A hostel needs 1,350 litres of milk for
90 children for 28 days. For how many
children will 1,800 litres of milk suffice fo
30 days?

Question

A hostel needs 1,350 litres of milk for 90 children for 28 days. For how many children will 1,800 litres of milk suffice fo 30 days?

UpStudy AI · Accepted Answer

To determine how many children can be accommodated with 1,800 liters of milk for 30 days, we can use the relationship between the number of children, the amount of milk, and the number of days.

**Step 1: Understand the given information.**
- **Initial Scenario:**
  - **Milk required:** 1,350 liters
  - **Number of children:** 90
  - **Number of days:** 28

- **New Scenario:**
  - **Milk available:** 1,800 liters
  - **Number of days:** 30
  - **Number of children:** $$ x $$ (this is what we need to find)

**Step 2: Establish the relationship.**
The amount of milk consumed is directly proportional to the number of children and the number of days.

$$ \text{Milk} = \text{Number of Children} \times \text{Number of Days} \times \text{Consumption per Child per Day} $$

Let's denote the consumption per child per day as $$ k $$.

**Step 3: Find the consumption rate ($$ k $$).**

From the initial scenario:
$$ 1350 = 90 \times 28 \times k $$
$$ k = \frac{1350}{90 \times 28} $$
$$ k = \frac{1350}{2520} $$
$$ k = \frac{15}{28} \text{ liters per child per day} $$

**Step 4: Apply the consumption rate to the new scenario.**

$$ 1800 = x \times 30 \times \frac{15}{28} $$

Solving for $$ x $$:
$$ x = \frac{1800 \times 28}{30 \times 15} $$
$$ x = \frac{50400}{450} $$
$$ x = 112 $$

**Conclusion:**
1,800 liters of milk will suffice for **112 children** for 30 days.

**Answer:**  
112 children
112 children

A hostel needs 1,350 litres of milk for
90 children for 28 days. For how many
children will 1,800 litres of milk suffice fo
30 days?

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