RBSE Solutions Class 6 Maths Chapter 13 Ratio and Proportion Exercise 13.1

Rajasthan Board RBSE Class 6 Maths Chapter 13 Ratio and Proportion Ex 13.1

Question 1. A social Awareness camp was organized in the summer vacations this year. 25 girls and 15 boys participate in the camp and put water bowl for birds.
(i) What is the ratio of number of girls to the number of boys ?
(ii) What is the ratio of number of girls to the number of participants?
Answer:
Number of girls = 25
Number of boys = 15
Total number of participants = 25 + 15 = 40

(i) The ratio of the number of girls to the number of boys is:
Required ratio \( = \frac { 25 }{ 15 } = \frac { 5 }{ 3 } = 5:3 \)

(ii) The ratio of the number of girls to the number of participants is:
Required ratio \( = \frac { 25 }{ 40 } = \frac { 5 }{ 8 } = 5:8 \)
In simple words: First, count the girls, boys, and total people. Then, divide the number of girls by the number of boys to get the first ratio. For the second ratio, divide the number of girls by the total number of people at the camp.

🎯 Exam Tip: Always make sure the units are the same before finding a ratio. If they are different (like girls to total participants), calculate the total first.

Question 2. During a Tree Plantation programme in a school, students of 6th Class planted 8 Neem trees, 13 mango trees and 19 Guava trees.
(i) What is the ratio of number of Neem trees planted to the number of Mango trees planted ?
(ii) What is the ratio of total number of trees planted to the number of Neem trees planted ?
Answer:
Number of Neem trees = 8
Number of Mango trees = 13
Number of Guava trees = 19
Total number of trees = 8 + 13 + 19 = 40

(i) The ratio of Neem trees to Mango trees is:
Required ratio \( = \frac { 8 }{ 13 } = 8:13 \)

(ii) The ratio of total trees to Neem trees is:
Required ratio \( = \frac { 40 }{ 8 } = 5:1 \)
In simple words: Count each type of tree and the total. To find a ratio, simply divide the count of the first item by the count of the second item and simplify the fraction.

🎯 Exam Tip: Ratios can be written as fractions or using a colon. Always simplify the ratio to its lowest terms, just like simplifying a fraction.

Question 3. the ratio of :
Answer:
In the figure:
Number of triangles = 4
Number of circles = 2
Number of squares = 2
Total number of figures = 4 + 2 + 2 = 8

(i) The ratio of the number of triangles to the number of circles is:
Required ratio \( = \frac { 4 }{ 2 } = \frac { 2 }{ 1 } = 2:1 \)

(ii) The ratio of the number of squares to all the figures is:
Required ratio \( = \frac { 2 }{ 8 } = \frac { 1 }{ 4 } = 1:4 \)

(iii) The ratio of the number of triangles to all the figures is:
Required ratio \( = \frac { 4 }{ 8 } = \frac { 1 }{ 2 } = 1:2 \)
In simple words: Count how many of each shape there are. Then, divide the number of the first shape by the number of the second shape to find the ratio. Always simplify the fraction to its smallest form.

🎯 Exam Tip: When dealing with ratios of geometric figures, count carefully. Ensure you are comparing the correct two quantities as specified in the question.

Question 4. Fill in the following blanks
\( \frac { 15 }{ 21 } = \frac { 5 }{ \Box } = \frac { \Box }{ 14 } = \frac { 25 }{ \Box } \)
Answer:
Given the fraction: \( \frac { 15 }{ 21 } \)

First, simplify \( \frac { 15 }{ 21 } \)
\( \frac { 15 \div 3 }{ 21 \div 3 } = \frac { 5 }{ 7 } \)

So, we have: \( \frac { 5 }{ 7 } \)

Now, let's find the missing numbers.

To find the denominator for \( \frac { 5 }{ \Box } \):
\( \frac { 15 }{ 21 } = \frac { 5 }{ x } \)
\( 15x = 21 \times 5 \)
\( 15x = 105 \)
\( x = \frac { 105 }{ 15 } \)
\( x = 7 \)

So, \( \frac { 15 }{ 21 } = \frac { 5 }{ 7 } \)

To find the numerator for \( \frac { \Box }{ 14 } \):
\( \frac { 5 }{ 7 } = \frac { y }{ 14 } \)
\( 7y = 5 \times 14 \)
\( 7y = 70 \)
\( y = \frac { 70 }{ 7 } \)
\( y = 10 \)

So, \( \frac { 5 }{ 7 } = \frac { 10 }{ 14 } \)

To find the denominator for \( \frac { 25 }{ \Box } \):
\( \frac { 5 }{ 7 } = \frac { 25 }{ z } \)
\( 5z = 7 \times 25 \)
\( 5z = 175 \)
\( z = \frac { 175 }{ 5 } \)
\( z = 35 \)

So, \( \frac { 5 }{ 7 } = \frac { 25 }{ 35 } \)

Therefore, the completed blanks are:
\( \frac { 15 }{ 21 } = \frac { 5 }{ 7 } = \frac { 10 }{ 14 } = \frac { 25 }{ 35 } \)
In simple words: We first simplified the given fraction \( \frac { 15 }{ 21 } \) to its simplest form, which is \( \frac { 5 }{ 7 } \). Then, we used this simplest form to find the missing numbers by making sure the fractions were all equal.

