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CHAPTER 1 — LARGE NUMBERS AROUND US
Class VII Mathematics — Practice Paper Set 2
Preeti Kushwah Classes
General Instructions:
1. All questions are compulsory.
2. Section A: 6 questions of 1 mark each.
3. Section B: 5 questions of 2 marks each.
4. Section C: 4 questions of 3 marks each.
5. Section D: 2 questions of 4 marks each. (6+10+12+8 = 36 marks + 4 bonus = 40)
6. Show all working clearly.
1. All questions are compulsory.
2. Section A: 6 questions of 1 mark each.
3. Section B: 5 questions of 2 marks each.
4. Section C: 4 questions of 3 marks each.
5. Section D: 2 questions of 4 marks each. (6+10+12+8 = 36 marks + 4 bonus = 40)
6. Show all working clearly.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
Write the number name for 8,04,06,503 in the Indian system.
Q2.1
How many millions are equal to 3 crores?
Q3.1
What is the place value of 6 in 9,56,23,018?
Q4.1
The difference between the place values of two 5s in 5,03,50,427 is ___.
Q5.1
Round 7,84,96,310 to the nearest ten lakh.
Q6.1
The product of a 4-digit number and a 3-digit number has at most ___ digits and at least ___ digits.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Arrange in ascending order:
45,67,893 ; 4,56,78,930 ; 4,56,789 ; 45,67,89,300
45,67,893 ; 4,56,78,930 ; 4,56,789 ; 45,67,89,300
Q8.2
Write the numeral for each:
(a) Six crore forty lakh three thousand seventy-five
(b) Nine hundred eight million fifty-two thousand four hundred
(a) Six crore forty lakh three thousand seventy-five
(b) Nine hundred eight million fifty-two thousand four hundred
Q9.2
A calculator has buttons: +1, +10, +100, +1000, +10000. What is the minimum number of button clicks to reach 3,56,789?
Q10.2
Calculate using a shortcut (show the trick):
(a) 372 × 50 (b) 456 × 125
(a) 372 × 50 (b) 456 × 125
Q11.2
The population of a town increased from 23,45,678 in 2011 to 31,20,450 in 2021. Find the increase in population and express it in words (Indian system).
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Using the digits 2, 0, 4, 7, 9, 1 (each used exactly once):
(a) Write the largest 6-digit number.
(b) Write the smallest 6-digit number.
(c) Find the difference and express it in words (Indian system).
(a) Write the largest 6-digit number.
(b) Write the smallest 6-digit number.
(c) Find the difference and express it in words (Indian system).
Q13.3
A milk dairy supplies 25,750 litres of milk daily to a city.
(a) How many litres are supplied in a month of 30 days?
(b) If the price of 1 litre is ₹54, find the total revenue in a month.
(c) Express the monthly revenue in International system (in words).
(a) How many litres are supplied in a month of 30 days?
(b) If the price of 1 litre is ₹54, find the total revenue in a month.
(c) Express the monthly revenue in International system (in words).
Q14.3
A number when rounded to the nearest thousand becomes 47,000 and when rounded to the nearest hundred becomes 46,800. Find all possible values the number can take. How many such numbers are there?
Q15.3
Study the data and answer:
(a) How many times is India’s area approximately compared to Sri Lanka’s? (Round suitably)
(b) Find the total area of all four countries. Express in International system words.
(c) Round India’s area to the nearest lakh.
| Country | Area (sq km) |
|---|---|
| India | 32,87,263 |
| Pakistan | 8,81,913 |
| Bangladesh | 1,47,570 |
| Sri Lanka | 65,610 |
(b) Find the total area of all four countries. Express in International system words.
(c) Round India’s area to the nearest lakh.
Section D — (4 Marks Each) [2 × 4 = 8]
Q16.4
A car manufacturing company produces 450 cars per day. The company works 25 days a month and 12 months a year.
(a) Find the total number of cars produced in a year.
(b) If the cost of one car is ₹8,75,000, what is the total value of cars produced in a year? Express in crores.
(c) The company plans to increase production by 15% next year. How many extra cars will be produced daily?
(d) Will the total production next year cross 2 lakh cars? Justify.
(a) Find the total number of cars produced in a year.
(b) If the cost of one car is ₹8,75,000, what is the total value of cars produced in a year? Express in crores.
