Percentage Problems in Mathematics Class 10
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Questions and Answers

What is the passing percentage if a student scores 55% and passes with 240 marks?

  • 50% (correct)
  • 35%
  • 45%
  • 39%

Calculate the passing percentage if a student scoring 36% fails by 32 marks and scores 48% passes by 64 marks.

  • 40%
  • 50% (correct)
  • 35%
  • 45%

Determine the passing percentage if a student scoring 40% fails by 50 marks and scores 50% passes by 40 marks.

  • 45%
  • 42%
  • 50% (correct)
  • 40%

If a man borrowed Rs. 30,000 in total, part at 12% and the rest at 10%, and paid back Rs. 36,480 after 2 years, how much was borrowed at 12%?

<p>11000 (B)</p> Signup and view all the answers

What is the calculated passing percentage for a student who scores 30% and fails by 5 marks but scores 40% and gets 10 more than passing marks?

<p>50% (D)</p> Signup and view all the answers

How much profit does a salesman make if he sells a watch and a wall clock, buying them for Rs. 390 and making a profit of 10% and 15% respectively, resulting in Rs. 51.5 total profit?

<p>30% (A)</p> Signup and view all the answers

What is the passing percentage if a student scoring 45 marks still fails and when scoring 55 marks passes?

<p>50% (A)</p> Signup and view all the answers

If a student scores 48% marks and passes by 64 marks, while at 36% he fails by 32 marks, what could be the passing percentage?

<p>50% (D)</p> Signup and view all the answers

What is the total salary of Gaurav and Azam after their respective increases?

<p>Rs. 59928 (C)</p> Signup and view all the answers

What percentage does Gaurav's salary increase by?

<p>23% (C)</p> Signup and view all the answers

What is the original total salary of Gaurav and Azam before the increase?

<p>Rs. 47520 (B)</p> Signup and view all the answers

If Geeta scored 30% and failed by 50 marks, how many marks are required to pass?

<p>150 (B)</p> Signup and view all the answers

What was the number of males in the village before the increase?

<p>5000 (B)</p> Signup and view all the answers

Rajiv scored 20% marks and failed by 11 marks; what are the passing marks?

<p>33 (A)</p> Signup and view all the answers

What is the increase in population of males if the male population increased by 8%?

<p>800 (A)</p> Signup and view all the answers

What is the difference in the number of boys and girls based on the given population percentage?

<p>26 (B)</p> Signup and view all the answers

What is the new male population after a 14.2% increase to the original male population of 9500?

<p>10935 (D)</p> Signup and view all the answers

What is the total increase in the female population, given that it increased by 17.7%?

<p>1610 (A)</p> Signup and view all the answers

If 15% of the total male population of 9500 are boys, how many boys are there?

<p>1425 (A)</p> Signup and view all the answers

How many female population are there if the total female population is increased by 17.7%?

<p>4500 (C)</p> Signup and view all the answers

What is the present population of the town if the males increased by 5% and females by 9% to reach 6500?

<p>6000 (B)</p> Signup and view all the answers

How many books were in the fiction category in 2015 if the total number of books increased from 11500 to 12760 over five years?

<p>6600 (B)</p> Signup and view all the answers

If a student scores 25% of the marks and fails by 210 marks, what are the maximum marks?

<p>980 (B)</p> Signup and view all the answers

What is the difference between the number of boys and girls if 15% are boys and 18% are girls in a total population of 9500?

<p>150 (C)</p> Signup and view all the answers

What is the passing percentage if a student scoring 40% fails by 50 marks and scores 50% passes with 40 marks?

<p>120 (A)</p> Signup and view all the answers

What was the amount borrowed at 12% per annum if a man paid Rs. 36,480 to settle a loan of Rs. 30,000 over 2 years?

<p>12000 (B)</p> Signup and view all the answers

If Gaurav's salary increases by 23% and Azam's by 30%, leading to a new total salary of Rs. 59928, what was their original total salary?

<p>47520 (A)</p> Signup and view all the answers

When a student scores 30% marks, he fails by 5 marks. What does this indicate?

<p>The passing marks are 35. (C)</p> Signup and view all the answers

If a student scores 40% marks and gets 10 more marks than passing marks, what can be inferred about the passing score?

<p>The passing score is greater than 40. (C)</p> Signup and view all the answers

How much in total did a student need to score to pass if the passing percentage is indirectly given through failing margins?

<p>40 marks (B)</p> Signup and view all the answers

What is the significance of the Rs. 36,480 figure when referring to the man who borrowed money?

<p>It is the total settlement amount. (A)</p> Signup and view all the answers

What does a score increase from 30% to 40% reflect in terms of passing criteria?

<p>A successful transition to passing status. (C)</p> Signup and view all the answers

What is the minimum marks required to pass if Anita scored 31% and failed by 16 marks?

<p>100 marks (C)</p> Signup and view all the answers

How many fiction books were in the library in 2015 considering a 10% increase from 2010?

