Question

Find the dividend when a number is divided by 45 and the quotient is 21 and remainder is 14.
A.234
B.789
C.959
D.1623

Answer 1

Hint: Here we will use the remainder theorem which states that the dividend is equal to the sum of the product of divisor and quotient and the remainder. So we will use this formula and we will substitute the value of divisor, remainder and the quotient in the formula. We will simplify it further to get the value of dividend.

Formula used:
 \[{\rm{Dividend}} = \left( {{\rm{divisor}} \times {\rm{quotient}}} \right) + {\rm{remainder}}\]

Complete step-by-step answer:
Here we need to find the value of dividend where the value of the remainder, quotient and the divisor is given.
It is given that the value of divisor is equal to 45, the quotient is equal to 21 and the remainder is equal to 14.
We will use the remainder theorem here.
\[ \Rightarrow {\rm{Dividend}} = \left( {{\rm{divisor}} \times {\rm{quotient}}} \right) + {\rm{remainder}}\]
Now, we will substitute the value of the remainder, quotient and the divisor in the above equation.
\[ \Rightarrow {\rm{Dividend}} = \left( {45 \times 21} \right) + 14\]
On multiplying the terms, we get
\[ \Rightarrow {\rm{Dividend}} = 945 + 14\]
On adding the numbers, we get
\[ \Rightarrow {\rm{Dividend}} = 959\]
Hence, the correct option is option C.

Note: Here, we have used the remainder theorem to find the answer. The remainder theorem states that the dividend is equal to the sum of the product of divisor and quotient and the remainder. In division operation, the number which is divided is called the dividend, and the number which divides it is called the divisor. When a number is completely divisible by another number, then the remainder is 0.