Class 6 Mathematics Chapter 1, Exercise 1.2, “Knowing our Numbers,” is an exercise about large numbers in various contexts. This chapter enhances students’ understanding of basic mathematical operations like addition, subtraction, multiplication, and division in real-world cases. Students should try understanding large numbers and their usage, which is applicable daily. It helps in calculating expenses, understanding distances, etc.
Consider a book exhibition held for four consecutive days. If the number of tickets sold each day were 1094, 1812, 2050, and 2751, respectively, one has to add these numbers to find the total number of tickets sold. Take Shekhar, a famous cricket player who has scored 6980 runs in test matches and aims to reach 10,000 runs. Calculating how many more runs he needs involves basic subtraction. It shows how maths is integral to sports analytics.
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NCERT Solutions for Class 6 Maths Exercise 1.2 Chapter 1 Knowing our Numbers
Question 1. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.
Solution:
Total tickets sold = 1094 (Day 1) + 1812 (Day 2) + 2050 (Day 3) + 2751 (Day 4).
Calculating the sum, Total = 1094 + 1812 + 2050 + 2751 = 7707.
Total tickets sold = 7707.
Question 2. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?
Solution:
To find out how many more runs Shekhar needs, subtract his current runs from his target.
Runs needed = 10,000 (target) – 6980 (current).
Calculating the difference, Runs needed = 10,000 – 6980 = 3020.
Runs needed = 3020.
Question 3. In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?
Solution:
Winning margin = Votes of successful candidate – Votes of rival.
Margin = 5,77,500 – 3,48,700.
Calculating the difference, Margin = 5,77,500 – 3,48,700 = 2,28,800.
Winning margin = 2,28,800 votes.
Question 4. Kirti bookstore sold books worth ₹ 2,85,891 in the first week of June and books worth ₹ 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?
Solution:
Total sale = Sale in the first week + Sale in the second week.
Total sale = ₹2,85,891 + ₹4,00,768.
Calculating the sum, Total sale = ₹2,85,891 + ₹4,00,768 = ₹6,86,659.
To find the week with higher sales, subtract the first week’s sales from the second week’s.
Higher sale difference = ₹4,00,768 – ₹2,85,891 = ₹1,14,877.
Total sale = ₹6,86,659; Second week higher by ₹1,14,877.
Question 5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.
Solution:
Greatest number = Arrange digits in descending order = 76432.
Least number = Arrange digits in ascending order = 23467.
Difference = Greatest number – Least number.
Difference = 76432 – 23467.
Calculating the difference, Difference = 76432 – 23467 = 52965.
Difference = 52965.
Question 6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
Solution:
Total production = Daily production × Number of days in January.
January 2006 had 31 days.
Total screws = 2,825 screws/day × 31 days.
Calculating the total, Total = 2,825 × 31 = 87,575.
Total screws produced = 87,575.
Question 7. A merchant had ₹ 78,592 with her. She placed an order for purchasing 40 radio sets at ₹ 1200 each. How much money will remain with her after the purchase?
Solution:
Total cost of radios = Number of radios × Cost per radio.
Total cost = 40 radios × ₹1200 each = ₹48,000.
Remaining money = Initial amount – Total cost of radios.
Remaining money = ₹78,592 – ₹48,000 = ₹30,592.
Remaining money = ₹30,592.
Question 8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications?)
Solution:
Incorrect product = 7236 × 65.
Correct product = 7236 × 56.
Difference = Incorrect product – Correct product.
Difference = (7236 × 65) – (7236 × 56).
This simplifies to 7236 × (65 – 56) = 7236 × 9.
Difference = 7236 × 9 = 65,124.
Difference = 65,124.
Question 9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint: convert data in cm.)
Solution:
Convert everything to centimeters: 2 m 15 cm = 215 cm, 40 m = 4000 cm.
Number of shirts = Total cloth in cm / Cloth needed for one shirt.
Number of shirts = 4000 cm / 215 cm = 18 (rounded down).
Remaining cloth = Total cloth – (Number of shirts × Cloth per shirt).
Remaining cloth = 4000 cm – (18 × 215 cm) = 4000 cm – 3870 cm = 130 cm.
18 shirts can be stitched, 130 cm cloth remains.
Question 10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
Solution:
Convert weights to grams for ease of calculation: 4 kg 500 g = 4500 g, 800 kg = 800,000 g.
Number of boxes = Total carrying capacity / Weight of one box.
Number of boxes = 800,000 g / 4500 g = 177.78.
