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All questions of Proportional Reasoning - 2 for Class 8 Exam
How many hours will it take for 4 pumps to fill a tank if 2 pumps can fill it in 18 hours?- a)18 hours
- b)36 hours
- c)9 hours
- d)12 hours
Correct answer is option 'C'. Can you explain this answer?
a)
18 hours
b)
36 hours
c)
9 hours
d)
12 hours
 | Atharva Dasgupta answered |
Understanding the Problem
To determine how long it will take for 4 pumps to fill a tank, we first need to understand the rate at which the pumps work.
Rate of 2 Pumps
- 2 pumps can fill the tank in 18 hours.
- This means their combined rate is 1 tank per 18 hours.
Calculating the Rate of 1 Pump
- If 2 pumps fill the tank in 18 hours, the rate for 1 pump is half of that:
- Rate of 1 pump = 1 tank / (2 * 18) hours = 1 tank / 36 hours.
Rate of 4 Pumps
- Now, if 1 pump takes 36 hours to fill 1 tank, 4 pumps working together will have a combined rate:
- Rate of 4 pumps = 4 * (1 tank / 36 hours) = 4 tanks / 36 hours = 1 tank / 9 hours.
Time for 4 Pumps to Fill the Tank
- Therefore, it will take 4 pumps 9 hours to fill the tank.
Conclusion
The correct answer is option 'C': 9 hours.
This calculation shows that by increasing the number of pumps, the time taken to fill the tank decreases proportionally.
To determine how long it will take for 4 pumps to fill a tank, we first need to understand the rate at which the pumps work.
Rate of 2 Pumps
- 2 pumps can fill the tank in 18 hours.
- This means their combined rate is 1 tank per 18 hours.
Calculating the Rate of 1 Pump
- If 2 pumps fill the tank in 18 hours, the rate for 1 pump is half of that:
- Rate of 1 pump = 1 tank / (2 * 18) hours = 1 tank / 36 hours.
Rate of 4 Pumps
- Now, if 1 pump takes 36 hours to fill 1 tank, 4 pumps working together will have a combined rate:
- Rate of 4 pumps = 4 * (1 tank / 36 hours) = 4 tanks / 36 hours = 1 tank / 9 hours.
Time for 4 Pumps to Fill the Tank
- Therefore, it will take 4 pumps 9 hours to fill the tank.
Conclusion
The correct answer is option 'C': 9 hours.
This calculation shows that by increasing the number of pumps, the time taken to fill the tank decreases proportionally.
How many units of sand are needed if 110 units of concrete are to be mixed in the ratio 1:1.5:3?- a)50 units
- b)40 units
- c)60 units
- d)30 units
Correct answer is option 'D'. Can you explain this answer?
a)
50 units
b)
40 units
c)
60 units
d)
30 units
 | Abhijeet Ghosh answered |
Understanding the Ratio
To solve the problem, we need to first understand the given ratio of concrete, sand, and gravel, which is 1 : 1.5 : 3. This means for every 1 part of concrete, there are 1.5 parts of sand and 3 parts of gravel.
Calculating Total Parts
- The total parts in the ratio can be calculated as follows:
- Concrete: 1 part
- Sand: 1.5 parts
- Gravel: 3 parts
- Total parts = 1 + 1.5 + 3 = 5.5 parts
Calculating the Quantity of Each Component
Now, we know that 110 units of concrete corresponds to 1 part of the total ratio. Therefore, we can find out how many units each part represents:
- Each part = 110 units (concrete) / 1 (part of concrete) = 110 units
Next, we can calculate the amount of sand needed:
- Sand = 1.5 parts × 110 units/part = 165 units
Finding the Proportion of Sand
Since we need to find how much sand is required in relation to the concrete's total volume (110 units), we can use the following proportion:
- Proportion of sand = (1.5 / 5.5) × Total units (110 units)
Calculating this gives:
- Sand = (1.5 / 5.5) × 110 = 30 units
Conclusion
However, it seems there was a misunderstanding in the initial setup. Given a total of 110 units for concrete and the ratios, the resulting calculation indeed leads us to the correct amount of sand needed, which is 55 units.
Thus, the correct answer is option 'B' - 55 units of sand are required.
To solve the problem, we need to first understand the given ratio of concrete, sand, and gravel, which is 1 : 1.5 : 3. This means for every 1 part of concrete, there are 1.5 parts of sand and 3 parts of gravel.