<p>3156 (B)</p> Signup and view all the answers

What is the present population of males if the total population is 5000 and the increases in males and females result in a population of 5540 after 1 year?

<p>6000 (C)</p> Signup and view all the answers

What is the sum of the interest paid to the two persons if Rs. 16000 was borrowed, paying 6% to one and 10% to another resulting in Rs. 1120 total interest?

<p>Rs. 2830 (A)</p> Signup and view all the answers

If the population of a village increased by 8% for males and 5% for females, what was the population at present if it becomes 10,272 after one year?

<p>11000, 5000 (A)</p> Signup and view all the answers

What was the profit earned from selling a watch and a wall clock for Rs. 390 if the profits were 10% and 15% respectively?

<p>Rs. 51.5 (C)</p> Signup and view all the answers

How much was borrowed at the 10% rate if a total interest of Rs. 1120 was paid on Rs. 16000 borrowed from two lenders?

<p>Rs. 8000 (D)</p> Signup and view all the answers

What was the difference between the original prices of a watch and a wall clock if the total purchase cost was Rs. 390 and a profit of Rs. 51.5 was made?

<p>Rs. 40.5 (A)</p> Signup and view all the answers

If a student scores 250 marks yet fails by 38 marks, what is the maximum marks for the examination?

<p>750 (D)</p> Signup and view all the answers

What passing percentage can be determined if a student scores 25% marks and fails by 210 marks, but passes at 55% marks with 240 marks?

<p>45% (A)</p> Signup and view all the answers

If Geeta scored 30% and failed by 50 marks, while Sandeep scored 45% and exceeded the passing marks by 25, what can be inferred about their performance?

<p>Geeta scored less than Sandeep (B)</p> Signup and view all the answers

Rajiv scored 20% marks and failed by 11 marks. If he scored 50%, how much does he exceed the passing marks?

<p>4 marks (B)</p> Signup and view all the answers

What is the minimum marks required to pass if Anita scored 31% and failed by 16 marks, while Sunita scored 40% and passed by 56 marks?

<p>120 marks (D)</p> Signup and view all the answers

If a student scores 36% marks and fails by 32 marks, but passes at a score of 48%, how much is the passing score?

<p>120 marks (A)</p> Signup and view all the answers

What is the possibility of passing percentage if a student scoring 64% has a certain mark threshold?

<p>60% (A)</p> Signup and view all the answers

If Sandeep received 45% and passed by 25 marks, how much did Geeta likely score given her failure of 50 marks?

<p>30 marks (B)</p> Signup and view all the answers

Flashcards

Passing Percentage Calculation 1

A student scores 240 marks, which is 55% of the total marks needed to pass. Calculate the passing percentage.

Passing Percentage Calculation 2

A student needs to score 32 more marks to pass when they get 36%, but passes with 64 marks more when they get 48%. Determine the passing percentage.

Passing Percentage Calculation 3

A student fails with 50 marks less when scoring 40%, but passes with 40 marks more when scoring 50%. Calculate the passing percentage.

Passing Percentage Calculation 4

A student fails by 5 marks when scoring 30%, but gets 10 marks more than needed to pass when scoring 40%. Find the passing percentage.

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Percentage Increase

The percentage change in a quantity over a period of time, calculated by dividing the difference between the final value and the initial value by the initial value and multiplying by 100.

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Total Population

The total population of a town or city is the sum of its male and female populations.

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Percentage of Population

A percentage of the total population that represents a specific group.

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Difference between males and females

The difference between the number of males and females in a population.

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Passing Marks

The percentage of marks required to pass an exam or assessment.

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Maximum Marks

The total number of marks possible on an exam or assessment.

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Marks Scored

The percentage of marks a student receives on an exam or assessment.

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Passing Percentage

The percentage of marks a student needs to receive in order to pass an exam or assessment.

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Total Number of Books

The total number of books available in a library.

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Percentage Increase in Book Category

The percentage increase in the number of books in a specific category over a period of time.

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Number of Books in a Category

The number of books in a specific category (fiction or non-fiction) in a library.

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Number of Males

The current number of males in a town.

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Amount Borrowed at a Rate

The amount of money borrowed at a specific interest rate per year.

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Calculating Marks Percentage

Calculate the percentage of marks a student got in an exam.

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Score Difference

The difference between the marks obtained by two students.

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Marks Needed to Pass

The extra marks required to pass an exam, calculated by subtracting the passing percentage from the student's current score.

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Exam Score Relationship

Relationship between the marks needed to pass, the marks a student scores, and the maximum marks.

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Marks for a Percentage

Determine how many marks represent a particular percentage in an exam.

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Marks failed by

The difference between the marks needed to pass and the marks the student actually scored, when the student fails.

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Marks passed by

The difference between the marks the student actually scored and the passing marks, when the student passes.

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Passing percentage problem

A mathematical problem where you need to calculate the passing percentage based on the marks the student earned in relation to the total marks and the passing marks.

