Question

A monospaced font is a font in which all characters are exactly of same width. A document uses a monospaced font for typesetting where each character is exactly 0.6 cm wide. A text line in this document contains only 10 words, where each word contains 6 characters. What is the length of the line in cm?
 

Answer 1

Correct Answer: 41.4

The problem requires calculating the total length of a text line in a document that uses a monospaced font where each character is exactly \(0.6 \, \text{cm}\) wide. The line contains 10 words, each consisting of 6 characters. 

Step 1: Understanding the problem Each word consists of \(6\) characters. There are \(10\) words in the line. Each character occupies a width of \(0.6 \, \text{cm}\). A space is present between each pair of words. Since there are \(10\) words, there will be \(9\) spaces in total. Each space also occupies \(0.6 \, \text{cm}\), as the font is monospaced.

Step 2: Calculating the total length of the line The total width contributed by the characters in the 10 words: \[ \text{Width of characters} = 10 \, (\text{words}) \times 6 \, (\text{characters per word}) \times 0.6 \, \text{cm} = 36 \, \text{cm}. \] The total width contributed by the spaces between the words: \[ \text{Width of spaces} = 9 \, (\text{spaces}) \times 0.6 \, \text{cm} = 5.4 \, \text{cm}. \] The total length of the line is the sum of the two contributions: \[ \text{Total length} = 36 \, \text{cm} + 5.4 \, \text{cm} = 41.4 \, \text{cm}. \] 

Conclusion The length of the text line in the document is: \[ \boxed{41.4 \, \text{cm}}. \]

Answer 2

This line has ten words of six characters each, separated by single spaces. The goal is to find its total printed length. Instead of adding character width and space width separately, this method groups each word with the space right after it into one block. It handles the last word on its own, since nothing follows it.

Each of the first nine words, together with the space right after it, takes up \( 6 + 1 = 7 \) character widths. At \( 0.6 \) cm per character width, that block measures \( 7 \times 0.6 = 4.2 \) cm. There are nine such word and space blocks, since only the tenth word has no trailing space. That gives \( 9 \times 4.2 = 37.8 \) cm. The tenth word stands alone with no space after it, taking up just its own six characters, or \( 6 \times 0.6 = 3.6 \) cm.

Adding the nine word and space blocks to the final lone word gives \( 37.8 + 3.6 = 41.4 \) cm. the answer is \( 41.4 \) cm