Find the Number Questions are an important part of the Percentage chapter. In these questions, the percentage and the part value are already given, and we have to find the original or total value.
Such questions are frequently asked in SSC, RRB, Banking, Defence, Railway, and school examinations.
Formula:
Total Value = (Part ÷ Percentage) × 100
or
Total Value = (Part × 100) ÷ Percentage
Let us solve some important Find the Number Questions with detailed solutions and shortcuts.
Question 1: If 25% of a journey is 800 km, find the total distance of the journey.
Solution:
Let the total distance of the journey be A km.
Given:
25% of A = 800
(25/100)xA=800
(1/4)xA=800
Multiplying both sides by 4:
A=800×4= 3200
Answer: The total distance of the journey is 3200 km.
Shortcut for SSC/RRB and other competitive Exams
25%= ¼
¼ x A=800
A=800×4=3200 km.
Question 2: If 90% of A = 315, find the value of A.
Solution:
(90/100) × A = 315
(9/10) × A = 315
9A = 315 × 10
9A = 3150
A = 3150/9
A = 350
Answer: A = 350
Question 3: 30% of A is 450. Find the value of A.
Solution:
(30/100) × A = 450
(3/10) × A = 450
3A = 450 × 10
3A = 4500
A = 4500/3
A = 1500
Answer: A = 1500
Question 4: 35% of A is 280. Find the value of A.
Solution:
(35/100) × A = 280
35A = 280 × 100
A = (280 × 100)/35
A = 800
Answer: A = 800
Question 5: 45% of a number is 405. Find the number.
Solution:
Let the number be A.
45% of A = 405
(45/100) × A = 405
45A = 405 × 100
A = (405 × 100)/45
A = 900
Answer: The number is 900.
Question 6: 20% of a number is 140, find that number.
Solution:
Let the number be A.
20% of A = 140
(20/100) × A = 140
(1/5) × A = 140
A = 140 × 5
A = 700
Answer: The number is 700.
Question 7: A student scored 72 marks, which is 80% of the total marks. Find the total marks.
Solution:
Let the total marks be A.
80% of A = 72
(80/100) × A = 72
A = (72 × 100)/80
A = 90
Answer: The total marks are 90.
Shortcut for competitive Exams:
80% = 4/5
(4/5) × A = 72
A = 72 × (5/4)
A = 18 × 5
A = 90
Question 8: 45% of the population of a village is 900. Find the total population of the village.
Solution:
Let the total population of the village be A.
45% of A = 900
(45/100) × A = 900
A = (900 × 100)/45
A = 2000
Answer: The total population of the village is 2000.
Shortcut for Competitive Exams:
45% = 9/20
If 9/20 of the population = 900
Then 1/20 of the population = 900/9 = 100
Therefore,
Total population = 100 × 20
= 2000
Question 9: 25% of the candidates in an examination equals 450 students. Find the total number of candidates.
Solution:
Let the total number of candidates be A.
25% of A = 450
(25/100) × A = 450
(1/4) × A = 450
A = 450 × 4
A = 1800
Answer: The total number of candidates is 1800.
Shortcut for SSC/RRB/Defence/Banking Exams
25% = 1/4
If 1/4 of A = 450
Then A = 450 × 4
= 1800
Answer: 1800
Question 10: A worker saves ₹18,000, which is 60% of his salary. Find his salary.
Solution:
Let the salary of the worker be A.
60% of A = 18,000
(60/100) × A = 18,000
60A = 18,000 × 100
A = (18,000 × 100)/60
A = 30,000
Answer: The salary of the worker is ₹30,000.
Shortcut for competitive Exams
60% = 3/5
3/5 of A = 18,000
A = (18,000 × 5)/3
A = 30,000
Answer: ₹30,000
Question 11: 75% of a shopkeeper’s stock equals 150 items. Find the total stock.
Solution:
Let the total stock be A.
75% of A = 150
(75/100) × A = 150
(3/4) × A = 150
3A = 150 × 4
3A = 600
A = 600/3
A = 200
Answer: The total stock is 200 items.
Shortcut for competitive exams:
75% = 3/4
3/4 of A = 150
1/4 of A = 150/3 = 50
Therefore,
A = 50 × 4
= 200
Answer: 200 items
Question 12: 40% of the books in a library equals 600 books. Find the total number of books.
Solution:
Let the total number of books be A.
40% of A = 600
(40/100) × A = 600
(2/5) × A = 600
2A = 600 × 5
2A = 3000
A = 3000/2
A = 1500
Answer: The total number of books in the library is 1500.
Shortcut for competitive exams:
40% = 2/5
2/5 of A = 600
1/5 of A = 300
Therefore,
A = 300 × 5
= 1500
Answer: 1500 books
Question 13: Ramesh deposited 20% of his money in a bank. He then spent 20% of the remaining amount and was left with ₹4800. Find the amount of money he originally had.
Solution:
Let Ramesh initially have ₹A.
He deposits 20% of A.
Deposited amount = (20/100) × A = A/5
Remaining money = A – A/5
= 4A/5
Now he spends 20% of the remaining money.
Money left after spending = 80% of 4A/5
= (80/100) × 4A/5
= (4/5) × 4A/5
= 16A/25
Given:
16A/25 = 4800
16A = 4800 × 25
A = (4800 × 25)/16
A = 7500
Answer: Ramesh initially had ₹7500.
SSC/RRB and other competitive Exams Shortcut
20% deposited ⇒ 80% remains
After spending 20% of the remaining money:
Money left = 80% of 80%
= (80/100) × (80/100)
= 64%
Therefore,
64% of A = 4800
(64/100) × A = 4800
A = (4800 × 100)/64
A = 7500
Answer: Ramesh originally had ₹7500.
Question 14: In a test, there are three papers each of 100 marks. Rahul
obtained 53 marks in the first paper and 75 marks in the second
paper. How many marks must Rahul obtain in the third
paper to get an overall of 70 per cent marks?
Solution:
Total marks of all three papers
= 100 + 100 + 100
= 300
Rahul has to obtain 70% of 300 marks.
70% of 300
= (70/100) × 300
= 210 marks
Marks already obtained
= 53 + 75
= 128 marks
Therefore, marks required in the third paper
= 210 − 128
= 82 marks
Answer: Rahul must obtain 82 marks in the third paper.
Important Values to remember in Find the Number Questions
25% = 1/4
20% = 1/5
40% = 2/5
50% = 1/2
60% = 3/5
75% = 3/4
80% = ⅘
FAQ: Find the Number Questions of percentage
- What is the formula to find the total value in percentage questions?
Total Value = (Part ÷ Percentage) × 100
- If 25% of a number is 400, then find that number.
25% of A = 400
(25/100) × A = 400
(1/4) × A = 400
A = 400 × 4
A = 1600
(25/100)xA=400
A=1600
- Are Find the Number Questions asked in SSC, RRB, Banking, and Defence exams?
Yes. Find the Number Questions are frequently asked in SSC, RRB, Banking, Railway, Defence, and various school examinations.
Important Resources to Percentage
- Finding Percentage Questions with Answers
- Fraction to Percentage Questions with Answers
- Basic Percentage Questions with Answers and Solutions
- Percentage: Meaning, Formula, Examples & Questions for Exams
- Percentage to Fraction Questions with Answers (Solved Examples)
- Percentage Formula: Formulas, Examples, Increase, Decrease & Formula Sheet
- Percentage Increase Questions with Answers
- Percentage Decrease Questions with Answers and Solutions
- Successive Percentage Questions with Answers and Solutions
- Percentage Practice Questions with Answers | MCQs, Quiz & Practice Set