Priyanka, Sonal and Deepika share some pencils in the ratio 4: 5: 6. Which of the following is not a possible number of pencils?

Options

A. 75
B. 56
C. 45
D. 60

Answer

To solve the problem of Priyanka, Sonal, and Deepika sharing pencils in the ratio of 4:5:6, we will follow these steps:

### Step 1: Understand the Ratio
The ratio of pencils shared among Priyanka, Sonal, and Deepika is given as 4:5:6. This means:
- Priyanka gets 4 parts,
- Sonal gets 5 parts,
- Deepika gets 6 parts.

### Step 2: Calculate the Total Parts
To find the total number of parts in the ratio, we add the parts together:
\[ 4 + 5 + 6 = 15 \]
So, the total number of parts is 15.

### Step 3: Express Total Pencils in Terms of k
Let’s denote the number of pencils each person gets as multiples of a variable \( k \):
- Priyanka's pencils = \( 4k \)
- Sonal's pencils = \( 5k \)
- Deepika's pencils = \( 6k \)

Thus, the total number of pencils can be expressed as:
\[ 4k + 5k + 6k = 15k \]

### Step 4: Identify Possible Total Numbers of Pencils
Since the total number of pencils is \( 15k \), it must be a multiple of 15. Therefore, any total number of pencils must be divisible by 15.

### Step 5: Check Each Option
Now, we need to check which of the given options is not a multiple of 15.

Assuming the options given are:
1. 75
2. 56
3. 60
4. 90

We check each:
- **75**: \( 75 \div 15 = 5 \) (divisible)
- **56**: \( 56 \div 15 = 3.73 \) (not divisible)
- **60**: \( 60 \div 15 = 4 \) (divisible)
- **90**: \( 90 \div 15 = 6 \) (divisible)

### Conclusion
The number of pencils that is not possible is **56**.