Question

In division algorithm a=bq+r, b=4, q=5 and r=1, then what is the value of a?

• A. 20
• B. 21
• C. 25
• D. 31

Hint:

Always remember the components of the division algorithm: Dividend = (Divisor \(\times\) Quotient) + Remainder. This is a fundamental concept in number theory.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question is based on Euclid's Division Algorithm. The algorithm states that for any two positive integers 'a' (dividend) and 'b' (divisor), there exist unique integers 'q' (quotient) and 'r' (remainder) such that a = bq + r, where 0 \(\le\) r \(<\) b.

Step 2: Key Formula or Approach:
The formula to use is the division algorithm itself:
\[ a = bq + r \]

Step 3: Detailed Explanation:
We are given the values:
Divisor, \(b = 4\)
Quotient, \(q = 5\)
Remainder, \(r = 1\)
We need to find the dividend, 'a'.
Substitute the given values into the formula:
\[ a = (4 \times 5) + 1 \] \[ a = 20 + 1 \] \[ a = 21 \]

Step 4: Final Answer:
The value of 'a' is 21. This corresponds to option (B).