Class 6 Maths Chapter 12 Exercise 12.3 Ratio and Proportion

Exercise 12.3 is the last exercise for chapter 12 of Ratio & Proportion. As we have already learnt, is a fundamental concept in mathematics which we are learning. Ratio is a method to compare quantities, showing how many times one value contains another. For example, if you have two apples and three oranges, the ratio of apples to oranges is 2 to 3, written as 2:3.

Proportion is an equation that shows two ratios are equal. For example, if four pens cost ₹100, we expect eight pens to cost ₹200. This equality of ratios (4 pens/₹100 = 8 pens/₹200) is what we call proportion.

As we dive deep into the questions, we will see real-world examples like calculating cloth costs or determining earnings over time. These practical problems show how ratios and proportions are part of everyday life.

NCERT Solutions for Class 6 Maths Exercise 12.1 Chapter 12 Ratio & Proportion

Question 1. If the cost of 7 m of cloth is ₹ 1470, find the cost of 5 m of cloth.

Solution:
To find the cost of 5 meters of cloth, we first determine the cost of 1 meter of cloth by dividing the total cost by the number of meters.

Cost of 1 meter of cloth = Total cost / Number of meters
Cost of 1 meter of cloth = ₹ 1470 / 7 m = ₹ 210

Now we can find the cost of 5 meters:
Cost of 5 meters = Cost per meter × Number of meters
Cost of 5 meters = ₹ 210 × 5 = ₹ 1050

The cost of 5 meters of cloth is ₹ 1050.

Question 2. Ekta earns ₹ 3000 in 10 days. How much will she earn in 30 days?

Solution:
We can determine Ekta’s earnings in 30 days by setting up a proportion where her earnings are directly proportional to the number of days she works.

Earnings for 10 days = ₹ 3000
Earnings for 1 day = ₹ 3000 / 10
Earnings for 1 day = ₹ 300

Earnings for 30 days = Earnings for 1 day × 30
Earnings for 30 days = ₹ 300 × 30 = ₹ 9000

Ekta will earn ₹ 9000 in 30 days.

Question 3. If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.

Solution:
First, we find the rate of rainfall per day, then calculate for a week (7 days), and convert the result to centimeters.

Rainfall in 3 days = 276 mm
Rainfall in 1 day = 276 mm / 3 days = 92 mm

Rainfall in 7 days = Rainfall in 1 day × 7
Rainfall in 7 days = 92 mm/day × 7 days = 644 mm

To convert millimeters to centimeters:
Rainfall in 7 days = 644 mm ÷ 10 = 64.4 cm

64.4 cm of rain will fall in one full week.

Question 4. Cost of 5 kg of wheat is ₹ 91.50.

(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased in ₹ 183?

Solution:
(a) First, calculate the cost per kg of wheat, then find the cost for 8 kg.

Cost per kg = Total cost / Quantity
Cost per kg = ₹ 91.50 / 5 kg = ₹ 18.30 per kg

Cost for 8 kg = Cost per kg × Quantity
Cost for 8 kg = ₹ 18.30 × 8 = ₹ 146.40

The cost of 8 kg of wheat is ₹ 146.40.

(b) To find the quantity that can be purchased for ₹ 183, divide the total money by the cost per kg.

Quantity that can be purchased = Total money / Cost per kg
Quantity that can be purchased = ₹ 183 / ₹ 18.30 = 10 kg

10 kg of wheat can be purchased for ₹ 183.

Question 5. The temperature dropped 15 degree celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?

Solution:
First, find the rate of temperature drop per day:
Rate of temperature drop = Total drop / Number of days
Rate of temperature drop = 15°C / 30 days = 0.5°C per day

Now, calculate the drop over the next ten days:
Temperature drop in ten days = Rate per day × Number of days
Temperature drop in ten days = 0.5°C/day × 10 days = 5°C

The temperature will drop 5°C in the next ten days.

Question 6. Shaina pays ₹ 15000 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?

Solution:
First, find the monthly rent:
Monthly rent = Total rent for 3 months / Number of months
Monthly rent = ₹ 15000 / 3 months = ₹ 5000 per month

Now, calculate the rent for a whole year:
Rent for a year = Monthly rent × Number of months in a year
Rent for a year = ₹ 5000/month × 12 months = ₹ 60000

Shaina has to pay ₹ 60000 for a whole year.

