The strength of a Day Boarding School increases and decreases every alternate year. It starts with increase by 10% and thereafter the perce…

Let the initial strength be x in 1997

∴ the strength after 10% increase in 1998 = x + 10x/100 = 11x/10

In 1999, there will be again decrease by 10%

∴ strength in 1999 = 11x/10 – 10% of 11x/10 = 99x/100

Then the strength increase by 10% in 2000

∴ strength in 2000 = 99x/100 + 10% of 99x/100 = 1089x/1000

Finally, in 2001, the strength again decreases by 10%

∴ strength in 2001 = 1089x/1000 – (10(1089x/1000)/100) = 9801x/10000

Comparing the strength of 2001 with that in 1997, it is clear that the strength is decreased

Decrease in strength = x – (9801x/10000) = 199x/10000

Percentage decrease = ((199x/10000)/x) × 100 = 1.99% decrease which is approximately equal to 2% decrease.

Let the initial strength be x in 1997

∴ the strength after 10% increase in 1998 = x + 10x/100 = 11x/10

In 1999, there will be again decrease by 10%

∴ strength in 1999 = 11x/10 – 10% of 11x/10 = 99x/100

Then the strength increase by 10% in 2000

∴ strength in 2000 = 99x/100 + 10% of 99x/100 = 1089x/1000

Finally, in 2001, the strength again decreases by 10%

∴ strength in 2001 = 1089x/1000 – (10(1089x/1000)/100) = 9801x/10000

Comparing the strength of 2001 with that in 1997, it is clear that the strength is decreased

Decrease in strength = x – (9801x/10000) = 199x/10000

Percentage decrease = ((199x/10000)/x) × 100 = 1.99% decrease which is approximately equal to 2% decrease.