RBSE Solutions Class 6 Maths Chapter 13 Ratio and Proportion More Ques

Page No. 177

Question 1. Cost of a pen is Rs. 10 and cost of a pencil is Rs. 2. What will be the ratio of a pen's cost to a pencil's cost?
Answer: First, we note down the given costs. The cost of one pen is Rs. 10. The cost of one pencil is Rs. 2. To find the ratio, we compare the cost of the pen to the cost of the pencil.
Cost of a pen = Rs. 10
Cost of a pencil = Rs. 2
The ratio of pen's cost to pencil's cost \( = 10 : 2 \)
We can simplify this fraction by dividing both numbers by 2.
\( = \frac { 10 }{ 2 } \)
\( = \frac {5}{1} \)
The simplified ratio is 5:1.
In simple words: A pen costs Rs. 10 and a pencil costs Rs. 2. The ratio of their costs is 5:1, which means the pen is 5 times more expensive than the pencil.

🎯 Exam Tip: Always make sure to write ratios in their simplest form by dividing both parts by their greatest common divisor.

Question 2. Ravi walks 6 km in an hour while Suraj walks 4 km in an hour. What is the ratio of the distance covered by Ravi to the distance covered by Suraj?
Answer: We are given the distances Ravi and Suraj walk in one hour. Ravi walks 6 km, and Suraj walks 4 km. We need to find the ratio of the distance Ravi covers to the distance Suraj covers.
Distance covered by Ravi every hour = 6 km
Distance covered by Suraj every hour = 4 km
According to the question, the required ratio is Ravi's distance to Suraj's distance.
\( = 6:4 \)
We can simplify this ratio by dividing both numbers by their common factor, which is 2.
\( = \frac {6}{4} \)
\( = \frac {3}{2} \)
Therefore, the ratio of the distance covered by Ravi and Suraj is 3:2.
In simple words: Ravi walks 6 km and Suraj walks 4 km in the same time. The ratio of how far they walk is 3:2. This means Ravi walks a little farther than Suraj.

🎯 Exam Tip: When finding a ratio, ensure the quantities are in the same units. If they are not, convert them before calculating the ratio.

Page No. 178

Question 1. The numbers of vehicles passing on the road between 9 a.m to 10 a.m are recorded in the table below.

Page No. 179

Question 1. What is the ratio of number of two wheelers to the number of cars?
Answer: Based on the context provided in the original problem (and the solution values), let's assume the number of two-wheelers is 24 and the number of cars is 60. We need to find the ratio of two-wheelers to cars.
Number of two wheelers = 24
Number of cars = 60
Ratio of number of two wheelers to the number of cars:
\( = 24: 60 \)
To simplify this ratio, we divide both numbers by their greatest common factor, which is 12.
\( = \frac { 24 }{ 60 } \)
\( = \frac {2}{5} \)
So, the ratio of two wheelers to cars is 2:5. This means for every 2 two-wheelers, there are 5 cars.
In simple words: If there are 24 two-wheelers and 60 cars, the simplest way to compare them using a ratio is 2:5.

🎯 Exam Tip: Always make sure to write ratios in their simplest form to show the most basic relationship between the quantities.

Question 2. What is the ratio of number of total vehicles to the number of trucks?
Answer: From the context (and solution values), let's assume the numbers for two-wheelers, cars, and trucks are 24, 60, and 40 respectively. We need to find the ratio of the total vehicles to the number of trucks.
Number of two wheelers = 24
Number of cars = 60
Number of trucks = 40
Total number of vehicles \( = 24 + 60 + 40 = 124 \)
Ratio of total vehicles to the number of trucks:
\( = (24 + 60 + 40) : 40 \)
\( = 124 : 40 \)
To simplify this ratio, we divide both numbers by their greatest common factor, which is 4.
\( = \frac { (24+ 60 + 40) }{40} \)
\( = \frac { 124 }{ 40 } \)
\( = \frac {31}{10} \)
So, the ratio of total vehicles to trucks is 31:10. This shows that there are many more vehicles overall compared to just trucks.
In simple words: If you add up all the vehicles and then compare that total to just the trucks, the ratio is 31 to 10.

🎯 Exam Tip: When dealing with total quantities, remember to sum up all relevant individual quantities correctly before forming the ratio.