Question 7. Cost of 4 dozen bananas is ₹ 180. How many bananas can be purchased for ₹ 90?

Solution:
First, find the cost per banana:
Cost per dozen bananas = Total cost / Number of dozens
Cost per dozen bananas = ₹ 180 / 4 dozens = ₹ 45 per dozen

Since one dozen contains 12 bananas, the cost per banana is:
Cost per banana = Cost per dozen / 12
Cost per banana = ₹ 45 / 12 = ₹ 3.75 per banana

Now, calculate the number of bananas that can be purchased for ₹ 90:
Number of bananas = Total money / Cost per banana
Number of bananas = ₹ 90 / ₹ 3.75 ≈ 24 bananas

Approximately 24 bananas can be purchased for ₹ 90.

Question 8. The weight of 72 books is 9 kg. What is the weight of 40 such books?

Solution:
First, find the weight of one book:
Weight of one book = Total weight / Number of books
Weight of one book = 9 kg / 72 books = 0.125 kg per book

Now, calculate the weight of 40 books:
Weight of 40 books = Weight of one book × Number of books
Weight of 40 books = 0.125 kg/book × 40 books = 5 kg

The weight of 40 books is 5 kg.

Question 9. A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?

Solution:
First, find the diesel required per kilometer:
Diesel per kilometer = Total diesel / Distance covered
Diesel per kilometer = 108 liters / 594 km = 0.1818 liters per km

Now, calculate the diesel required for 1650 km:
Diesel for 1650 km = Diesel per kilometer × Distance
Diesel for 1650 km = 0.1818 liters/km × 1650 km ≈ 300 liters

The truck will require approximately 300 liters of diesel to cover 1650 km.

Question 10. Raju purchases 10 pens for ₹ 150 and Manish buys 7 pens for ₹ 84. Can you say who got the pens cheaper?

Solution:
First, find the cost per pen for Raju:
Cost per pen for Raju = Total cost / Number of pens
Cost per pen for Raju = ₹ 150 / 10 pens = ₹ 15 per pen

Now, find the cost per pen for Manish:
Cost per pen for Manish = Total cost / Number of pens
Cost per pen for Manish = ₹ 84 / 7 pens = ₹ 12 per pen

Since Manish’s cost per pen is ₹ 12, compared to Raju’s ₹ 15, Manish got the pens cheaper.

Question 11. Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?

Solution:
First, calculate the runs per over for Anish:
Runs per over for Anish = Total runs / Number of overs
Runs per over for Anish = 42 runs / 6 overs = 7 runs per over

Now, calculate the runs per over for Anup:
Runs per over for Anup = Total runs / Number of overs
Runs per over for Anup = 63 runs / 7 overs = 9 runs per over

Anup made more runs per over with 9 runs, compared to Anish’s 7 runs per over.

Additional Worksheet Questions for Exercise 12.1 Ratio and Proportion for Class 6

If 3 machines take 5 hours to complete a task, how long will 5 machines take, assuming they all work at the same rate?

A car travels 360 km on 20 liters of petrol. How far can it travel on 35 liters of petrol?

If 8 liters of paint can paint two rooms, how many liters are needed to paint 5 rooms of the same size?

The ratio of boys to girls in a class is 3:4. If there are 12 boys, how many girls are there?

A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to use 10 cups of flour, how much sugar do you need?

If a worker is paid ₹800 for 4 days of work, how much will he be paid for 15 days of work?

A map is drawn to scale with a ratio of 1:10000. If two cities are 5 cm apart on the map, what is the actual distance between them in kilometers?

In a fruit salad, the ratio of apples to oranges is 2:3. If there are 10 apples, how many oranges are there?

A photocopy machine can copy 150 pages in 3 minutes. How many pages can it copy in 20 minutes?

The ratio of the amount of ingredient A to ingredient B in a mixture is 7:5. If there are 35 grams of ingredient A, how many grams of ingredient B are there?

Answers

1. 3 hours.
2. 630 km.
3. 20 liters.
4. 16 girls.
5. 15 cups of sugar.
6. ₹3000.
7. 10 kilometers.
8. 15 oranges.
9. 1000 pages.
10. 25 grams of ingredient B.