During the first year, the strength of a school increased by 12%, in the second year it decreased by 12% and in the third year it increased by 10%. At the end of the third year its strength was nearly 10842. What was the strength at the beginning of the first year?

Correct option is B

Let the initial strength be x.
After 1st year, strength
=> x ×(1 + 12/100) = x × 1.12
After 2nd year, strength
=> x × 1.12 × (1 - 12/100) = x × 1.12 × 0.88
After 3rd year, strength,
=> x × 1.12 × 0.88 × (1 + 10/100)
=> x × 1.12 × 0.88 × 1.10
We know that after the 3rd year, the strength is 10842.
=> x × 1.12 × 0.88 × 1.10 = 10842
=> x = 10842 / (1.12 × 0.88 × 1.10)
=> x = 10842 / 1.08384
=> x ≈ 10000
∴ The strength of the school at the beginning of the first year was nearly 10000.

Alternate Method: