A and B are two numbers. A is 1255 more than B. If A is divided by B, the…
2024
A and B are two numbers. A is 1255 more than B. If A is divided by B, the quotient is 2 and the remainder is 25. What is the value of B?
- A.
1230
- B.
1250
- C.
1280
- D.
2535
Attempted by 7 students.
Show answer & explanation
Correct answer: A
Concept: The division algorithm states that for any division with a divisor and remainder, Dividend = (Divisor × Quotient) + Remainder. When two numbers are linked both by a difference relation and by a division relation, express both relations as equations in the same two unknowns and solve the resulting system by substitution.
Let the two numbers be A and B.
"A is 1255 more than B" gives the first equation: A = B + 1255.
"A divided by B gives quotient 2 and remainder 25" gives, by the division algorithm, the second equation: A = 2B + 25.
Equate the two expressions for A: B + 1255 = 2B + 25.
Solve for B: 1255 − 25 = 2B − B, so B = 1230.
Cross-check: With B = 1230, A = B + 1255 = 2485. Dividing 2485 by 1230 gives 2 × 1230 = 2460, and 2485 − 2460 = 25 — exactly the stated quotient and remainder, confirming B = 1230.
Reference working:
