CBSE Class 6 Maths Ratio and Proportion HOTs

2. The length of a pencil is 16 cm and its diameter is 6 mm. What is the ratio of the diameter of the pencil to that of its length?
Answer: 3 : 80

3. A certain club has 100 members, out of which 25 play tennis, 28 play badminton, 12 play chess and the rest do not play any game. Find the ratio of the number of members who play
a. badminton to the number of those who play chess.
b. badminton to the number of those who do not play any game.
c. tennis to the number of those who do not play any game.
d. tennis to the number of those who play either badminton or chess.
Answer: a. 7 :3 b. 4 : 5 c. 5 : 7 d. 5 : 8

4. Do the ratios 15 cm to 3 m and 25seconds to 3 minutes form a proportion?
Answer: No

5. Divide ₹ 500 among Suresh and Awanti in the ratio 3:7.
Answer: Suresh ₹ 150, Awanti ₹ 350

6. The ratio between the number of men and women in an office is 5 : 7. If the number of women working in the office is 42, find the number of men working in the office.
Answer: 30

7. The ages of Garima and Deepa are in the ratio 5 : 3. If Garima's age is 15 years, find the age of Deepa.
Answer: 9 years

8. The ratio of the number of girls to that of boys in a school is 9 : 11. If the number of boys in the school is 2035, find :
a. the number of girls in the school.
b. the number of students in the school.
Answer: a. 1665 b. 3700

9. The ratio of income to expenditure of a family is 7 : 6. Find the savings if the income of the family is ₹ 42000.
Answer: 6000

10. An employee earns ₹ 72,000 in 3 months.
a. How much does he earn in 7 months?
b. In how many months will he earn ₹ 3,60,000?
Answer: a. ₹ 168000 b. 15

11. A train travels 110 km in 2 hours and a car travels 245 km in 3(1)/2 hours. What is the ratio of the speed of the train to that of the car?
Answer: 55 : 104

12. Fifteen postcards cost ₹ 2.25. What will be the cost of 36 postcards? How many postcards can we buy in ₹ 45?
Answer: ₹ 5.40; 300

13. Set up all proportions from the numbers 9, 150, 105, 1750.
Answer:  9:150::105:1750, 150:9::1750:105, 105:1750::9:150, 1750:105::150:9

14. If 4, x, 9 are in continued proportion, find the value of x.
Answer:  6

15. If in a proportion, the first, second and fourth terms are 32, 112, and 217 respectively, find the third term.
Answer: 62

16. The ratio of copper and zinc in an alloy is 9 : 7. If the weight of zinc in the alloy is 9.8kg, find the weight of copper in the alloy.
Answer: 12.6 kg

17. Mixed fruit juice is made from mango, papaya and orange juice in the ratio 3:1:4. Aarushi has 400ml of orange juice. If she uses it all, then find
a. how much mango and papaya juice will she need?
b. how much tropical fruit juice will she make altogether?
Answer: a. 300 ml orange juice; 100 ml papaya juice b. 800 ml

18. The monthly expenses of a student have increased from ₹ 350 to ₹ 500. Find the ratio of a. increase in expenses to original expenses.
b. original expenses to increased expenses.
c. increased expenses to increase in expenses.
Answer: a. 3 : 7 b. 7 : 10 c. 10 : 3

19. Sapna weighs 5.4kg on the Earth and 9 kg on the Moon. If a monkey weighs 3.5kg on the Moon, then how much will it weigh on the Earth?
Answer: 2.1 kg

20. Irfan deposits ₹ 10,000 in a bank for a certain time and gets ₹ 600 as interest. If he deposits ₹ 8000 at the same rate of interest for the same time period, then find the interest he will get at the end.
Answer: ₹ 480

HOTS

1. If a : b = 2 : 5, find the value of 3a + 2b/4a + b .
Answer: 16/13

2. The mean proportional of a and b is 10 and the value of a is 4 times the value of b. If a > 0, b > 0, find the value of a + b.
Answer: 25

3. Divide ₹ 1400 among Reema, Rakesh and Seema such that Reema gets twice of what Rakesh gets and Seema gets half the amount of what Rakesh gets?
Answer: Reema - ₹ 8000; Rakesh - ₹ 2000; Seema - ₹ 4000

4. If 5 men can do a certain construction work in 14 days, then how long will 7 men take to complete the same construction work?
Answer: 10 days