In a division question, the divisor is 10 times the quotient and 5 times the…

Concept

In any division, the four quantities are related by the division algorithm: Dividend = (Divisor × Quotient) + Remainder. When a problem gives the divisor as separate multiples of the quotient and of the remainder, use the remainder-based multiple first (since the remainder is given directly) to find the divisor, then use the quotient-based multiple to find the quotient.

Application

1. Given: remainder = 46.

2. Divisor = 5 × remainder = 5 × 46 = 230 (since the divisor is 5 times the remainder).

3. Divisor = 10 × quotient, so quotient = Divisor ÷ 10 = 230 ÷ 10 = 23.

4. Apply the division algorithm: Dividend = (Divisor × Quotient) + Remainder = (230 × 23) + 46.

5. 230 × 23 = 5290.

6. Dividend = 5290 + 46 = 5336.

Cross-check

Dividing 5336 by 230 gives quotient 23 with remainder 46 (230 × 23 = 5290; 5336 − 5290 = 46), confirming divisor = 230 = 5 × 46 and quotient = 23 = 230 ÷ 10, consistent with the given conditions.