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Passing percentage problem with two scenarios

A problem where you need to find the passing percentage using two different scenarios where a student either fails or passes based on their scores.

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Salary Difference: Gaurav and Azam

The difference in salary between Gaurav and Azam is the value of the salary difference before either salary is increased. We can find this difference by setting up a system of equations and solving for the initial salary of Azam and then subtracting it from the initial salary of Gaurav. The initial salary of Gaurav and Azam can be found by denoting their initial salaries as x and y respectively. The new salary of Gaurav is 1.23x and the new salary of Azam is 1.30y. The total new salary is 1.23x + 1.30y = 59928. The total initial salary is x + y = 47520 . Solving for x and y in the system and finding x - y provides us with the difference in their initial salaries.

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Initial Male Population

The population of the village increases by 658 people. The increase in males is 8% of the male population and the increase in females is 5% of the female population. The population is the sum of the male and female populations and using the equation: m + f = 9800 and 1.08m+1.05f = 10458, m and f can be found, and then m can be found, which gives us the initial male population.

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Salary Difference

The difference in salary between Gaurav and Azam is the value of the salary difference before either salary is increased. We can find this difference by setting up a system of equations and solving for the initial salary of Azam and then subtracting it from the initial salary of Gaurav. The initial salary of Gaurav and Azam can be found by denoting their initial salaries as x and y respectively. The new salary of Gaurav is 1.23x and the new salary of Azam is 1.30y. The total new salary is 1.23x + 1.30y = 59928. The total initial salary is x + y = 47520 . Solving for x and y in the system and finding x - y provides us with the difference in their initial salaries.

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Study Notes

Percentage Problems

  • Types of animals and biscuits: There are cats and dogs in a room. Each cat eats 7 biscuits and each dog eats 9 biscuits. If 45 animals eat 355 biscuits, find the number of cats and dogs.
  • Zoo animals (heads and legs): A zoo has rabbits and pigeons. There are 280 heads and 820 legs. Determine the number of pigeons.
  • Population increase (males and females): A town's current population is 5000. If males increase by 6% and females by 14%, the population will be 5540 in a year. Find the present number of males.
  • Village population increase: The population of a village is 9600. If males increase by 8% and females by 5%, the population will be 10,272 in a year. Find the current male population.
  • Town population increase: A town's current population is 9800. With an 8% increase in males and a 5% increase in females, the population becomes 10458. What was the number of males initially?
  • Town population (males and females): A town's population is 6000. If males increase by 5% and females by 9%, the population becomes 6500. Find the present number of males and females.
  • City population (males and females): The total population of a city is 9500. Male population increases by 14.2% and female population increases by 17.7%. The new total population is 11003. If 15% of the total male population is boys and 18% of the total female population is girls, find the difference between the number of boys and girls.

Percentage in Examinations

  • Passing marks: Passing marks are 40%. A student gets 250 marks but fails by 38 marks. What is the maximum mark?
  • Passing percentage: A student scores 25% marks and fails by 210. If he scores 55% marks, he passes with 240 marks. Find the passing percentage.
  • Passing percentage: A student gets 36% marks and fails by 32 marks. If the student gets 48% marks, they pass by 64 marks. Find the passing percentage.
  • Passing marks: A student gets 40% marks and fails by 50 marks. If they score 50%, they pass with 40 marks. Find the passing marks and passing percentage.
  • Examination scores: A student gets 30% and fails by 50 marks. Another student, scoring 45%, gets 25 marks more than the passing marks. What score did Vimal get by scoring 64%?
  • Examination scores: Rajiv got 20% and failed by 11 marks. If he scored 50%, he gets 4 marks more than the passing marks. What is the passing marks?
  • Examination scores: Anita scored 31% and failed by 16. Sunita scored 40% and scored 56 marks more than the passing marks. Determine the minimum passing marks.

Library and Loan Problems

  • Fiction and Non-Fiction Books: In 2010, a library had 11500 books (fiction and non-fiction). In 2015, it had 12760. Fiction increased by 10%, and non-fiction by 12%. How many fiction books were there in 2015?

  • Loan Interest Rates: A person borrowed Rs. 16000 from two sources at 6% and 10% per annum. In one year, he paid Rs. 1120 interest. How much was borrowed at each rate?

  • Salary Increase: Gaurav and Azam have a total salary of Rs. 47520. If Gaurav's salary rises by 23% and Azam's by 30%, the total salary becomes Rs. 59928. Calculate the difference in their salaries.

Sales and Purchase Problems

  • Watch and Clock Purchase: A salesman purchased a watch and a clock for Rs. 390. He sold the watch with a 10% profit and the clock with a 15% profit, earning a total profit of Rs. 51.5. Find the difference between the original prices of the watch and clock.

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Percentage Sheet -04 PDF

Description

Test your skills in solving percentage problems with this quiz designed for 10th-grade mathematics. You'll tackle real-world scenarios involving populations, animals, and their respective increases. Can you find the number of cats, dogs, and the male populations based on the given percentages?

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