Proportional Reasoning-1

Circle the following statements of proportion that are true. (i) 4 : 7 :: 12 : 21 (ii) 8 : 3 :: 24 : 6 (iii) 7 : 12 :: 12 : 7 (iv) 21 : 6 :: 35 : 10 (v) 12 : 18 :: 28 : 12 (vi) 24 : 8 :: 9 : 3

Give 3 ratios that are proportional to 4 : 9. ____ : ____ ____ : ____ ____ : ____

Fill in the missing numbers for these ratios that are proportional to 18 : 24. 3 : ____ 12 : ____ 20 : ____ 27 : ____

Let us draw some human figures. Measure your friend's body—the lengths of their head, torso, arms, and legs. Write the ratios as mentioned below— head : torso ___ : ___ torso : arms ___ : ___ torso : legs ___ : ___. Now, draw a figure with head, torso, arms, and legs with equivalent ratios as above. Does the drawing look more realistic if the ratios are proportional? Why? Why not?

The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week?

Divide ₹4,500 into two parts in the ratio 2 : 3.

In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?

To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?

I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the ratio of red paint to yellow paint in the new mixture?

Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio of orange juice to apple juice in its simplest form.

Last year, we hired 3 buses for the school trip. We had a total of 162 students and teachers who went on that trip and all the buses were full. This year we have 204 students. How many buses will we need? Will all the buses be full?

The area of Delhi is 1,484 sq. km and the area of Mumbai is 550 sq. km. The population of Delhi is approximately 30 million and that of Mumbai is 20 million people. Which city is more crowded? Why do you say so?

A crane of height 155 cm has its neck and the rest of its body in the ratio 4:6. For your height, if your neck and the rest of the body also had this ratio, how tall would your neck be?

Harmain is a 1-year-old girl. Her elder brother is 5 years old. What will be Harmain's age when the ratio of her age to her brother's age is 1:2?

The mass of equal volumes of gold and water are in the ratio 37:2. If 1 litre of water is 1 kg in mass, what is the mass of 1 litre of gold?

It is good farming practice to apply 10 tonnes of cow manure for 1 acre of land. A farmer is planning to grow tomatoes in a plot of size 200 ft by 500 ft. How much manure should he buy? (Please refer to the section on Unit Conversions earlier in this chapter).

A tap takes 15 seconds to fill a mug of water. The volume of the mug is 500 mL. How much time does the same tap take to fill a bucket of water if the bucket has a 10-litre capacity?

One acre of land costs ₹15,00,000. What is the cost of 2,400 square feet of the same land?

A tractor can plough the same area of a field 4 times faster than a pair of oxen. A farmer wants to plough his 20-acre field. A pair of oxen takes 6 hours to plough an acre of land. How much time would it take if the farmer used a pair of oxen to plough the field? How much time would it take him if he decides to use a tractor instead?

The following table shows the different ratios in which Manjunath mixes coffee decoction with milk. Write in the last column if the coffee is stronger or lighter than the regular coffee. Regular coffee ratio: 15:35. Table: (300 mL decoction, 600 mL milk), (150 mL decoction, 500 mL milk), (200 mL decoction, 400 mL milk), (24 mL decoction, 56 mL milk), (100 mL decoction, 300 mL milk).