The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?
Show Hint
- 70
- 65
- 40
- 90
The Correct Option is C
Solution and Explanation
Let the original number be x.
Step 2: Express both transformed values.
The number increased by 25% becomes x + 0.25x = 1.25x.
The original number decreased by 30% becomes x - 0.30x = 0.70x.
Step 3: Form the equation from the given difference.
The difference between these two values is 22, so 1.25x - 0.70x = 22.
Step 4: Simplify and solve for x.
1.25x - 0.70x = 0.55x. So 0.55x = 22, which gives x = 22 / 0.55 = 40.
Step 5: Verify and match with the options.
Check: 1.25 x 40 = 50, and 0.70 x 40 = 28. The difference is 50 - 28 = 22, which matches the given condition. So the original number is 40, which is option (3). Options (1), (2) and (4) do not satisfy the equation 0.55x = 22.
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