Chapter 7 Proportional Reasoning-1 (Class 8 - Latest Maths NCERT (Ganita Prakash I) Solutions)

Question 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) $24 : 8 :: 9 : 3$

Question 2. Give 3 ratios that are proportional to $4 : 9$.

______ : ______ , ______ : ______ , ______ : ______

Question 3. Fill in the missing numbers for these ratios that are proportional to $18 : 24$.

$3$ : ______ , $12$ : ______ , $20$ : ______ , $27$ : ______

Question 4. Look at the following rectangles. Which rectangles are similar to each other? You can verify this by measuring the width and height using a scale and comparing their ratios.

Question 5. Look at the following rectangle. Can you draw a smaller rectangle and a bigger rectangle with the same width to height ratio in your notebooks? Compare your rectangles with your classmates’ drawings. Are all of them the same? If they are different from yours, can you think why? Are they wrong?

Question 6. The following figure shows a small portion of a long brick wall with patterns made using coloured bricks. Each wall continues this pattern throughout the wall. What is the ratio of grey bricks to coloured bricks? Try to give the ratios in their simplest form.

Question 7. 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

______ : ______

Question 1. The Earth travels approximately $940$ million kilometres around the Sun in a year. How many kilometres will it travel in a week?

Question 2. A mason is building a house in the shape shown in the diagram. He needs to construct both the outer walls and the inner wall that separates two rooms. To build a wall of $10$ feet, he requires approximately $1450$ bricks. How many bricks would he need to build the house? Assume all walls are of the same height and thickness.

Question 1. Divide $\textsf{₹}4,500$ into two parts in the ratio $2 : 3$.

Question 2. 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?

Question 3. Blue and yellow paints are mixed in the ratio of $3 : 5$ to produce green paint. To produce $40$ mL of green paint, how much of these two colours are needed?

To make the paint a lighter shade of green, I added $20$ mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?

Question 4. 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?

Question 5. 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?

Question 1. 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.

Question 2. 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?

Question 3. 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?

Question 4. 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?

Question 5. Let us try an ancient problem from Lilavati. At that time weights were measured in a unit named palas and niskas was a unit of money.

“If $2 \frac{1}{2}$ palas of saffron costs $37$ niskas, O expert businessman! tell me quickly what quantity of saffron can be bought for $9$ niskas?”

Question 6. 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 $1 : 2$?

Question 7. 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?

Question 8. 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).

Question 9. 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?

Question 10. One acre of land costs $\textsf{₹}15,00,000$. What is the cost of $2,400$ square feet of the same land?

Question 11. 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?

Question 12. The $\textsf{₹}10$ coin is an alloy of copper and nickel called ‘cupro-nickel’. Copper and nickel are mixed in a $3 : 1$ ratio to get this alloy. The mass of the coin is $7.74$ grams. If the cost of copper is $\textsf{₹}906$ per kg and the cost of nickel is $\textsf{₹}1,341$ per kg, what is the cost of these metals in a $\textsf{₹}10$ coin?