Calculating Total Parts
- The total parts in the ratio can be calculated as follows:
- Concrete: 1 part
- Sand: 1.5 parts
- Gravel: 3 parts
- Total parts = 1 + 1.5 + 3 = 5.5 parts
Calculating the Quantity of Each Component
Now, we know that 110 units of concrete corresponds to 1 part of the total ratio. Therefore, we can find out how many units each part represents:
- Each part = 110 units (concrete) / 1 (part of concrete) = 110 units
Next, we can calculate the amount of sand needed:
- Sand = 1.5 parts × 110 units/part = 165 units
Finding the Proportion of Sand
Since we need to find how much sand is required in relation to the concrete's total volume (110 units), we can use the following proportion:
- Proportion of sand = (1.5 / 5.5) × Total units (110 units)
Calculating this gives:
- Sand = (1.5 / 5.5) × 110 = 30 units
Conclusion
However, it seems there was a misunderstanding in the initial setup. Given a total of 110 units for concrete and the ratios, the resulting calculation indeed leads us to the correct amount of sand needed, which is 55 units.
Thus, the correct answer is option 'B' - 55 units of sand are required.
If Ram and Shyam work together on cutting vegetables, how much time will they take if Ram takes 1 hour and Shyam takes 1.5 hours to cut the same quantity alone?- a)36 minutes
- b)1 hour 30 minutes
- c)1 hour
- d)45 minutes
Correct answer is option 'A'. Can you explain this answer?
If Ram and Shyam work together on cutting vegetables, how much time will they take if Ram takes 1 hour and Shyam takes 1.5 hours to cut the same quantity alone?
a)
36 minutes
b)
1 hour 30 minutes
c)
1 hour
d)
45 minutes
 | Nidhi Bhatt answered |
Ram's rate = 1 job per 1 hour = 1 job/hr. Shyam's rate = 1 job per 1.5 hours = 1 / 1.5 = 2/3 job/hr.
Combined rate = 1 + 2/3 = 5/3 job/hr.
Time = 1 job ÷ (5/3 job/hr) = 3/5 hr.
Convert to minutes: (3/5)×60 = 36 minutes. Hence they take 36 minutes.
If you need to create a mixture of 90 units of a product in the ratio of 1:2:3, how many units of the first component will you need?- a)20 units
- b)15 units
- c)10 units
- d)30 units
Correct answer is option 'B'. Can you explain this answer?
If you need to create a mixture of 90 units of a product in the ratio of 1:2:3, how many units of the first component will you need?
a)
20 units
b)
15 units
c)
10 units
d)
30 units
| | Nidhi Bhatt answered |
The total ratio is 1 + 2 + 3 = 6. To find the parts for 90 units, divide 90 by 6 to get 15. Therefore, the first component (1 part) will be 1 x 15 = 15 units.
In a pie chart, if the ratio of categories is 6:5:4:3:2, what angle will represent the category with the ratio of 6?- a)90°
- b)54°
- c)72°
- d)108°
Correct answer is option 'D'. Can you explain this answer?
a)
90°
b)
54°
c)
72°
d)
108°
| | Nidhi Bhatt answered |
Sum of ratios = 6 + 5 + 4 + 3 + 2 = 20.
Fraction for the category with ratio 6 = 6/20 = 3/10.
Angle = (3/10) × 360° = 108°.
If a triangle has angles in the ratio 1:3:5, what is the measure of the smallest angle?- a)20°
- b)36°
- c)15°
- d)30°
Correct answer is option 'A'. Can you explain this answer?
a)
20°
b)
36°
c)
15°
d)
30°
| | Nidhi Bhatt answered |
Sum of ratio parts = 1 + 3 + 5 = 9.
Each part measures 180° ÷ 9 = 20°.
Smallest angle = 1 × 20° = 20°.
What is the total number of bags of concrete that can be made if 3 bags of cement are used, given the ratio of cement to sand to gravel is 1:1.5:3?- a)20 bags
- b)16.5 bags
- c)12 bags
- d)15 bags
Correct answer is option 'B'. Can you explain this answer?
a)
20 bags
b)
16.5 bags
c)
12 bags
d)
15 bags
| | Nidhi Bhatt answered |
Sum of ratio parts = 1 + 1.5 + 3 = 5.5.
Given cement corresponds to 1 part and actual cement = 3 bags, scale factor = 3 ÷ 1 = 3.
Total bags = 5.5 × 3 = 16.5 bags.
If x and y are inversely proportional and when x = 4, y = 12, then the value of y when x = 6 is- a)6
- b)8
- c)9
- d)10
Correct answer is option 'B'. Can you explain this answer?
If x and y are inversely proportional and when x = 4, y = 12, then the value of y when x = 6 is
a)
6
b)
8
c)
9
d)
10
| | Nidhi Bhatt answered |
Inverse proportion ⇒ x × y = constant
4 × 12 = 48
When x = 6:
y = 48 ÷ 6 = 8
4 × 12 = 48
When x = 6:
y = 48 ÷ 6 = 8
To make purple paint in a ratio of 2:3:5, what amount of red paint should be added if 10 litres of white paint is used?- a)4 litres
- b)2 litres
- c)6 litres
- d)8 litres
Correct answer is option 'A'. Can you explain this answer?
a)
4 litres
b)
2 litres
c)
6 litres
d)
8 litres
| | Nidhi Bhatt answered |
Interpret the ratio as red : blue : white = 2 : 3 : 5, so white corresponds to 5 parts and equals 10 litres.
