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A number is increased first by 20% and then it is again increased by 15%. What is the percentage change in the number?
- a)31% increase
- b)38% increase
- c)50% increase
- d)35% increase
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A number is increased first by 20% and then it is again increased by 1...
Let, the number = x
After 20% increase, number = x + x × 20/100 = 1.2x
After 15% increase, number = 1.2x + 1.2x × 15/100 = 1.38x
∴ Increase = 1.38x - x = 0.38x
∴ Percentage increase,
⇒ 0.38x/x × 100%
⇒ 38%
Most Upvoted Answer
A number is increased first by 20% and then it is again increased by 1...
Understanding the Problem
To find the overall percentage change when a number is increased first by 20% and then by 15%, we will use the following approach:
Step 1: Initial Value
- Let's assume the original number is \( x \).
Step 2: First Increase by 20%
- After a 20% increase, the new value becomes:
\[
x + 0.20x = 1.20x
\]
Step 3: Second Increase by 15%
- Now, we increase the new value \( 1.20x \) by 15%:
\[
1.20x + 0.15(1.20x) = 1.20x + 0.18x = 1.38x
\]
Step 4: Calculate Overall Change
- The final value is \( 1.38x \).
- The change from the original value \( x \) to \( 1.38x \) is:
\[
1.38x - x = 0.38x
\]
Step 5: Calculate Percentage Change
- The percentage change is given by:
\[
\left(\frac{0.38x}{x}\right) \times 100 = 38\%
\]
Conclusion
Thus, the overall percentage increase after applying both increases is **38%**. Hence, the correct answer is option 'B'.
To find the overall percentage change when a number is increased first by 20% and then by 15%, we will use the following approach:
Step 1: Initial Value
- Let's assume the original number is \( x \).
Step 2: First Increase by 20%
- After a 20% increase, the new value becomes:
\[
x + 0.20x = 1.20x
\]
Step 3: Second Increase by 15%
- Now, we increase the new value \( 1.20x \) by 15%:
\[
1.20x + 0.15(1.20x) = 1.20x + 0.18x = 1.38x
\]
Step 4: Calculate Overall Change
- The final value is \( 1.38x \).
- The change from the original value \( x \) to \( 1.38x \) is:
\[
1.38x - x = 0.38x
\]
Step 5: Calculate Percentage Change
- The percentage change is given by:
\[
\left(\frac{0.38x}{x}\right) \times 100 = 38\%
\]
Conclusion
Thus, the overall percentage increase after applying both increases is **38%**. Hence, the correct answer is option 'B'.
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A number is increased first by 20% and then it is again increased by 15%. What is the percentage change in the number?a)31% increaseb)38% increasec)50% increased)35% increaseCorrect answer is option 'B'. Can you explain this answer?
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