Question

In a division sum, the divisor \(d=457\), the quotient \(q=110\), and the remainder \(r=242\). Find the dividend.

• A. \(50512\)
• B. \(50270\)
• C. \(50272\)
• D. \(50702\)

Hint:

Always recall the division identity: \(N = dq + r\) with \(0 \le r < d\). Compute \(dq\) first, then add \(r\), and finally verify \(r<d\).

Answer 1

The Correct Option is A

Solution:
Step 1 (Use the division algorithm).
Dividend \(= \text{Divisor} \times \text{Quotient} + \text{Remainder}\). That is: \[ N = d \cdot q + r. \] Step 2 (Substitute the given values).
\[ N = 457 \times 110 + 242. \] Step 3 (Compute the product carefully).
\[ 457 \times 110 = 457 \times (100 + 10) = 45700 + 4570 = 50270. \] Step 4 (Add the remainder).
\[ N = 50270 + 242 = 50512. \] Step 5 (Verification).
Check the remainder is smaller than the divisor: \(242 < 457\) (vali(d). Also, \[ 50512 - 457 \times 110 = 50512 - 50270 = 242, \] so the quotient and remainder are consistent.
\[ {50512 \ \text{(Option (a)}} \]