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. |
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A. 3200 |
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B. 3000 |
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C. 3600 |
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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? |
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A. 9000 |
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B. 3150 |
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C. 5850 |
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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. |
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A. 28000 |
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B. 32000 |
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C. 40000 |
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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. |
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A. 300 |
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B. 400 |
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C. 200 |
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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. |
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A. 300 |
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B. 160 |
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C. 400 |
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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. |
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A. 200 |
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B. 400 |
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C. 300 |
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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? |
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A. 195 |
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B. 165 |
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C. 185 |
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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. |
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A. 850 |
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B. 600 |
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C. 650 |
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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. |
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A. 120 |
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B. 300 |
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C. 240 |
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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. |
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A. 1000 |
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B. 10000 |
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C. 6000 |
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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. |
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A. 400 |
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B. 165 |
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C. 155 |
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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. |
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A. 200 |
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B. 300 |
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C. 120 |
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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