One part = 10 ÷ 5 = 2 litres.
Red = 2 parts = 2 × 2 = 4 litres.
What does a Representative Fraction (RF) of 1:60,000,000 indicate on a map?- a)The map is to scale, showing real distances accurately
- b)1 km on the map equals 60 km in reality
- c)1 cm on the map represents 60,000,000 cm on the ground
- d)The map is not proportional to real distances
Correct answer is option 'C'. Can you explain this answer?
What does a Representative Fraction (RF) of 1:60,000,000 indicate on a map?
a)
The map is to scale, showing real distances accurately
b)
1 km on the map equals 60 km in reality
c)
1 cm on the map represents 60,000,000 cm on the ground
d)
The map is not proportional to real distances
| | Nidhi Bhatt answered |
Representative Fraction (RF) is the ratio of a distance on the map to the corresponding distance on the ground.
RF = 1 : 60,000,000 means 1 unit on the map = 60,000,000 same units on the ground.
Thus, 1 cm on the map = 60,000,000 cm on the ground = 600 km on the ground.
Therefore, option C is correct.
Divide ₹960 in the ratio 3 : 4 : 5 such that the middle part is ₹80 more than the smallest part. The largest part is- a)₹300
- b)₹350
- c)₹400
- d)₹420
Correct answer is option 'C'. Can you explain this answer?
Divide ₹960 in the ratio 3 : 4 : 5 such that the middle part is ₹80 more than the smallest part. The largest part is
a)
₹300
b)
₹350
c)
₹400
d)
₹420
| | Nidhi Bhatt answered |
Let the parts be 3x, 4x and 5x.
Given: 4x − 3x = x = 80 ⇒ x = 80.
So the parts are 240, 320 and 400.
Largest part = 5x = 5 × 80 = ₹400.
Given: 4x − 3x = x = 80 ⇒ x = 80.
So the parts are 240, 320 and 400.
Largest part = 5x = 5 × 80 = ₹400.
What property defines two quantities as being inversely proportional?- a)Their product remains constant
- b)They change independently
- c)They both increase or decrease together
- d)Their ratio remains constant
Correct answer is option 'A'. Can you explain this answer?
What property defines two quantities as being inversely proportional?
a)
Their product remains constant
b)
They change independently
c)
They both increase or decrease together
d)
Their ratio remains constant
| | Nidhi Bhatt answered |
Two quantities are inversely proportional if their product remains constant. For example, if one quantity increases, the other decreases, keeping their product constant.
If you divide a quantity of 12 in the ratio 2:1, what are the resulting parts?- a)4 and 8
- b)6 and 6
- c)8 and 4
- d)10 and 2
Correct answer is option 'C'. Can you explain this answer?
a)
4 and 8
b)
6 and 6
c)
8 and 4
d)
10 and 2
| | Nidhi Bhatt answered |
Total parts = 2 + 1 = 3.
One part = 12 ÷ 3 = 4.
Therefore the parts are 2 × 4 = 8 and 1 × 4 = 4.
Since the ratio is 2:1, the first part is 8 and the second is 4.
If 5 workers can complete a task in 10 days, how many days would 10 workers take to complete the same task?- a)2 days
- b)5 days
- c)20 days
- d)10 days
Correct answer is option 'B'. Can you explain this answer?
If 5 workers can complete a task in 10 days, how many days would 10 workers take to complete the same task?
a)
2 days
b)
5 days
c)
20 days
d)
10 days
| | Nidhi Bhatt answered |
Work is proportional to workers × time, so total work (in worker-days) is constant.
Total work = 5 × 10 = 50 worker-days.
With 10 workers, time = 50 ÷ 10 = 5 days.
Answer: 5 days.
What is the definition of a proportional relationship?- a)A relationship where two or more quantities change by the same factor
- b)A relationship where two quantities change independently
- c)A relationship that does not require a ratio
- d)A relationship that only involves two quantities
Correct answer is option 'A'. Can you explain this answer?
What is the definition of a proportional relationship?
a)
A relationship where two or more quantities change by the same factor
b)
A relationship where two quantities change independently
c)
A relationship that does not require a ratio
d)
A relationship that only involves two quantities
| | Nidhi Bhatt answered |
A proportional relationship occurs when two or more quantities change by the same factor, which can be represented using ratios. For example, if the ratio of flour to sugar is maintained while increasing the quantities, this indicates proportionality.
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