Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
1.Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
2.Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
3.Exam Preparedness: Sample Question Papers and Practice Questions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
4.Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sec A
1. A picture is 60cm wide and 1.8m long. The ratio of its width to its perimeter in lowest form.
(A) 1 : 2 (B) 1 : 3 (C) 1 : 4 (D) 1 : 8
2. The greatest ratio among the ratios 2 : 3, 5 : 8, 75 : 121 and 40 : 25
(A) 2 : 3 (B) 5 : 8 (C) 75 : 121 (D) 40 : 25
3. If a bus travels 160 km in 4 hours and a train travels 320km in 5 hours at uniform speeds, then the ratio of the distances travelled by them in one hour
(A) 1 : 2 (B) 4 : 5 (C) 5 : 8 (D) 8 : 5
4. Write the ratio of 6 to 18 in simplest form.
5. If there are 15 boys and 10 girls in a class, find the ratio of boys to girls.
6. Express the ratio 24:36 in its simplest form.
7. Write the ratio of 50 paise to ₹5 in its simplest form.
8. Compare the ratios 3:5 and 6:10. Are they equivalent? Find the ratio of 3 kg to 500 g.
Sec B
1. Which ratio is larger 10 : 21 or 21 : 93?
2. If the ratio of boys to girls in a class is 4:5 and there are 40 boys, find the number of girls.
3. Simplify and compare the ratios 9:15 and 12:20.
4. A recipe requires 2 cups of sugar for every 3 cups of flour. If you have 12 cups of flour, how much sugar will you need?
5. Divide ₹200 in the ratio 3:5.
6. Write the ratio of the following quantities in simplest form:
a) 50 cm to 2 m
b) 25 minutes to 2 hours
7. A car travels 120 km in 2 hours. Find the ratio of distance to time.
Sec C
1. An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 minutes. What is the ratio of lunch break to the total period in the office?
2. A tea merchant blends two varieties of tea costing her Rs 234 and Rs 130 per kg in the ratio of their costs. If the weight of the mixture is 84kg, then find the weight of each variety of tea.
3. If a rope of length 60 m is divided in the ratio 2:3, find the lengths of the two parts.
4. The monthly incomes of two friends are in the ratio 7:9. If the first friend earns ₹28000, find the income of the second friend.
5. A school has 240 students in Class 6 and 360 students in Class 7. Find the ratio of students in Class 6 to Class 7 in simplest form.
6. The ratio of the ages of two siblings is 5:3. If the elder sibling is 20 years old, find the age of the younger sibling.
Sec D
1. Shivangi is suffering from anaemia as haemoglobin level in her blood is lower than the normal range. Doctor advised her to take one iron tablet two times a day. If the cost of 10 tablets is Rs 17, then what amount will she be required to pay for her medical bill for 15 days?
2. A train travels 300 km in 5 hours. Find the ratio of the distance traveled to the time taken. Use this ratio to calculate the distance covered in 8 hours.
3. A bag contains red, blue, and green marbles in the ratio 3 : 5 : 7. If there are 105 marbles in total, find the number of marbles of each color.
4. A man distributes ₹4500 among his three children in the ratio 3 : 4 : 5. Find each child’s share.
5. A class has 24 boys and 16 girls. If 10 new boys and 8 new girls join the class, find the new ratio of boys to girls.
Problem 1
1. A school is planning a field trip and wants to maintain a ratio of teachers to students of 1:5 for safety reasons. If there are 120 students attending the trip, how many teachers should accompany them?
Problem 2
2. In a recipe, the ratio of flour to sugar is 3:1. If a chef wants to make a larger batch using 9 cups of flour, how much sugar is needed?
Q1
1. A recipe requires a ratio of 2:3 for ingredients A and B, respectively. If the chef decides to double the quantity of ingredient B, how will this change the ratio of A to B? Calculate the new ratio and discuss the implications of altering ingredient proportions in cooking.
Q2
2. In a survey, the ratio of boys to girls in a classroom is found to be 5:4. If the total number of students in the classroom is 81, how many more boys are there than girls? Analyze how this ratio can impact group activities and classroom dynamics.
Questions
1. The length and breadth of a steel tape are 10m and 2.4cm, respectively. The ratio of the length to the breadth is?
(A) 5 : 1.2 (B) 25: 6 (C) 625: 6 (D) 1250: 3
2. State whether the given statements are true or false.
(a) 12 : 18 = 28 : 56
(b) 25 persons : 130 persons = 15kg : 78kg
3. Fill in the blanks.
If two ratios are ? , then they are in proportion.
4. Income of Rahim is Rs 12000 per month and that of Ami is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9960 per month find the ratio of their savings.
5. 20 tons of iron costs Rs 600000. Find the cost of 560kg of iron.
State weather true or false
6. hours : 30 hours = 8km : 20km
7. The ratio of 10kg to 100kg is 1:10
8. The ratio of 150cm to 1metre is 1:1.5.
9. 25kg : 20g = 50kg : 40g.
10. The ratio of 1 hour to one day is 1:1.
11. The ratio 4 : 16 is in its lowest form.
12. The ratio 5 : 4 is different from the ratio 4 : 5.
13. A ratio is a form of comparison by ?
14. 20m : 70m = Rs 8 : Rs ?.
15. A ratio expressed in lowest form has no common factor other than ? in its terms.
16. To find the ratio of two quantities, they must be expressed in ? units.
17. In a year, Ravi earns Rs 360000 and paid Rs 24000 as income tax. Find the ratio.
(a) income to income tax.
(b) income tax to income after paying income tax.
18. Of the 288 persons working in a company, 112 are men and the remaining are women. Find the ratio.
(a) men to that of women.
(b) men to the total number of persons.
(c) women to the total number of persons.
19. An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 minutes. What is the ratio of lunch break to the total period in the office?
20. In a school, the ratio of the number of large classrooms to small classrooms is 3:4. If the number of small rooms is 20, then find the number of large rooms.
21. When Chinmay visted chowpati at Mumbai on a holiday, he observed that the ratio of North Indian food stalls to South Indian food stalls is 5:4. If the total number of food stalls is 117, find the number of each type of food stalls.
22. A train takes 2 hours to travel from Ajmer to Jaipur, which are 130km apart. How much time will it take to travel from Delhi to Bhopal which are 780km apart if the train is travelling at the uniform speed?
23. A tea merchant blends two varieties of tea costing her Rs 234 and Rs 130 per kg in the ratio of their costs. If the weight of the mixture is 84kg, then find the weight of each variety of tea.
24. Bachhu Manjhi earns Rs 24000 in 8 months. At this rate.
(a) how much does he earn in one year?
(b) in how many months does he earn Rs 42000?
25. A metal pipe 3 metre long was found to weigh 7.6kg. What would be the weight of the same kind of 7.8m long pipe?
Q1
Scenario: A group of students organized a sports day. The ratio of participants in the track events to those in the field events was 3:2. If there were 30 participants in the track events, how many participants were there in the field events?
Sol 1
Solution :
Given the ratio of track to field participants is 3:2.
Let the number of participants in field events be x.
Using the ratio:
Cross-multiplying gives: 3x=60⟹x=20
There were 20 participants in the field events.
Q2
Scenario: A teacher divides the class into groups for a project, maintaining a ratio of boys to girls of 2:3. If there are 24 boys in the class, how many girls are there?
Sol 2
Solution :
Let the number of girls be y.
Given the ratio of boys to girls is 2:3 =
Cross-multiplying gives: 2y=72⟹y=36
There are 36 girls in the class.