Question 3. Weight of a car is 3300 pounds and weight of a bicycle is 22 pounds. What is the ratio of the weight of bicycle to the weight of car ?
Answer: We are given the weight of a car and a bicycle. The car weighs 3300 pounds, and the bicycle weighs 22 pounds. We need to find the ratio of the weight of the bicycle to the weight of the car.
Weight of car = 3300 pounds
Weight of bicycle = 22 pounds
According to the question, the required ratio is bicycle's weight to car's weight.
\( = 22 : 3300 \)
To simplify this ratio, we divide both numbers by their greatest common factor, which is 22.
\( = \frac {22}{3300 } \)
\( = \frac {1}{150} \)
So, the ratio of the weight of the bicycle to the weight of the car is 1:150. This highlights how much lighter a bicycle is compared to a car.
In simple words: A bicycle weighs 22 pounds and a car weighs 3300 pounds. The ratio of their weights, bicycle to car, is 1:150.

🎯 Exam Tip: Always pay attention to the order in which the ratio is requested (e.g., bicycle to car, not car to bicycle) to avoid errors.

Question 1. Find the ratio of number of doors and the number of windows in year classroom.
Answer: We need to find the ratio between the number of doors and windows in a classroom. Let's assume typical numbers for a classroom as shown in the solution.
Number of doors = 2
Number of windows = 3
According to the question, the ratio of the number of doors and the number of windows is 2:3. This means for every two doors, there are three windows.
In simple words: If a classroom has 2 doors and 3 windows, the ratio of doors to windows is 2:3.

🎯 Exam Tip: Ratios are often used to compare parts of a whole, like how many doors versus how many windows in a room.

Question 2. Draw any rectangle and find the ratio of its length of its breadth.
Answer: To find the ratio of a rectangle's length to its breadth, we can represent the length as 'x' and the breadth as 'y'. The ratio would then be \( x:y \). Let's take an example by drawing a rectangle with specific measurements to demonstrate. Imagine a rectangle where the length is 15 units and the breadth is 10 units.
Let, length of rectangle = x
and, breadth of rectangle = y
The ratio is \( \frac {x}{y} \).
For example, if we choose:
Length \( x = 15 \)
Breadth \( y = 10 \)
The required ratio is:
\( = \frac {15}{10} \)
To simplify, we divide both by 5.
\( = \frac { 3 }{2} \)
So, the ratio of length to breadth for this example is 3:2. This means the length is 1.5 times the breadth.
In simple words: For any rectangle, you can compare its length to its width using a ratio. For example, if a rectangle is 15 units long and 10 units wide, the ratio of its length to width is 3:2.

🎯 Exam Tip: Remember that the ratio of length to breadth depends on the specific dimensions of the rectangle. Always simplify the ratio to its lowest terms.

Page No. 181

Question 1. The length and diameter of a straw are 12 cm and 6 mm respectively. What is the ratio of its diameter to its length?
Answer: To find the ratio, the units must be the same. The length of the straw is given in centimeters, and the diameter is in millimeters. We should convert the length to millimeters.
Length of a straw = 12 cm
Since 1 cm = 10 mm, then 12 cm = \( 12 \times 10 = 120 \) mm.
Its diameter = 6 mm
According to the question, we need the ratio of diameter to length.
Required ratio = Diameter : Length
\( = 6 : 120 \)
To simplify this ratio, we divide both numbers by their greatest common factor, which is 6.
\( = \frac {6}{120} \)
\( = \frac {1}{20} \)
So, the ratio of the straw's diameter to its length is 1:20. This indicates that the straw is much longer than it is wide.
In simple words: A straw is 12 cm long and 6 mm wide. First, change 12 cm to 120 mm. Then, the ratio of its width to its length is 6:120, which simplifies to 1:20.

🎯 Exam Tip: It is crucial to convert all quantities to the same unit before calculating a ratio to ensure accuracy.

Question 2. Anand takes 25 minutes to reach school from his house and Anshul takes one hour to reach school from his house. Find the ratio of the time taken by Anand to the time taken by Anshul.
Answer: We need to find the ratio of the time Anand takes to the time Anshul takes. First, we must make sure both times are in the same units. Anand's time is in minutes, and Anshul's time is in hours.
Time taken by Anand = 25 minutes
Time taken by Anshul = 1 hour
Since 1 hour = 60 minutes, Anshul takes 60 minutes.
According to the question, the required ratio is Anand's time to Anshul's time.
\( = 25 : 60 \)
To simplify this ratio, we divide both numbers by their greatest common factor, which is 5.
\( = \frac {25}{60} \)
\( = \frac {5}{12} \)
So, the ratio of the time taken by Anand to Anshul is 5:12. This shows Anand reaches school much faster than Anshul.
In simple words: Anand takes 25 minutes, and Anshul takes 1 hour (which is 60 minutes). The ratio of Anand's time to Anshul's time is 25:60, which simplifies to 5:12.

