In a school number of students increases in each year by 10%. If in the first…

Concept: In successive percentage change, when a quantity grows by the same rate r% at the end of every period, each period's increase is calculated on that period's already-grown total, not on the original amount again. After n periods the amount equals the original amount multiplied by (1 + r/100), applied once per period.

Application:

1. Year 1 count = 500 (given).

2. Apply the first year's 10% increase to get Year 2: 500 × 1.10 = 550.

3. Apply the second year's 10% increase to Year 2's total to get Year 3: 550 × 1.10 = 605.

Cross-check: Two successive 10% increases multiply the original amount by 1.10 × 1.10 = 1.21, so 500 × 1.21 = 605 — matching the step-by-step result. (Simply adding 10% + 10% = 20% of the original 500 directly would ignore that the second increase applies to the grown total, giving the wrong figure of 600.)

So the number of students in the third year is 605.