NCERT Class 8 Maths · Chapter 5
NCERT Solutions Class 8 Maths Chapter 5 — Number Patterns & Puzzles
Step-by-step solutions for all exercises in NCERT Class 8 Maths Number Patterns & Puzzles.
Chapter Overview
Explore divisibility rules, number patterns, and mathematical puzzles.
This chapter is part of the NCERT Mathematics textbook for Class 8 and is important for CBSE school examinations. The concepts covered here build the foundation for more advanced topics in higher classes.
Below you will find solved examples from this chapter. Each solution includes detailed step-by-step working so you can understand the method, not just the answer.
Solved Examples from Number Patterns & Puzzles
1A two-digit number has 'a' in the tens place and 'b' in the units place. Which of the following expressions correctly represents the value of this number?
Answer: 10a + b
Solution:
Step 1: In a two-digit number, the digit in the tens place represents its value multiplied by 10.
Step 2: The digit in the units place represents its value multiplied by 1.
Step 3: So, if 'a' is in the tens place and 'b' is in the units place, the number is (a × 10) + (b × 1). [Number = 10a + b]
2A three-digit number has 'x' in the hundreds place, 'y' in the tens place, and 'z' in the units place. If the digits are reversed, what will be the new number in its generalized form?
Answer: 100z + 10y + x
Solution:
Step 1: The original number in generalized form is 100x + 10y + z.
Step 2: When the digits are reversed, 'z' moves to the hundreds place, 'y' remains in the tens place, and 'x' moves to the units place.
Step 3: Therefore, the new number will be (z × 100) + (y × 10) + (x × 1). [New number = 100z + 10y + x]
3The sum of a two-digit number and the number obtained by reversing its digits is 132. If the units digit is 4, what is the tens digit of the original number?
Answer: 8
Solution:
Step 1: Let the tens digit be 'a' and the units digit be 'b'. The original number is 10a + b.
Step 2: The number obtained by reversing its digits is 10b + a.
Step 3: Given that the units digit b = 4. So, the original number is 10a + 4, and the reversed number is 10(4) + a = 40 + a.
Step 4: The sum of the two numbers is (10a + 4) + (40 + a) = 11a + 44.
Step 5: We are given that the sum is 132. So, 11a + 44 = 132.
Step 6: Subtract 44 from both sides: 11a = 132 - 44 = 88.
Step 7: Divide by 11: a = 88 / 11 = 8. Thus, the tens digit of the original number is 8.
4In the addition problem below, A and B each represent a single digit. Find the value of B. A 8 + 2 B ----- 7 1
Answer: 3
Solution:
Step 1: From the units column, we have 8 + B. The result's units digit is 1. Since B is a single digit (0-9), 8 + B must be 11 (as 8+B cannot be 1 or 21).
Step 2: So, B = 11 - 8 = 3.
Step 3: This also means there is a carry-over of 1 to the tens column.
Step 4: From the tens column, we have A + 2 + (carry-over 1) = 7. So, A + 3 = 7. This implies A = 4.
Step 5: Thus, the value of B is 3.
5Which of the following numbers is divisible by 10?
Answer: 210
Solution:
Step 1: The divisibility rule for 10 states that a number is divisible by 10 if and only if its units digit is 0.
Step 2: Let's check the units digit of each option:
Step 3: A) 105 (units digit is 5) - Not divisible by 10.
Step 4: B) 210 (units digit is 0) - Divisible by 10.
Step 5: C) 345 (units digit is 5) - Not divisible by 10.
Step 6: D) 501 (units digit is 1) - Not divisible by 10.
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