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A school hostel has enough food for 500 children for 18 days. How long will the food last if 100 more children join them?

Mathematics

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Step-by-step solution

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Here's how to solve the problem:

  1. Calculate the total amount of food available in "child-days".

    Total food units=Number of children×Number of days\text{Total food units} = \text{Number of children} \times \text{Number of days} Total food units=500 children×18 days=9000 child-days\text{Total food units} = 500 \text{ children} \times 18 \text{ days} = 9000 \text{ child-days}

  2. Determine the new total number of children.

    New number of children=Initial children+Additional children\text{New number of children} = \text{Initial children} + \text{Additional children} New number of children=500+100=600 children\text{New number of children} = 500 + 100 = 600 \text{ children}

  3. Calculate how many days the food will last for the new number of children.

    New number of days=Total food unitsNew number of children\text{New number of days} = \frac{\text{Total food units}}{\text{New number of children}} New number of days=9000 child-days600 children=15 days\text{New number of days} = \frac{9000 \text{ child-days}}{600 \text{ children}} = 15 \text{ days}

    The food will last for 15 days.

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