A tailor cuts shirt pieces from rolls of fabric. Each roll is cut into 10 equal pieces, and he makes cuts at the rate of 45 cuts per minute. How many rolls can he completely cut in 24 minutes?

Introduction / Context:
This arithmetic reasoning question deals with rates of work and careful interpretation of what a “cut” means in the context of cutting fabric into pieces. A tailor has rolls of fabric, and each roll must be cut into equal shirt pieces. The cutting speed is given as a certain number of cuts per minute, and you must determine how many complete rolls can be processed in a given time. Such questions improve your understanding of time, work, and discrete operations.

Given Data / Assumptions:

• Each roll is cut into 10 equal pieces.
• To get 10 pieces, only 9 cuts are required (each cut increases the number of pieces by one).
• The tailor makes 45 cuts per minute.
• Total time available is 24 minutes.
• We assume no time is wasted between cuts and cuts are uniform.

Concept / Approach:
The key idea is to recognise that the number of cuts is one less than the number of resulting pieces. Many students incorrectly assume that 10 pieces require 10 cuts, but actually, starting from a single roll, each cut divides one piece into two, so the number of pieces increases by one with every cut. Once we know how many cuts are needed per roll, we can compute the total number of cuts possible in 24 minutes and divide to find the number of rolls that can be fully cut.

Step-by-Step Solution:
Step 1: Each roll must be cut into 10 pieces.Step 2: To get 10 pieces from 1 roll, we need 10 - 1 = 9 cuts.Step 3: The tailor makes 45 cuts in one minute.Step 4: In 24 minutes, the total number of cuts he can make is 45 * 24 = 1080.Step 5: Number of complete rolls he can cut = total cuts / cuts per roll = 1080 / 9.Step 6: Compute 1080 / 9 = 120.Step 7: Therefore, he can completely cut 120 rolls.

Verification / Alternative check:
To verify, we can reverse check. If he cuts 120 rolls, and each roll needs 9 cuts, total cuts required are 120 * 9 = 1080. With 45 cuts per minute, the time needed is 1080 / 45 = 24 minutes, which matches the given time exactly. Since the numbers fit perfectly, there is no partial roll or leftover cutting capacity, confirming that 120 rolls is the correct count.

Why Other Options Are Wrong:
Option A (32 rolls): 32 * 9 = 288 cuts, which would require only 288 / 45 = 6.4 minutes, much less than 24 minutes.
Option B (54 rolls): 54 * 9 = 486 cuts, which is still only 486 / 45 = 10.8 minutes.
Option C (108 rolls): 108 * 9 = 972 cuts, requiring 972 / 45 = 21.6 minutes, which is less than the available time, so more rolls can be cut.

Common Pitfalls:
A very common error is to assume that 10 pieces require 10 cuts, which would incorrectly suggest that cuts per roll equal the number of pieces. Another mistake is to miscalculate the total number of cuts or to forget to divide correctly to get the number of rolls. Careful attention to the relationship between cuts and pieces helps avoid such errors.

Final Answer:
The tailor can completely cut 120 rolls of fabric in 24 minutes.