Two numbers differ by 40, when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 - x). State whether the statement is true or false.
Solution:
Given, two numbers differ by 40.
Each number is increased by 8, the bigger becomes thrice the lesser number.
If one number is x, then the other number is (40 - x).
We have to determine if the given statement is true or false.
Let one number be x
Other number = 40 - x
Let us consider x as a smaller number and 40 - x as a bigger number.
Increasing each number by 8,
Smaller number = x + 8
Bigger number = 40 - x + 8
= 48 - x
According to the question,
48 - x = 3(x + 8)
48 - x = 3x + 24
By grouping of common terms,
3x + x = 48 - 24
4x = 24
x = 24/4
x = 6
Now, 40 - x = 40 - 6 = 34
Difference between two numbers = 34 - 6 = 28
Therefore, the difference is not 40.
✦ Try This: Two numbers differ by 20, when each number is increased by 5, the bigger becomes twice the lesser number. If one number is x, then the other number is (20 - x). State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 2
NCERT Exemplar Class 8 Maths Chapter 4 Problem 48
Two numbers differ by 40, when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 - x). State whether the statement is true or false.
Summary:
The given statement, ”Two numbers differ by 40, when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 - x)” is false.
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