the base to solve many questions of percentage and its related topics such as Profit & Loss, Simple Interest & Compound Interest.
EX1. 20% of a number is 30. What is the number?
20 % = 30
100% = 150 ^{(30}/_{20} × 100)
Ex.2. In a class 60% of students are boys and the number of girls is 28. Find the total number of students in the class.
Boys = 60%, girls = 40%
40 % = 28
100 % = 70 ^{(28}/_{40} × 100)
NOTE: To solve these kinds of questions, we must know:
How much % = What actual number is given
So that We can get 100% or our required %
Ex3. In an exam, one student gets 25% mark and fails by 30 marks. Another student gets 40% marks which is 60 marks more than the pass mark. Find the maximum mark in the exam.
Difference in percentage = 40%  25% = 15%
Difference in actual marks = 60  (30) = 90
15% = 90
100%= 600
Ex. 4 In an election contest between 2 candidates, one candidate gets 60% votes and wins by a majority of 4000 votes. Find the total number of votes.
Winner = 60%
Looser = 40%
Winner wins by 20% votes = 4000
100% = 20000
Q1. 
In an election contest between two candidates, one candidate gets 20% votes and defeated by a majority of 2400 votes. Find the number of votes received by the winner. 
A. 3200 

B. 3000 

C. 3600 

D. 4000 
Looser = 20%
Winner= 80%
Hence 60 % = 2400
80% = ^{2400} / _{60} × 80 = 3200
Q2. 
In an election contest between two candidates, one candidate gets 65% votes and won the election by a majority of 2700 votes. How many votes did the other candidate get? 
A. 9000 

B. 3150 

C. 5850 

D. 6000 
Winner = 65%
Looser = 35%
Hence 30 % = 2700
35% = ^{2700} / _{30} × 35 = 3150
Q3. 
In an election contest between two candidates, one candidate gets 70% votes and won the election by a majority of 16000 votes. Find the total number of votes. 
A. 28000 

B. 32000 

C. 40000 

D. 30000 
Winner = 70%
Looser = 30%
Hence 40 % = 16000
100% = ^{16000} / _{40} × 100 = 40000
Q4. 
A student requires 40% mark to pass in an examination. He scored 110 marks and failed by 10 marks. Find the maximum mark in the exam. 
A. 300 

B. 400 

C. 200 

D. 250 
40% = 120
100% =^{ 120}/_{40 } × 100 = 300
Q5. 
In an examination, a student has to get 40% to pass. He got 50% and 30 marks more than the pass mark. Find the pass mark in the exam. 
A. 300 

B. 160 

C. 400 

D. 120 
10% = 30
40% =^{ 30}/_{10} × 100 = 120
Q6. 
In an examination, a student has to get 35% to pass. He got 30% and fails by 20 marks. Find the maximum marks. 
A. 200 

B. 400 

C. 300 

D. 500 
5% = 20
100% = ^{20}/5 × 100 = 400
Q7. 
The difference between 60% and 40% of a number is 37. What is the number? 
A. 195 

B. 165 

C. 185 

D. 175 
20% = 37
100% = ^{37}/_{20} × 100 = 185
Q8. 
60% of students in a school are boys and the number of girls is 340. Find the strength of the school. 
A. 850 

B. 600 

C. 650 

D. 510 
40% = 340
100% = ^{340}/_{40} × 100 = 850
Q1. 
A shopkeeper sells an article at a loss of 10%. Had he sold the same for ₹ 60 more, he could have got a profit of 5%. Find the cost price of the article. 
A. 120 

B. 300 

C. 240 

D. 400 
Let the cost price = 100%
Initial selling price = 90%
New selling price = 105%
Difference = 15%
15% = 60
100% = 400
Q2. 
In an election contest between two candidates, 10% of voters didn't vote. The winner gets 60% of the votes polled and wins by a majority of 1800 votes. Find the total number of votes. 
A. 1000 

B. 10000 

C. 6000 

D. 4000 
Let the total number votes = 100%
Voted = 90%
Winner = 54%
Looser = 36%
Hence 18 % = 1800
100% = ^{1800} / _{18} × 100 =10000
Q3. 
In an examination, a student gets 30% and failed by 35 marks. Another student gets 45% which is 25 marks more than the pass mark. Find the pass mark. 
A. 400 

B. 165 

C. 155 

D. 145 
Percentage mark difference = 45%  30% = 15%
Actual mark difference = 35 + 25 = 60 (difference of +35 & 20)
Hence 15 % = 60
45 % = ^{60} / _{15} × 45 = 180
Pass mark = 180  25 = 155
Q4. 
In an examination, a student gets 30% and failed by 20 marks. Another student gets 45% which is 10 marks more than the pass mark. Find the maximum mark in the examination. 
A. 200 

B. 300 

C. 120 

D. 250 
Percentage mark difference = 45%  30% = 15%
Actual mark difference = 20 + 10 = 30 (difference of +20 & 10)
Hence 15 % = 30
100% = ^{30} / _{15} × 100 = 200