120 men consume 720 kg of rice in 30 days. In how many days can 90 men consume 270 kg?

Options

A. 18
B. 12
C. 9
D. 15

Answer

To solve the problem step by step, we will use the relationship between men, days, and work (rice consumption) as described in the video transcript.

### Step 1: Understand the Variables
- Let \( M_1 \) = 120 men
- Let \( D_1 \) = 30 days
- Let \( W_1 \) = 720 kg of rice

We need to find \( D_2 \) (the number of days for 90 men to consume 270 kg of rice).

### Step 2: Set Up the Equation
Using the formula:
\[ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} \]
Where:
- \( M_2 \) = 90 men
- \( W_2 \) = 270 kg of rice
- \( D_2 \) = unknown (the number of days we want to find)

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ \frac{120 \times 30}{720} = \frac{90 \times D_2}{270} \]

### Step 4: Simplify the Left Side
Calculating the left side:
\[ \frac{120 \times 30}{720} = \frac{3600}{720} = 5 \]

### Step 5: Set Up the Right Side
Now, we can set up the equation:
\[ 5 = \frac{90 \times D_2}{270} \]

### Step 6: Cross-Multiply to Solve for \( D_2 \)
Cross-multiplying gives:
\[ 5 \times 270 = 90 \times D_2 \]
\[ 1350 = 90 \times D_2 \]

### Step 7: Solve for \( D_2 \)
Now, divide both sides by 90:
\[ D_2 = \frac{1350}{90} = 15 \]

### Final Answer
Thus, 90 men can consume 270 kg of rice in **15 days**.

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