Jagmohan, Rooplal and Pandeyji rented a video cassette for one week at a rent of Rs. 350. If they use it for 6 hours, 10 hours and 12 hours respectively. The rent to be paid by Pandeyji is

Options

A. Rs. 75
B. Rs. 125
C. Rs. 135
D. Rs. 150

Answer

To find out how much rent Pandeyji has to pay, we can follow these steps:

### Step 1: Determine the usage hours
Jagmohan, Rooplal, and Pandeyji used the video cassette for the following hours:
- Jagmohan: 6 hours
- Rooplal: 10 hours
- Pandeyji: 12 hours

### Step 2: Calculate the total usage hours
Add the hours used by all three:
\[ \text{Total hours} = 6 + 10 + 12 = 28 \text{ hours} \]

### Step 3: Determine the ratio of usage
Now, we can express the usage of each person as a ratio:
- Jagmohan's usage: 6 hours
- Rooplal's usage: 10 hours
- Pandeyji's usage: 12 hours

The ratio of their usage can be simplified:
\[ \text{Ratio} = 6 : 10 : 12 \]
Dividing each term by 2 gives:
\[ \text{Ratio} = 3 : 5 : 6 \]

### Step 4: Calculate the total parts in the ratio
Now, we add the parts of the ratio:
\[ \text{Total parts} = 3 + 5 + 6 = 14 \]

### Step 5: Calculate the share of Pandeyji
To find Pandeyji's share of the rent, we use the ratio part corresponding to him (which is 6) and the total rent (Rs. 350):
\[ \text{Pandeyji's share} = \frac{\text{Pandeyji's part}}{\text{Total parts}} \times \text{Total rent} \]
\[ \text{Pandeyji's share} = \frac{6}{14} \times 350 \]

### Step 6: Simplify the calculation
Now, simplify the fraction:
\[ \frac{6}{14} = \frac{3}{7} \]
So,
\[ \text{Pandeyji's share} = \frac{3}{7} \times 350 \]

### Step 7: Calculate the final amount
Now, calculate:
\[ \text{Pandeyji's share} = 3 \times 50 = 150 \]

### Final Answer
Thus, the rent to be paid by Pandeyji is **Rs. 150**.

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