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Solve the following: \[85 \div .......... = 8500\]
A. 5
B. 1
C. 0.01
D. 0.001

Answer Verified Verified
Hint: Take the unknown value as a variable. Then divide the obtained value accordingly. So, use this concept to reach the solution of the problem.

Complete step-by-step answer:
Given \[85 \div .......... = 8500\]
Let the unknown value be \[x\], then it becomes as
\[
   \Rightarrow 85 \div x = 8500 \\
   \Rightarrow \dfrac{{85}}{x} = 8500 \\
\]
Multiplying both sides with \[x\], then we get
\[ \Rightarrow x \times \dfrac{{85}}{x} = x \times 8500\]
Cancelling the common terms, we have
\[
   \Rightarrow 85 = 8500x \\
   \Rightarrow 8500x = 85 \\
\]
Dividing both sides with 8500, we have
\[
   \Rightarrow 8500x \div 8500 = 85 \div 8500 \\
   \Rightarrow \dfrac{{8500x}}{{8500}} = \dfrac{{85}}{{8500}} \\
\]
Cancelling the common terms, we have
 \[ \Rightarrow x = \dfrac{{85}}{{8500}}\]
Since \[85 \times 100 = 8500\], we have
\[ \Rightarrow x = \dfrac{{85}}{{85 \times 100}}\]
Cancelling the common terms, we get
\[ \Rightarrow x = \dfrac{1}{{100}}\]
Converting \[\dfrac{1}{{100}}\] in to decimals, we have
\[
   \Rightarrow x = \dfrac{1}{{100}} = 0.01 \\
  \therefore x = 0.01 \\
\]
So, the unknown value is 0.01.
Thus, the correct option is C. 0.01.

Note: Since the given options are in decimals, we need to convert the obtained answer which is in fraction into decimals. We can recheck the answer by substituting the answer in the given problem.
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