🎯 Exam Tip: Always remember to convert different units of time (like hours and minutes) into a single, common unit before calculating ratios to avoid mistakes.

Page No. 183

Question 1. Determine if the following are in proportion
(i) 3: 5 and 1:15
(ii) 4: 12 and 9 : 27
(iii) Rs. 10, is to Rs. 15 and 4 is to 6
Answer: For two ratios to be in proportion, the product of their means (inner terms) must be equal to the product of their extremes (outer terms). If \( a:b \) and \( c:d \) are in proportion, then \( a \times d = b \times c \).
(i) For 3:5 and 1:15:
We check if \( 3 \times 15 = 5 \times 1 \).
\( 45 = 5 \)
This is not true, as \( 45 \ne 5 \).
So, 3:5 and 1:15 are not in proportion.
(ii) For 4:12 and 9:27:
We check if \( 4 \times 27 = 12 \times 9 \).
\( 108 = 108 \)
This is true.
So, 4:12 and 9:27 are in proportion.
(iii) For Rs. 10:Rs. 15 and 4:6:
We check if \( 10 \times 6 = 15 \times 4 \).
\( 60 = 60 \)
This is true.
So, Rs. 10:Rs. 15 and 4:6 are in proportion.
In simple words: To see if two ratios are in proportion, multiply the first number of the first ratio by the last number of the second ratio, and then multiply the second number of the first ratio by the first number of the second ratio. If both answers are the same, the ratios are in proportion. If not, they are not.

🎯 Exam Tip: Always remember the "product of means equals product of extremes" rule (\( a \times d = b \times c \)) to quickly check if two ratios form a proportion.

Page No. 185

Question 1. Read the table and fill in the boxes.
Answer: The table shows the price paid for books by Reshma and Seema. We need to fill in the missing prices, assuming the price per book is consistent. Let's find the unit price for each person first.
For Reshma:
2 Books cost Rs. 50, so 1 Book costs \( \frac{50}{2} = \) Rs. 25.
For Seema:
2 Books cost Rs. 70, so 1 Book costs \( \frac{70}{2} = \) Rs. 35.
Now we can fill the table:
For Reshma:
1 Book: Rs. 25 (given)
5 Books: \( 5 \times 25 = \) Rs. 125
For Seema:
1 Book: Rs. 35 (calculated from 2 books)
5 Books: \( 5 \times 35 = \) Rs. 175
The completed table is shown below. This shows that Seema pays more per book than Reshma.

In simple words: We find out how much one book costs for Reshma and for Seema. Then we use those prices to fill in the missing costs for 1 book and 5 books for both of them.
🎯 Exam Tip: When filling tables based on proportional relationships, always find the unit rate (price per item, distance per hour, etc.) first, as this makes all other calculations easier and more accurate.

Question. Read the table and fill in the boxes.

Answer: To fill the table, we need to find the relationship between the first and second quantities. We calculate how many times the second quantity is larger than the first, and vice-versa, then write the ratios.
1. For 500 gm Jaggery and 1000 gm Jaggery:
- 1000 gm is \( \frac{1000}{500} = 2 \) times 500 gm.
- Ratio (2nd to 1st) = 2:1.
- 500 gm is \( \frac{500}{1000} = \frac{1}{2} \) (half) of 1000 gm.
- Ratio (1st to 2nd) = 1:2.
2. For T-shirt Rs. 200/- and Jacket Rs. 1000/-:
- Rs. 1000 is \( \frac{1000}{200} = 5 \) times Rs. 200.
- Ratio (2nd to 1st) = 5:1.
- Rs. 200 is \( \frac{200}{1000} = \frac{1}{5} \) (fifth part) of Rs. 1000.
- Ratio (1st to 2nd) = 1:5.
The completed table shows these relationships clearly.

In simple words: For each pair of items, figure out how many times bigger the second item is than the first. Then, do the opposite and find out how much smaller the first item is compared to the second. Write these relationships as simple ratios.
🎯 Exam Tip: Always read the column headers carefully to determine which quantity is compared to which (e.g., "2nd to 1st" vs. "1st to 2nd") to avoid reversing the ratio.