In a division problem, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend?

Given data

• Divisor d = 10 × quotient q
• Divisor d = 5 × remainder r
• Remainder r = 46

Concept / Approach

• From d = 5r, find d. Then from d = 10q, find q. Finally use Dividend = dq + r.

Step-by-step calculation
d = 5r = 5 × 46 = 230d = 10q ⇒ q = d / 10 = 230 / 10 = 23Dividend = dq + r = 230 × 23 + 46 = 5290 + 46 = 5336

Validity check
Remainder r = 46 < d = 230, which is valid.

Final Answer
5336