In the above question if Pravesh served every guest who were sitting on the chair number 3,6,9,12,15….etc. with chapatis and to those who were , sitting on the chair number 5,10, 15,20,..etc. with poori and to the rest with Idli. The number of guests who has not recevied the Idli is :

Options

A. a. 38
B. b. 47
C. c. 41
D. d. none of these

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Identify the total number of guests
The total number of guests is given as 100.

### Step 2: Determine who receives chapatis
Guests sitting on chair numbers that are multiples of 3 receive chapatis. The multiples of 3 up to 100 are:
- 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.

To find how many guests received chapatis, we divide 100 by 3:
\[ \text{Number of guests receiving chapatis} = \left\lfloor \frac{100}{3} \right\rfloor = 33 \]

### Step 3: Determine who receives puris
Guests sitting on chair numbers that are multiples of 5 receive puris. The multiples of 5 up to 100 are:
- 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.

To find how many guests received puris, we divide 100 by 5:
\[ \text{Number of guests receiving puris} = \left\lfloor \frac{100}{5} \right\rfloor = 20 \]

### Step 4: Determine overlap (those who received both chapatis and puris)
Guests sitting on chair numbers that are multiples of both 3 and 5 (i.e., multiples of 15) receive both chapatis and puris. The multiples of 15 up to 100 are:
- 15, 30, 45, 60, 75, 90.

To find how many guests received both, we divide 100 by 15:
\[ \text{Number of guests receiving both} = \left\lfloor \frac{100}{15} \right\rfloor = 6 \]

### Step 5: Calculate total guests who received either chapatis or puris
Using the principle of inclusion-exclusion:
\[ \text{Total guests receiving chapatis or puris} = (\text{Number receiving chapatis}) + (\text{Number receiving puris}) - (\text{Number receiving both}) \]
\[ = 33 + 20 - 6 = 47 \]

### Step 6: Calculate the number of guests who received idlis
The guests who received idlis are those who did not receive either chapatis or puris. Thus:
\[ \text{Number of guests receiving idlis} = \text{Total guests} - \text{Total guests receiving chapatis or puris} \]
\[ = 100 - 47 = 53 \]

### Step 7: Final answer
The number of guests who have not received idlis (i.e., those who received either chapatis or puris) is:
\[ \text{Number of guests who did not receive idlis} = 47 \]

### Conclusion
The final answer is that 47 guests did not receive idlis.

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