Question

The ratio of civil cases to criminal cases in a court is 4 : 7. If there are 420 civil cases, then the total number of cases in the court is

• A. 1455
• B. 1155
• C. 1255
• D. 1055

Hint:

Since the total ratio units are \(4 + 7 = 11\), the final answer must be a multiple of \(11\).
Testing the options, only \(1155\) is perfectly divisible by \(11\) (\(1155 \div 11 = 105\)).
This helps identify the correct option instantly without fully writing out the math.

Answer 1

The Correct Option is B

Step 1: Set up variables using the ratio.
Ratio of civil to criminal cases = 4:7. Let civil cases = 4x and criminal cases = 7x.
Step 2: Solve for x.
Civil cases = 420, so 4x = 420, giving x = 105.
Step 3: Calculate the total number of cases.
Criminal cases = 7 x 105 = 735. Total = 420 + 735 = 1155.
\[ \boxed{1155} \]