In a survey it was found that YTC sells the cigarettes of Rs. 15990 per day. If the cost of a pack is not less than Rs. 100 then what can be the price of each pack which it sells per day is :

Options

A. 150
B. 420
C. 78
D. 205

Answer

To solve the problem, we need to determine the possible price of each pack of cigarettes sold by YTC, given that they sell cigarettes worth Rs. 15,990 per day and that the cost of a pack is not less than Rs. 100.

### Step-by-Step Solution:

1. **Identify the total sales amount**:
The total sales amount per day is Rs. 15,990.

2. **Set the minimum price per pack**:
The problem states that the cost of a pack is not less than Rs. 100. Therefore, we can denote the price of each pack as \( P \) where \( P \geq 100 \).

3. **Calculate the number of packs sold**:
The number of packs sold can be calculated by dividing the total sales amount by the price per pack. This can be expressed as:
\[ \text{Number of packs sold} = \frac{15990}{P} \]

4. **Ensure the number of packs is an integer**:
For \( \frac{15990}{P} \) to be an integer, \( P \) must be a divisor of 15,990. We need to find the divisors of 15,990 that are greater than or equal to 100.

5. **Find the divisors of 15,990**:
First, we can factor 15,990 to find its divisors:
\[ 15990 = 2 \times 3 \times 5 \times 7 \times 17 \]
The divisors of 15,990 can be calculated from its prime factorization.

6. **List the divisors**:
The divisors of 15,990 that are greater than or equal to 100 include:
- 105
- 110
- 119
- 130
- 150
- 170
- 210
- 238
- 255
- 330
- 357
- 510
- 714
- 1190
- 1599
- 15990

7. **Select valid prices**:
From the list of divisors, we can see that the valid prices for each pack of cigarettes that are greater than or equal to Rs. 100 are:
- 105
- 110
- 119
- 130
- 150
- 170
- 210
- 238
- 255
- 330
- 357
- 510
- 714
- 1190
- 1599
- 15990

### Conclusion:
The possible prices for each pack of cigarettes that YTC can sell per day, while ensuring that the total sales amount is Rs. 15,990 and the price per pack is not less than Rs. 100, are the divisors listed above.