Question

When a number is divided by 24. The quotient is 15 and the remainder is 7. Find the number.
A.456
B.164
C.367
D.763

Answer 1

Hint: Here, we will use the relationship between the Dividend, Divisor, Quotient and Remainder. We will substitute the given values in the formula and solve it further to get the required number.

Formula Used:
We will use the formula Dividend \[ = \] Divisor \[ \times \] Quotient \[ + \] Remainder.

Complete step-by-step answer:
According to the question,
Divisor \[ = 24\]
Quotient \[ = 15\]
Remainder \[ = 7\]
We have to find the Dividend.
Now, in division, the number which we divide is known as the Dividend.
The number by which we divide the dividend is called the divisor.
After dividing, the result obtained is called the Quotient.
And, the number which is left is called the Remainder.
Now, there is a relationship between the Dividend, Divisor, Quotient and the Remainder.
This relationship is called the division algorithm.
According to this algorithm, Dividend \[ = \] Divisor \[ \times \] Quotient \[ + \] Remainder
Here, substituting the given values, we get
Dividend \[ = 24 \times 15 + 7\]
Multiplying the terms, we get
\[ \Rightarrow \] Dividend \[ = 360 + 7 = 367\]
Therefore, when 367 is divided by 24, the quotient is 15 and the remainder is 7.
Hence, 367 is the required number.
Therefore, option C is the correct answer.

Note: This relationship between Dividend, Divisor, Quotient and Remainder is shown by the Euclid’s Division Lemma. According to Euclid’s division lemma, it states that for any integer \[a\] and any positive integer \[b\], there exists unique integers \[q\] and \[r\] such that \[a = bq + r\] ( where \[r\] is greater than or equal to 0 and less than \[b\] or \[0 \le r < b\]). We say that \[a\] is the dividend, \[b\] is the divisor, \[q\] is the quotient and \[r\] is the remainder.