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MATHS 2 Marks Questions

Proportional Reasoning-1 · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 30 questions.

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Question 12 Marks
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.
Image
Answer
(a) Grey bricks : Coloured bricks $=18: 33=6: 11$.
(b) Gey bricks : Coloured bricks $=48: 71$.
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Question 22 Marks
Fill in the missing numbers for these ratios that are proportional to $18 : 24$.
3 : __________ 12 : __________ 20 : __________ 27 : __________
Answer
Simplifying $18 : 24$
$\text { H.C.F }=6 \rightarrow 18 / 6 : 24 / 6=3 : 4 .$
So any proportional ratio must equal $3 : 4$.
(i) 3 : __________ $=3 : 4$
(ii) 12 : __________ $=3 \times 4 : 4 \times 4=12 : 16$.
(iii) 20 : __________ $=3 \times 20 / 3 : 4 \times 20 / 3=20 : 80 / 3$.
(iv) 27 : __________ $=3 \times 9 : 4 \times 9=27 : 36$.
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Question 32 Marks
Give 3 ratios that are proportional to 4 : 9.
Answer
To find ratios proportional to $4: 9$, we multiply both terms by the same number :
$\begin{array}{l}4 \times 2 : 9 \times 2=8: 18 \\4 \times 3 : 9 \times 3=12: 27 \\4 \times 5 : 9 \times 5=20 : 45\end{array}$
So, three ratios proportional to $4: 9$ are $8 : 18 ; 12 : 27$; and $20: 45$.
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Question 42 Marks
The 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 ₹906 per kg and the cost of nickel is ₹1,341 per kg, what is the cost of these metals in a ₹10 coin?
Answer
self
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Question 52 Marks
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?
Answer
self
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Question 72 Marks
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?
Answer
self
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Question 82 Marks
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).
Answer
self
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Question 92 Marks
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?
Answer
self
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Question 102 Marks
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?
Answer
self
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Question 112 Marks
Let us try an ancient problem from Lilavati. At that 4 time weights were measured in a unit named palas 22 and niskas was a unit of money. "If $2 \frac{1}{2}$ palas of saffron costs $\frac{3}{7}$niskas, O expert businessman! tell me quickly what quantity of saffron can be bought for 9 niskas?"
Answer
self
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Question 122 Marks
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?
Answer
self
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Question 132 Marks
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?
Answer
self
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Question 142 Marks
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?
Answer
self
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Question 152 Marks
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.
Answer
self
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Question 162 Marks
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?
Answer
self
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Question 172 Marks
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?
Answer
self
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Question 182 Marks
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?
Answer
self
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Question 192 Marks
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?
Answer
self
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Question 212 Marks
A mixture of 40 kg contains sand and cement in the ratio of 3: 1. How much cement should be added to the mixture to make the ratio of sand to cement 5: 2?
Answer
Let us find the quantity of sand and cement in the original mixture. The ratio is 3:1 and the total weight is 40 kg.
So, the weight of sand is $\frac{3}{(3+1)} \times 40=30 kg$.
The weight of cement is $\frac{1}{(3+1)} \times 40=10 kg.$
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Question 222 Marks
Prashanti and Bhuvan started a food cart business near their school. Prashanti invested ₹ 75,000 and Bhuvan invested ₹ 25,000. At the end of the first month, they gained a profit of ₹4,000. They decided that they would share the profit in the same ratio as that of their investment. What is each person's share of the profit?
Answer
The ratio of their investment is 75000: 25000.
Reducing this ratio to its simplest form, we get 3: 1.
3+1 is 4 and dividing the profit of 4000 by 4, we get 1000.
So, Prashanti's share is 3 × 1000 and Bhuvan's share is 1 × 1000.
So, Prashanti would get ₹3,000 and Bhuvan would get ₹1,000 of the profit.
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Question 232 Marks
Go to the market and collect the prices of different sizes of shampoo containers of the same shampoo and create a table like the one given below. See if the volume of shampoo is proportional to the price.
ContainerVolumePrice
Sachet6 mL₹ 2
Small Bottle180 mL₹ 154
Medium Bottle340 mL₹ 276
Large Bottle1000 mL₹ 540
Answer
self
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Question 242 Marks
Puneeth's father went from Lucknow to Kanpur in 2 hours by riding his motorcycle at a speed of 50 km/h. If he drives at 75 km/h, how long will it take him to reach Kanpur? Can we form this problem as a proportion -
50 : 2 :: 75 : ____
Answer
self
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Question 252 Marks
A mason is building a house in the shape shown in the diagram. He needs to construct both are 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 thichness.
Image
Answer
self
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Question 262 Marks
The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week?
Answer
self
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Question 272 Marks
A small farmer in Himahal Pradesh sells each 200 g packet of tea for ₹200. A large estate in Meghalaya sells each 1 kg packet of tea for ₹800. Are the weight-to-price ratios in both places proportional? Which tea is more expensive?
Answer
The ratio of weight to price of the Himachal tea is 200 : 200.
What is the weight to price ratio of the Meghalaya tea ? Is it 1 : 800?
This would not be appropriate, because we considered the weight in grams in the case of Himachal. So, the weight to price ratio is 1000 : 800 in Meghalaya after we convert the weight to grams.
To check if the ratios are proportional, we need to see if both ratios are the same in their simplest forms.
The Himachal tea ratio in its simplest form is 1 : 1.
The Meghalaya tea ratio in its simplest form in 5:4.
So, the ratios are not proportional.
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Question 282 Marks
How can you find the distance covered in 240 minutes?
Discuss with your classmates and find the answer using different strategies.
Answer
self
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Question 292 Marks
Is this the right way to formulate the question ?
No, because 150 is in minutes, but 4 is in hours, The second ratio should use the same units for times as the first ratio. Since 4 houes is 240 minutes, the right form is 150 : 90 :: 240 : ?
Answer
self
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Question 302 Marks
A car travels 90 km in 150 minutes. If it continues at the same speed, what distance will it cover in 4 hours?
If it continues at the same speed, the ratio of the time taken should be proportional to the ratio of the distance covered.
150 : 90 :: 4 : ?
Answer
self
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