🎯 Exam Tip: Always simplify the initial fraction to its lowest terms first. This makes it easier to find the equivalent fractions with missing parts.

Question 5. Find the ratio of the following
(i) 25 to 150
(ii) 72 to 36
(iii) 55 km to 121 km
(iv) 35 minute to 55 minute
Answer:
(i) Required ratio \( = \frac { 25 }{ 150 } = \frac { 1 }{ 6 } = 1:6 \)

(ii) Required ratio \( = \frac { 72 }{ 36 } = \frac { 2 }{ 1 } = 2:1 \)

(iii) Required ratio \( = \frac { 55 \text{ km} }{ 121 \text{ km} } = \frac { 5 }{ 11 } = 5:11 \)

(iv) Required ratio \( = \frac { 35 \text{ minute} }{ 55 \text{ minute} } = \frac { 7 }{ 11 } = 7:11 \)
In simple words: To find a ratio, simply write the first number over the second number as a fraction. Then, divide both the top and bottom numbers by their biggest common factor until the fraction cannot be made any smaller.

🎯 Exam Tip: Remember that ratios only make sense when comparing quantities of the same type or units. If units are different, convert them first before finding the ratio.

Question 6. Find the ratio of the following
(i) 60 paise and 3 Rupees
(ii) 800 gm and 5 kg
(iii) 15 minute and 1 hour
Answer:
(i) To find the ratio of 60 paise and 3 Rupees, we need to convert them to the same unit.
1 Rupee = 100 paise
So, 3 Rupees \( = 3 \times 100 = 300 \) paise
Required ratio \( = \frac { 60 \text{ paise} }{ 300 \text{ paise} } = \frac { 6 }{ 30 } = \frac { 1 }{ 5 } = 1:5 \)

(ii) To find the ratio of 800 gm and 5 kg, we need to convert them to the same unit.
1 kg = 1000 gm
So, 5 kg \( = 5 \times 1000 = 5000 \) gm
Required ratio \( = \frac { 800 \text{ gm} }{ 5000 \text{ gm} } = \frac { 8 }{ 50 } = \frac { 4 }{ 25 } = 4:25 \)

(iii) To find the ratio of 15 minutes and 1 hour, we need to convert them to the same unit.
1 hour = 60 minutes
Required ratio \( = \frac { 15 \text{ minutes} }{ 60 \text{ minutes} } = \frac { 1 }{ 4 } = 1:4 \)
In simple words: Before comparing two different amounts, like rupees and paise or grams and kilograms, you must change them so they are both in the same unit. Once they are in the same unit, you can easily form a ratio and simplify it.

🎯 Exam Tip: Unit conversion is the first and most critical step when comparing quantities with different units. A common mistake is to form a ratio directly without converting, leading to an incorrect answer.

Question 7. During a year, a cowshed had received donations worth Rs. 3,25,000 out of which Rs. 3,00,000 were spend on the welfare of the cows. Find the ratio of donations received to the expenditure incurred.
Answer:
Donations received in a year = Rs. 3,25,000
Expenditure incurred = Rs. 3,00,000
Required ratio \( = \frac { 3,25,000 }{ 3,00,000 } \)
\( = \frac { 325 }{ 300 } \)
\( = \frac { 25 \times 13 }{ 25 \times 12 } \)
\( = \frac { 13 }{ 12 } = 13:12 \)
In simple words: The problem asks for the ratio of money received to money spent. We write these two amounts as a fraction and then simplify it by dividing both numbers by their largest common factor.

🎯 Exam Tip: When simplifying large numbers in a ratio, look for common factors like 10, 100, or 25 to divide by first, as this makes the process quicker.

