Five tailors A, B, C, D and E stich 1800 shirts in 90 days working alternatively. Find the minimum possible number of shirts that can be stiched in a single day by working together:

Options

A. 100
B. 20
C. 50
D. 4

Answer

To solve the problem, we need to determine how many shirts can be stitched in a single day by all five tailors working together. Let's break this down step by step.

### Step 1: Determine the total work done in shirts
The total number of shirts stitched by the five tailors in 90 days is given as 1800 shirts.

### Step 2: Calculate the work done per day
To find out how many shirts are stitched in one day, we can divide the total number of shirts by the total number of days:
\[ \text{Shirts per day} = \frac{\text{Total shirts}}{\text{Total days}} = \frac{1800}{90} = 20 \text{ shirts/day} \]

### Step 3: Understand the work pattern
Since the tailors are working alternatively, it means that in a cycle of 5 days, each tailor works once. Therefore, in 5 days, they will stitch a total of 20 shirts.

### Step 4: Calculate the work done by one tailor in one day
If 5 tailors can stitch 20 shirts in 5 days, then in one day, each tailor contributes to the stitching. Since they work alternatively, we can assume that each tailor stitches an equal amount of shirts over the cycle.

Let’s denote the number of shirts stitched by each tailor in one day as \( x \). Then in 5 days, the total work done would be:
\[ 5x = 20 \text{ shirts} \]
From this, we can find \( x \):
\[ x = \frac{20}{5} = 4 \text{ shirts} \]

### Step 5: Calculate the total work done by all tailors in one day
Since each tailor can stitch 4 shirts in a day, when all 5 tailors work together in one day, the total number of shirts stitched will be:
\[ \text{Total shirts in one day} = 5 \times 4 = 20 \text{ shirts} \]

### Conclusion
Thus, the minimum possible number of shirts that can be stitched in a single day by all tailors working together is **20 shirts**.

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