(c) The company plans to increase production by 15% next year. How many extra cars will be produced daily?
(d) Will the total production next year cross 2 lakh cars? Justify.
Q17.4
The Indian Railways carries approximately 2,30,00,000 passengers daily.
(a) How many passengers are carried in a year (365 days)? Express in crores.
(b) If the average ticket cost is ₹125, find the daily revenue.
(c) In the International system, express the daily revenue in millions.
(d) If the railways wants to carry 1,000 crore passengers in a year, by what percentage must daily passengers increase?
(a) How many passengers are carried in a year (365 days)? Express in crores.
(b) If the average ticket cost is ₹125, find the daily revenue.
(c) In the International system, express the daily revenue in millions.
(d) If the railways wants to carry 1,000 crore passengers in a year, by what percentage must daily passengers increase?
Bonus Question (Optional) [4 Marks]
Q18.4
★ A 7-digit number has the following properties:
• The digit in the lakhs place is 3 more than the digit in the ones place.
• The digit in the ten-thousands place is twice the digit in the hundreds place.
• The sum of all digits is 30.
• The digits in the thousands and tens place are both 4.
• The digit in the ten-lakhs place is 7.
• The digit in the hundreds place is 2.
Find the number and write it in words (Indian system).
• The digit in the lakhs place is 3 more than the digit in the ones place.
• The digit in the ten-thousands place is twice the digit in the hundreds place.
• The sum of all digits is 30.
• The digits in the thousands and tens place are both 4.
• The digit in the ten-lakhs place is 7.
• The digit in the hundreds place is 2.
Find the number and write it in words (Indian system).
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Answer Key & Detailed Solutions
Q1. [1 Mark]
8,04,06,503
= Eight crore four lakh six thousand five hundred three
= Eight crore four lakh six thousand five hundred three
Q2. [1 Mark]
1 crore = 1,00,00,000
3 crores = 3,00,00,000
1 million = 10,00,000
3,00,00,000 ÷ 10,00,000 = 30 million
3 crores = 3,00,00,000
1 million = 10,00,000
3,00,00,000 ÷ 10,00,000 = 30 million
Q3. [1 Mark]
In 9,56,23,018 the digit 6 is in the ten-lakhs place.
Wait — let’s identify carefully:
9 | 56 | 23 | 018
9 = crores, 5 = ten-lakhs, 6 = lakhs, 2 = ten-thousands, 3 = thousands, 0 = hundreds, 1 = tens, 8 = ones
The 6 is in the lakhs place.
Place value of 6 = 6,00,000 (Six lakh)
Wait — let’s identify carefully:
9 | 56 | 23 | 018
9 = crores, 5 = ten-lakhs, 6 = lakhs, 2 = ten-thousands, 3 = thousands, 0 = hundreds, 1 = tens, 8 = ones
The 6 is in the lakhs place.
Place value of 6 = 6,00,000 (Six lakh)
Q4. [1 Mark]
5,03,50,427
First 5 (leftmost): crores place → place value = 5,00,00,000
Second 5: ten-thousands place → place value = 50,000
Difference = 5,00,00,000 − 50,000 = 4,99,50,000
= Four crore ninety-nine lakh fifty thousand
First 5 (leftmost): crores place → place value = 5,00,00,000
Second 5: ten-thousands place → place value = 50,000
Difference = 5,00,00,000 − 50,000 = 4,99,50,000
= Four crore ninety-nine lakh fifty thousand
Q5. [1 Mark]
7,84,96,310
Ten-lakh digit: 4. Look at the next digit (lakh): 9.
Wait — to round to nearest ten lakh: 7,84,96,310. The ten-lakhs digit is 8. The lakhs digit is 4.
Since 4 < 5, round down.
Answer: 7,80,00,000
Ten-lakh digit: 4. Look at the next digit (lakh): 9.
Wait — to round to nearest ten lakh: 7,84,96,310. The ten-lakhs digit is 8. The lakhs digit is 4.
Since 4 < 5, round down.
Answer: 7,80,00,000
Q6. [1 Mark]
m = 4, n = 3
At most m + n = 4 + 3 = 7 digits
At least m + n − 1 = 4 + 3 − 1 = 6 digits
Verification: 1000 × 100 = 1,00,000 (6 digits) ✅; 9999 × 999 = 99,89,001 (7 digits) ✅
At most m + n = 4 + 3 = 7 digits
At least m + n − 1 = 4 + 3 − 1 = 6 digits
Verification: 1000 × 100 = 1,00,000 (6 digits) ✅; 9999 × 999 = 99,89,001 (7 digits) ✅
Q7. [2 Marks]
Let’s count the digits:
4,56,789 → 6 digits [1 mark for correct identification]
45,67,893 → 7 digits
4,56,78,930 → 8 digits
45,67,89,300 → 9 digits
Ascending order:
4,56,789 < 45,67,893 < 4,56,78,930 < 45,67,89,300 [1 mark]
4,56,789 → 6 digits [1 mark for correct identification]
45,67,893 → 7 digits
4,56,78,930 → 8 digits
45,67,89,300 → 9 digits
Ascending order:
4,56,789 < 45,67,893 < 4,56,78,930 < 45,67,89,300 [1 mark]
Q8. [2 Marks]
(a) Six crore forty lakh three thousand seventy-five [1 mark]
= 6,00,00,000 + 40,00,000 + 3,000 + 75
= 6,40,03,075
(b) Nine hundred eight million fifty-two thousand four hundred [1 mark]
= 908,000,000 + 52,000 + 400
= 908,052,400
In Indian system: 90,80,52,400
= 6,00,00,000 + 40,00,000 + 3,000 + 75
= 6,40,03,075
(b) Nine hundred eight million fifty-two thousand four hundred [1 mark]
= 908,000,000 + 52,000 + 400
= 908,052,400
In Indian system: 90,80,52,400
Q9. [2 Marks]
3,56,789 = 3 × 1,00,000 + 5 × 10,000 + 6 × 1,000 + 7 × 100 + 8 × 10 + 9 × 1
But we only have +10000 as maximum. So:
+10000 pressed: 35 times (to get 3,50,000) [1 mark]
+1000 pressed: 6 times (to add 6,000)
+100 pressed: 7 times (to add 700)
+10 pressed: 8 times (to add 80)
+1 pressed: 9 times (to add 9)
Total = 35 + 6 + 7 + 8 + 9 = 65 clicks [1 mark]
But we only have +10000 as maximum. So:
+10000 pressed: 35 times (to get 3,50,000) [1 mark]
+1000 pressed: 6 times (to add 6,000)
+100 pressed: 7 times (to add 700)
+10 pressed: 8 times (to add 80)
+1 pressed: 9 times (to add 9)
Total = 35 + 6 + 7 + 8 + 9 = 65 clicks [1 mark]
Q10. [2 Marks]
(a) 372 × 50 [1 mark]
Trick: 50 = 100 ÷ 2
372 × 100 = 37,200
37,200 ÷ 2 = 18,600
(b) 456 × 125 [1 mark]
Trick: 125 = 1000 ÷ 8
456 × 1000 = 4,56,000
4,56,000 ÷ 8 = 57,000
Trick: 50 = 100 ÷ 2
372 × 100 = 37,200
37,200 ÷ 2 = 18,600
(b) 456 × 125 [1 mark]
Trick: 125 = 1000 ÷ 8
456 × 1000 = 4,56,000
4,56,000 ÷ 8 = 57,000
Q11. [2 Marks]
Increase = 31,20,450 − 23,45,678 [1 mark]
= 7,74,772
In words: Seven lakh seventy-four thousand seven hundred seventy-two [1 mark]
= 7,74,772
In words: Seven lakh seventy-four thousand seven hundred seventy-two [1 mark]
Q12. [3 Marks]
Digits: 0, 1, 2, 4, 7, 9
(a) Largest 6-digit number: [1 mark]
Arrange in descending order: 9,74,210
(b) Smallest 6-digit number: [1 mark]
First digit cannot be 0. Use 1 (smallest non-zero).
Remaining in ascending: 0, 2, 4, 7, 9
Answer: 1,02,479
(c) Difference: [1 mark]
9,74,210 − 1,02,479 = 8,71,731
= Eight lakh seventy-one thousand seven hundred thirty-one
(a) Largest 6-digit number: [1 mark]
Arrange in descending order: 9,74,210
(b) Smallest 6-digit number: [1 mark]
First digit cannot be 0. Use 1 (smallest non-zero).
