Class 6 Maths Chapter 1 Exercise 1.2
NCERT solutions for Class 6 Maths Chapter 1 Exercise 1.2 – Knowing your Numbers. Find detailed step-by-step solutions to all the questions in this exercise.
[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.
- To find the total number of tickets sold on all four days, we need to add number of tickets sold on each day.
- tickets sold on the first day = 1094
tickets sold on the second day = 1812
tickets sold on the third day = 2050
tickets sold on the final day = 2751 - Total number of tickets sold = 1094 + 1812 + 2050 + 2751 = 7707
- Therefore, the total number of tickets sold is 7707.
[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?
- To find how many more runs Shekhar needs to complete 10,000 runs in test matches, we need to subtract the runs he has already scored from the target of 10,000 runs.
- Runs Shekhar has scored so far = 6980
Target runs = 10,000 - runs needed = Target runs – Runs scored so far
= 10,000 – 6980
= 3020 - Therefore, Shekhar needs 3020 more runs to complete 10,000 runs in test matches.
[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?
- To calculate the election margin, subtract the nearest rival’s votes from the successful candidate’s votes.
- No. of votes secured by the successful candidate = 5,77,500
No. of votes secured by the nearest rival = 3,48,700 - Margin of victory = No. of votes of successful candidate – No. of votes of nearest rival
= 5,77,500 – 3,48,700
= 2,28,800 - Therefore, the successful candidate won by a margin of 2,28,800 votes.
[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?
- To get the total sales for both weeks, add the sales of the first and second week.
- Sales first week of June = ₹2,85,891
Sales second week of June = ₹4,00,768 - Total sales for the two weeks = Sales first week + Sales second week
= ₹2,85,891 + ₹4,00,768
= ₹6,86,659 - Therefore, the total sales for the two weeks together is ₹6,86,659.
- To know which week had greater sales and by how much, we can compare the sales figures of the first and second week.
- first week sales: ₹2,85,891
second week sales : ₹4,00,768 - The sales in the second week (₹4,00,768) are greater than the sales in the first week (₹2,85,891).
- The difference in sales = Sales in the second week – Sales in the first week
= ₹4,00,768 – ₹2,85,891
= ₹1,14,877 - Therefore, the sales in the second week were greater than the sales in the first week by ₹1,14,877.
[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.
- The greatest 5-digit number formed using these digits is 76432.
- The least 5-digit number formed using these digits is 23467.
- Now, find the difference between these two numbers:
- 76432 – 23467 = 52965
- Therefore, the difference between the greatest and the least 5-digit number is 52,965.
[6] A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
- To calculate the number of screws produced in January 2006, we multiply the average number of screws produced per day by the number of days in January.
- Average number of screws manufactured per day = 2,825
- Number of days in January 2006 = 31
- Total screws produced in January 2006 = Average screws per day × Number of days
- Total screws produced in January 2006 = 2,825 screws/day × 31 days
- Total screws produced in January 2006 = 87,775 screws
- Therefore, the machine produced 87,775 screws in the month of January 2006.
[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?
- To calculate how much money will remain after purchasing 40 radio sets :
- Number of radio sets purchased = 40
Cost of each radio set = ₹1200 - Total cost of the radio sets = Number of radio × Cost of each radio set
- Total cost of the radio sets = 40 × ₹1200 = ₹48,000
- Remaining amount of money = Initial amount of money – Total cost of the radio sets
- Remaining amount of money = ₹78,592 – ₹48,000
- Remaining amount of money = ₹30,592
- Therefore, the merchant will have ₹30,592 remaining after purchasing 40 radio sets.
[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?)
- To know the student’s incorrect answer compared to the correct answer, we only need to calculate the difference between the incorrect product and the correct product.
- Let’s calculate both products:
- Incorrect product: 7236 multiplied by 65
Correct product: 7236 multiplied by 56 - We will subtract the correct product from the incorrect product to find the difference:
- Incorrect product – Correct product
- (7236 × 65) – (7236 × 56)
- Calculating this:
- 472,140 – 405,216
- = 66,924
- Therefore, the student’s answer was greater than the correct answer by 66,924.
[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?
- To know the number of shirts that can be stitched and the remaining cloth, we need to divide the total cloth by the cloth of 1 shirt.
- Cloth required to stitch one shirt = 2 meters 15 centimeters
- Total cloth available = 40 meters
- Since the total cloth is given in meters, we convert 2 meters 15 centimeters to meters.
- 2 meters 15 centimeters = 2 meters + 0.15 meters (1 meter = 100 centimeters)
- 2 meters 15 centimeters = 2.15 meters
- Now, we can find the number of shirts that can be stitched and the remaining cloth:
- Number of shirts = Total cloth available / Cloth required to stitch one shirt
- Number of shirts = 40 meters / 2.15 meters
- Number of shirts ≈ 18.60 (rounded down to the nearest whole number)
- Therefore, 18 shirts can be stitched using the cloth.
- Remaining cloth = Total cloth available – (Cloth required to stitch one shirt × Number of shirts)
- Remaining cloth = 40 meters – (2.15 meters × 18)
- Remaining cloth ≈ 40 meters – 38.70 meters
- Remaining cloth ≈ 1.30 meters
- Thus, after stitching 18 shirts, approximately 1.30 meters of cloth will remain.
[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?
- To calculate the number of boxes ,we need to know how many boxes with a weight of 4 kg 500g can loaded in a van which is 800 kg.
- Since 1 kilogram = 1000 grams,
- Now we can calculate the weight of each box in kilograms:
- 4 kg + 0.5 kg = 4.5 kilograms
- To know the number of boxes that can fit within the van’s weight capacity, we divide the maximum weight capacity of the van by the weight of each box:
- 800 kg / 4.5 kg ≈ 177.78
- Therefore, the van can carry a maximum of 177 boxes.
[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.
- The distance between the school and the student’s house is 1 km 875 m. Since she walks both ways, we need to calculate the round trip distance.
- Round trip distance = 2 * Distance between school and house
- We know 1 km = 1,000 m
- Now we can calculate the total round trip distance:
- Round trip distance = 2 * (1 km + 875 m)
= 2 * (1,000 m + 875 m)
= 2 * 1,875 m
= 3,750 m - In six days, the total distance covered by her = Total distance in six days = 6 * Round trip distance
= 6 * 3,750 m - = 22,500 m
- Therefore, she covers a total distance of 22,500 meters in six days.
[12] A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
- To find out qty of glasses, we need to convert vessel capacity in milliliters and then divide it by glass capacity.
- convert the volume of curd to milliliters: (since 1 litre = 1,000 ml)
- 4 litres = 4,000 ml + 500 ml (given)
- Total volume of curd = 4,000 ml + 500 ml = = 4,500 ml
- Next, divide the total volume of curd by the capacity of glass:
- Number of glasses = Total volume of curd / Capacity of each glass
= 4,500 ml / 25 ml = 180 - Therefore, the vessel can be filled with 180 glasses, each with a capacity of 25 ml.
