This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey alishabayambumagar — ready when you are. Here are the solutions for the remaining questions: 12. b) Find the sum and difference between the place values of two sevens in the number 6784037525. Step 1: Identify the place value of the first '7' (from the left) in 6,784,037,525. The first '7' is in the hundred millions place. Place value of first 7 = 7 × 100,000,000 = 700,000,000. Step 2: Identify the place value of the second '7' in 6,784,037,525. The second '7' is in the thousands place. Place value of second 7 = 7 × 1,000 = 7,000. Step 3: Calculate the sum of these place values. 700,000,000 + 7,000 = 700,007,000 The sum is 700,007,000. Step 4: Calculate the difference between these place values. 700,000,000 - 7,000 = 699,993,000 The difference is 699,993,000. 12. c) Find the sum and difference between the place values of nine in the numbers 49560327 and 1024968. Step 1: Find the place value of '9' in the first number, 49,560,327. The '9' is in the millions place. Place value of '9' in 49,560,327 = 9 × 1,000,000 = 9,000,000. Step 2: Find the place value of '9' in the second number, 1,024,968. The '9' is in the hundreds place. Place value of '9' in 1,024,968 = 9 × 100 = 900. Step 3: Calculate the sum of these place values. 9,000,000 + 900 = 9,000,900 The sum is 9,000,900. Step 4: Calculate the difference between these place values. 9,000,000 - 900 = 8,999,100 The difference is 8,999,100. 13. a) In an examination of Mathematics, Himmat got 85 marks and Chhiring got the marks formed by reversing the digits of Himmat's marks. (i) Find the marks obtained by Chhiring. Step 1: Himmat's marks are 85. Step 2: Reverse the digits of 85. The reversed number is 58. Chhiring's marks are 58. (ii) Find the sum and difference of their marks. Step 1: Calculate the sum of their marks. 85 + 58 = 143 The sum of their marks is 143. Step 2: Calculate the difference of their marks. 85 - 58 = 27 The difference of their marks is 27. 13. b) In a shop, the cost of an umbrella is Rs 468 and the cost of a school-bag is fixed by interchanging the digits at hundreds and tens place of the cost of the umbrella. (i) What is the cost of the school-bag? Step 1: The cost of the umbrella is Rs 468. Step 2: Identify the digit at the hundreds place (4) and the digit at the tens place (6). Step 3: Interchange these digits. The new number will have 6 at the hundreds place, 4 at the tens place, and 8 at the ones place. The cost of the school-bag is Rs 648. (ii) How much money do you need to pay to buy both items? Step 1: Cost of umbrella = Rs 468. Step 2: Cost of school-bag = Rs 648. Step 3: Calculate the total cost. 468 + 648 = 1116 You need to pay Rs 1116 to buy both items. (iii) Which item is more expensive and by how much? Step 1: Compare the costs: Umbrella = Rs 468, School-bag = Rs 648. The school-bag is more expensive. Step 2: Calculate the difference in cost. 648 - 468 = 180 The school-bag is more expensive by Rs 180. What's next?