Remaining in ascending: 0, 2, 4, 7, 9
Answer: 1,02,479
(c) Difference: [1 mark]
9,74,210 − 1,02,479 = 8,71,731
= Eight lakh seventy-one thousand seven hundred thirty-one
Q13. [3 Marks]
(a) Monthly supply: [1 mark]
25,750 × 30 = 7,72,500 litres
(b) Monthly revenue: [1 mark]
7,72,500 × 54
= 7,72,500 × 50 + 7,72,500 × 4
= 3,86,25,000 + 30,90,000
= ₹4,17,15,000
(c) In International system: [1 mark]
4,17,15,000 = 41,715,000
= Forty-one million seven hundred fifteen thousand
25,750 × 30 = 7,72,500 litres
(b) Monthly revenue: [1 mark]
7,72,500 × 54
= 7,72,500 × 50 + 7,72,500 × 4
= 3,86,25,000 + 30,90,000
= ₹4,17,15,000
(c) In International system: [1 mark]
4,17,15,000 = 41,715,000
= Forty-one million seven hundred fifteen thousand
Q14. [3 Marks]
Condition 1: Rounded to nearest thousand = 47,000 [1 mark]
This means: 46,500 ≤ N ≤ 47,499
Condition 2: Rounded to nearest hundred = 46,800 [1 mark]
This means: 46,750 ≤ N ≤ 46,849
Intersection: [1 mark]
max(46,500, 46,750) ≤ N ≤ min(47,499, 46,849)
46,750 ≤ N ≤ 46,849
Count = 46,849 − 46,750 + 1 = 100 numbers
This means: 46,500 ≤ N ≤ 47,499
Condition 2: Rounded to nearest hundred = 46,800 [1 mark]
This means: 46,750 ≤ N ≤ 46,849
Intersection: [1 mark]
max(46,500, 46,750) ≤ N ≤ min(47,499, 46,849)
46,750 ≤ N ≤ 46,849
Count = 46,849 − 46,750 + 1 = 100 numbers
Q15. [3 Marks]
(a) India ÷ Sri Lanka: [1 mark]
32,87,263 ÷ 65,610 ≈ 33,00,000 ÷ 66,000 = 50
India’s area is approximately 50 times Sri Lanka’s area.
(b) Total area: [1 mark]
32,87,263 + 8,81,913 + 1,47,570 + 65,610 = 43,82,356 sq km
In International: 4,382,356
= Four million three hundred eighty-two thousand three hundred fifty-six sq km
(c) India rounded to nearest lakh: [1 mark]
32,87,263 → ten-thousands digit is 8 (≥ 5), round up.
Answer: 33,00,000 (Thirty-three lakh)
32,87,263 ÷ 65,610 ≈ 33,00,000 ÷ 66,000 = 50
India’s area is approximately 50 times Sri Lanka’s area.
(b) Total area: [1 mark]
32,87,263 + 8,81,913 + 1,47,570 + 65,610 = 43,82,356 sq km
In International: 4,382,356
= Four million three hundred eighty-two thousand three hundred fifty-six sq km
(c) India rounded to nearest lakh: [1 mark]
32,87,263 → ten-thousands digit is 8 (≥ 5), round up.
Answer: 33,00,000 (Thirty-three lakh)
Q16. [4 Marks]
(a) Cars per year: [1 mark]
450 × 25 × 12 = 450 × 300 = 1,35,000 cars
(b) Total value: [1 mark]
1,35,000 × 8,75,000
= 1,35,000 × 8,75,000
= 1,181,25,00,000 → Wait, let me compute carefully:
135 × 875 = 1,18,125
So 1,35,000 × 8,75,000 = 1,18,125 × 105 × 103 ÷ 103
= 1,35,000 × 8,75,000 = 11,81,25,00,000
= ₹1,181.25 crore (approximately ₹1,181 crore)
(c) 15% increase: [1 mark]
Extra daily = 450 × 15/100 = 67.5 ≈ 68 extra cars/day
(d) Will it cross 2 lakh? [1 mark]
New daily = 450 + 68 = 518 cars
New yearly = 518 × 300 = 1,55,400
1,55,400 < 2,00,000 → No, it will NOT cross 2 lakh cars.
