Find the divisor, given that the dividend is 2200, remainder is 13, and the divisor is one-third of the quotient.

Given:

Dividend = 2200

Remainder = 13

Divisor = one-third of the Quotient

Formula used:

Dividend = Divisor × Quotient + Remainder

Divisor = Quotient ÷ 3

Calculation:

2200 = Divisor × Quotient + 13

⇒ 2200 - 13 = Divisor × Quotient

⇒ 2187 = Divisor × Quotient

Divisor = Quotient ÷ 3

⇒ 2187 = (Quotient ÷ 3) × Quotient

⇒ 2187 = Quotient² ÷ 3

⇒ Quotient² = 2187 × 3

⇒ Quotient² = 6561

⇒ Quotient = √6561

⇒ Quotient = 81

Divisor = Quotient ÷ 3

⇒ Divisor = 81 ÷ 3

⇒ Divisor = 27

∴ The correct answer is option (2).