If 42 persons consume 144 kg of wheat in 15 days, then in how many days will 30 persons consume 48 kg of wheat ?

Options

A. 8 days
B. 7 days
C. 12 days
D. 6 days

Answer

To solve the problem step by step, we will use the concept of work done by persons in terms of days and quantity of wheat consumed.

### Step 1: Understand the initial condition
We know that 42 persons consume 144 kg of wheat in 15 days.

### Step 2: Calculate the total work done in person-days
The total work done can be calculated in terms of person-days:
\[ \text{Total work} = \text{Number of persons} \times \text{Number of days} = 42 \text{ persons} \times 15 \text{ days} = 630 \text{ person-days} \]

### Step 3: Calculate the work done per kg of wheat
Now, we can find out how many person-days are required to consume 1 kg of wheat:
\[ \text{Work per kg} = \frac{\text{Total work}}{\text{Total wheat}} = \frac{630 \text{ person-days}}{144 \text{ kg}} \approx 4.375 \text{ person-days per kg} \]

### Step 4: Calculate the total work needed for 48 kg of wheat
Next, we need to find out how many person-days are required to consume 48 kg of wheat:
\[ \text{Total work for 48 kg} = 48 \text{ kg} \times 4.375 \text{ person-days per kg} = 210 \text{ person-days} \]

### Step 5: Determine how many days 30 persons will take to complete this work
Now we need to find out how many days (let's call it \( D \)) it will take for 30 persons to complete 210 person-days of work:
\[ \text{Total work} = \text{Number of persons} \times \text{Number of days} \]
\[ 210 \text{ person-days} = 30 \text{ persons} \times D \]
\[ D = \frac{210 \text{ person-days}}{30 \text{ persons}} = 7 \text{ days} \]

### Final Answer
Thus, 30 persons will consume 48 kg of wheat in **7 days**.

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