Question 8. Mahesh studies 4 hours and Laxmi studies 180 minutes daily. Find the ratio of study time of Mahesh to study time of Laxmi. (1 hour = 60 minutes).
Answer:
Mahesh studies everyday = 4 hours
Laxmi studies everyday = 180 minutes

To find the ratio, we must convert their study times to the same unit. Let's convert hours to minutes.
1 hour = 60 minutes
Mahesh's study time in minutes \( = 4 \times 60 = 240 \) minutes

Now, find the ratio of Mahesh's study time to Laxmi's study time:
Required ratio \( = \frac { 240 \text{ minutes} }{ 180 \text{ minutes} } \)
\( = \frac { 240 \div 60 }{ 180 \div 60 } \)
\( = \frac { 4 }{ 3 } = 4:3 \)
In simple words: First, change Mahesh's study time from hours into minutes so both times are in the same unit. Then, put Mahesh's time over Laxmi's time as a fraction and simplify it to get the ratio.

🎯 Exam Tip: Always choose the most convenient unit for conversion (e.g., convert hours to minutes) to avoid fractions or decimals during the conversion step.

Question 9. Out of 720 student in a school, 360 students stay at a hostel. Find the ratio of number of student staying at the hostel to the total number of students.
Answer:
Total number of students = 720
Number of students staying at the hostel = 360

The ratio of students staying at the hostel to the total number of students is:
Required ratio \( = \frac { 360 }{ 720 } \)
\( = \frac { 360 \div 360 }{ 720 \div 360 } \)
\( = \frac { 1 }{ 2 } = 1:2 \)
In simple words: You need to compare the number of students living in the hostel with the total number of students in the school. Write these as a fraction and then simplify it to its smallest form.

🎯 Exam Tip: When one number is a direct multiple of the other (like 360 and 720), simplifying the ratio is very straightforward as one quantity is exactly half of the other.

Question 10. Talisma and Gurumit started a business and invested money in the ratio 2 : 5. After one year the total profit was Rs. 35,000. Find the shares of profit for Talsima and Gurumit.
Answer:
The investment ratio of Talisma to Gurumit is 2:5.
Total profit after one year = Rs. 35,000

Sum of the ratio parts \( = 2 + 5 = 7 \)

Talisma's share of profit \( = \frac { 2 }{ 7 } \times 35,000 \)
\( = 2 \times 5,000 \)
\( = \text{Rs. } 10,000 \)

Gurumit's share of profit \( = \frac { 5 }{ 7 } \times 35,000 \)
\( = 5 \times 5,000 \)
\( = \text{Rs. } 25,000 \)
In simple words: First, add up the parts of the ratio to find the total number of shares. Then, divide the total profit by this sum to find the value of one share. Finally, multiply this value by each person's ratio part to find their individual profit.

🎯 Exam Tip: Always make sure the sum of the individual shares equals the total profit at the end, which helps verify your calculations.

Question 11. Consider the statement : Ratio of breadth and length of hall is 3:4 Complete the following table that show some possible breadths and lengths of the hall.
Answer:
The ratio of breadth to length of the hall is 3:4. This means for every 3 units of breadth, there are 4 units of length.

🎯 Exam Tip: To complete a ratio table, find the multiplier that changes one known value in the ratio (e.g., from 3 to 6). Then, apply the same multiplier to the other value in the ratio (e.g., from 4 to 8).

Question 12. Present age of father is 45 years and that of his son is 15 years. Find the ratio of
(i) Present age of father of the present age of son.
(ii) Age of father to the age to son, when son was 10 years old.
(iii) Age of father after 5 years to the age of son after 5 years.
(iv) Age of father to the age of son, when father will be 60 years old.
Answer:
Present age of father = 45 years
Present age of son = 15 years

(i) Ratio of present age of father to present age of son:
Required ratio \( = \frac { 45 }{ 15 } = \frac { 3 }{ 1 } = 3:1 \)

(ii) When the son was 10 years old, this was 5 years ago (\( 15 - 10 = 5 \)).
Age of father 5 years ago \( = 45 - 5 = 40 \) years
Age of son 5 years ago \( = 15 - 5 = 10 \) years
Required ratio \( = \frac { 40 }{ 10 } = \frac { 4 }{ 1 } = 4:1 \)

(iii) After 5 years:
Age of father after 5 years \( = 45 + 5 = 50 \) years
Age of son after 5 years \( = 15 + 5 = 20 \) years
Required ratio \( = \frac { 50 }{ 20 } = \frac { 5 }{ 2 } = 5:2 \)

(iv) When the father will be 60 years old:
The father's age will increase by \( 60 - 45 = 15 \) years.
So, this is 15 years from now.
Age of son after 15 years \( = 15 + 15 = 30 \) years
Required ratio \( = \frac { 60 }{ 30 } = \frac { 2 }{ 1 } = 2:1 \)
In simple words: For each part of the question, first figure out the father's and son's ages for that specific time (present, past, or future). Then, make a ratio of their ages and simplify it. It's important to calculate the correct ages for each scenario before finding the ratio.

🎯 Exam Tip: Pay close attention to keywords like "ago" or "after" to correctly calculate the ages of both individuals before forming the ratio.