450 × 25 × 12 = 450 × 300 = 1,35,000 cars
(b) Total value: [1 mark]
1,35,000 × 8,75,000
= 1,35,000 × 8,75,000
= 1,181,25,00,000 → Wait, let me compute carefully:
135 × 875 = 1,18,125
So 1,35,000 × 8,75,000 = 1,18,125 × 105 × 103 ÷ 103
= 1,35,000 × 8,75,000 = 11,81,25,00,000
= ₹1,181.25 crore (approximately ₹1,181 crore)
(c) 15% increase: [1 mark]
Extra daily = 450 × 15/100 = 67.5 ≈ 68 extra cars/day
(d) Will it cross 2 lakh? [1 mark]
New daily = 450 + 68 = 518 cars
New yearly = 518 × 300 = 1,55,400
1,55,400 < 2,00,000 → No, it will NOT cross 2 lakh cars.
Q17. [4 Marks]
(a) Passengers per year: [1 mark]
2,30,00,000 × 365 = 83,95,00,00,000 ≈ 839.5 crore
≈ 840 crore passengers per year
(b) Daily revenue: [1 mark]
2,30,00,000 × 125 = 287,50,00,000
= ₹287.5 crore per day
(= ₹2,87,50,00,000)
(c) In International system: [1 mark]
2,87,50,00,000 = 2,875,000,000
= Two billion eight hundred seventy-five million
(d) Percentage increase: [1 mark]
Target: 1,000 crore = 10,00,00,00,000 per year
Required daily = 10,00,00,00,000 ÷ 365 ≈ 2,73,97,260 per day
Current daily = 2,30,00,000
Increase needed = 2,73,97,260 − 2,30,00,000 = 43,97,260
Percentage = (43,97,260 / 2,30,00,000) × 100 ≈ 19.1% increase
2,30,00,000 × 365 = 83,95,00,00,000 ≈ 839.5 crore
≈ 840 crore passengers per year
(b) Daily revenue: [1 mark]
2,30,00,000 × 125 = 287,50,00,000
= ₹287.5 crore per day
(= ₹2,87,50,00,000)
(c) In International system: [1 mark]
2,87,50,00,000 = 2,875,000,000
= Two billion eight hundred seventy-five million
(d) Percentage increase: [1 mark]
Target: 1,000 crore = 10,00,00,00,000 per year
Required daily = 10,00,00,00,000 ÷ 365 ≈ 2,73,97,260 per day
Current daily = 2,30,00,000
Increase needed = 2,73,97,260 − 2,30,00,000 = 43,97,260
Percentage = (43,97,260 / 2,30,00,000) × 100 ≈ 19.1% increase
Q18. Bonus [4 Marks]
Let the 7-digit number be: _ _ _ _ _ _ _
Positions: TL L TTh Th H T O (Ten-Lakhs, Lakhs, Ten-Thousands, Thousands, Hundreds, Tens, Ones)
Given: [1 mark each clue]
• Ten-lakhs = 7
• Thousands = 4, Tens = 4
• Hundreds = 2
• Ten-thousands = 2 × Hundreds = 2 × 2 = 4
• Lakhs = Ones + 3
• Sum of all digits = 30
Known digits: 7, L, 4, 4, 2, 4, O
Sum: 7 + L + 4 + 4 + 2 + 4 + O = 30
21 + L + O = 30
L + O = 9
Also, L = O + 3
So: (O + 3) + O = 9 → 2O = 6 → O = 3
L = 3 + 3 = 6
The number is: 76,44,243
= Seventy-six lakh forty-four thousand two hundred forty-three
Positions: TL L TTh Th H T O (Ten-Lakhs, Lakhs, Ten-Thousands, Thousands, Hundreds, Tens, Ones)
Given: [1 mark each clue]
• Ten-lakhs = 7
• Thousands = 4, Tens = 4
• Hundreds = 2
• Ten-thousands = 2 × Hundreds = 2 × 2 = 4
• Lakhs = Ones + 3
• Sum of all digits = 30
Known digits: 7, L, 4, 4, 2, 4, O
Sum: 7 + L + 4 + 4 + 2 + 4 + O = 30
21 + L + O = 30
L + O = 9
Also, L = O + 3
So: (O + 3) + O = 9 → 2O = 6 → O = 3
L = 3 + 3 = 6
The number is: 76,44,243
= Seventy-six lakh forty-four thousand two hundred forty-three