As we can’t have a fraction of a box, it’s rounded down.
177 boxes can be loaded.
Question 11. The distance between the school and a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.
Solution:
Convert the distance to meters: 1 km 875 m = 1875 m.
Total daily distance (both ways) = 1875 m × 2.
Total distance in six days = Daily distance × 6.
Total distance = (1875 m × 2) × 6 = 22500 m.
Total distance = 22500 m.
Question 12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Solution:
Convert everything to milliliters: 4 liters 500 ml = 4500 ml.
Number of glasses = Total curd / Capacity of one glass.
Number of glasses = 4500 ml / 25 ml = 180.
180 glasses can be filled.
Extra Challenging MCQ Questions
1. A book exhibition was held for four days in a school. The number of tickets sold on the first, second, third, and fourth days were 1094, 1812, 2050, and 2751 respectively. What was the total number of tickets sold?
Hint: Sum the tickets sold each day.
a) 7707
b) 7700
c) 7710
d) 7697
Answer:
a) 7707
2. Shekhar is a famous cricket player. He has scored 6980 runs in test matches and aims to reach 10,000 runs. How many more runs does he need?
Hint: Subtract current runs from the target.
a) 3020
b) 2980
c) 3120
d) 3000
Answer:
a) 3020
3. In an election, the successful candidate secured 5,77,500 votes, and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win?
Hint: Subtract the rival’s votes from the successful candidate’s votes.
a) 2,28,800
b) 2,28,700
c) 2,29,000
d) 2,28,600
Answer:
a) 2,28,800
4. Kirti bookstore sold books worth ₹2,85,891 in the first week of June and ₹4,00,768 in the second week. What was the total sale for the two weeks?
Hint: Add the sales of both weeks.
a) ₹6,86,659
b) ₹6,86,559
c) ₹6,86,699
d) ₹6,86,600
Answer:
a) ₹6,86,659
5. In the previous question, by how much did the sales increase in the second week compared to the first week?
Hint: Subtract the first week’s sales from the second week’s sales.
a) ₹1,14,877
b) ₹1,14,878
c) ₹1,14,879
d) ₹1,14,876
Answer:
a) ₹1,14,877
6. Find the difference between the largest and the smallest numbers among 5,43,021; 1,52,760; 8,75,439; 4,00,000.
Hint: Identify the largest and smallest numbers, then subtract the smallest from the largest.
a) 7,22,679
b) 7,22,678
c) 7,22,680
d) 7,22,677
Answer:
a) 7,22,679
7. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?
Hint: Calculate the difference between 65 and 56, then multiply by 7236.
a) 65,124
b) 65,136
c) 65,148
d) 65,112
Answer:
a) 65,124
8. The product of two numbers is 12,768. If one number is 64, what is the other number?
Hint: Divide the product by one of the numbers.
a) 199
b) 200
c) 201
d) 198
Answer:
a) 199
9. A factory produces 2,345 toys per day. How many toys will it produce in the month of January (31 days)?
Hint: Multiply daily production by the number of days in January.
a) 72,695
b) 72,685
c) 72,705
d) 72,675
Answer:
a) 72,695
10. If the difference between two numbers is 1,46,295 and the larger number is 8,50,000, what is the smaller number?
Hint: Subtract the difference from the larger number.
a) 7,03,705
b) 7,03,705
c) 7,03,705
d) 7,03,705
Answer:
a) 7,03,705
Additional Worksheet Questions for Exercise 1.2 Knowing our Numbers for Class 6
- A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050, and 2751. Find the total number of tickets sold on all the four days.
- Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?
- In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?
- Kirti bookstore sold books worth ₹ 2,85,891 in the first week of June and books worth ₹ 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?
- Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.
- A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
- A merchant had ₹ 78,592 with her. She placed an order for purchasing 40 radio sets at ₹ 1200 each. How much money will remain with her after the purchase?
- A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications?)
- To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint: convert data in cm.)
- Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
- The distance between the school and a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.
- A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Answers
- Total tickets sold: 7707
- Runs needed to reach 10,000: 3020
- Winning margin: 2,28,800 votes
- Total sale: ₹ 6,86,659; Second week’s sale was greater by ₹ 1,14,877.
- Difference: 75231 (97632 – 22401)
- Total screws in January: 87,175 (31 days * 2,825 screws)
- Remaining money: ₹ 30,592
- Excess amount: 47,140
- Shirts stitched: 17; Cloth remaining: 1 meter 35 centimeters
- Number of boxes: 177
- Total distance: 11.25 km
- Number of glasses: 180
