The strength of a school increases and decreases every alternate year by 15\% . If it started with an increase in 2012, then the strength of the schoo - Quantitative Aptitude MCQ Prepp 2026 | ExamTest.live

Solution & Step-by-step Explanation

Let the initial strength of the school at the beginning of 2012 be

100

.
The change occurs every alternate year starting with an increase:

1. From beginning of 2012 to beginning of 2013 (Year 1): Increases by

15%

Strength at beginning of 2013 = 100 \times (1 + \frac{15}{100}) = 100 \times 1.15 = 115

2. From beginning of 2013 to beginning of 2014 (Year 2): Decreases by

15%

Strength at beginning of 2014 = 115 \times (1 - \frac{15}{100}) = 115 \times 0.85 = 97.75

3. From beginning of 2014 to beginning of 2015 (Year 3): Increases by

15%

Strength at beginning of 2015 = 97.75 \times (1 + \frac{15}{100}) = 97.75 \times 1.15 = 112.4125

Now, compare the final strength in 2015 with the initial strength in 2012:

Net Percentage Change = \frac{112.4125 - 100}{100} \times 100% = 12.4125%

Rounding off to two decimal places, we get an increase of

12.41%

The strength of a school increases and decreases every alternate year by $15%$ . If it started with an increase in 2012, then the strength of the school in the beginning of 2015, as compared to that in 2012, had (correct to two decimal places):