Question

a hostel with 300 students had enough food to last them for 30 days.however 200 new students arrived. For how long will the food last now? in step by step pls​

Answer 1

Given :

• A hostel with 300 students had enough food to last them for 30 days

To Find :

• If 200 new students arrived, how long will the food last now

Solution :

❑ Let the food will last for 'x' days

If 200 new students joined the hostel,

Total number of students = 300 + 200

$\sf\bold{⟹ 500 \: students}$

➙ Now, we have to find that in number of days the food will last if there are 500 students.

──────────────

Here, As it increases in number of students,

The number of days food will last decreases

So, They are in inverse proportion,⠀

$\sf\bold{⟹300 \times 30 = 500 \times x}$

$\sf\bold{⟹9000 = 500 \times x}$

$\sf\bold{⟹ \cancel{\dfrac{9000}{500} }= x}$

$\implies\boxed{ \purple{ \bf 18 = x}}$

Hence, The food will last in 18 days for 500 students

Answer 2

Step-by-step explanation:

Given :

A hostel with 300 students had enough food to last them for 30 days

To Find :

If 200 new students arrived, how long will the food last now

Solution :

❑ Let the food will last for 'x' days

If 200 new students joined the hostel,

Total number of students = 300 + 200

\sf\bold{⟹ 500 \: students}⟹500students

➙ Now, we have to find that in number of days the food will last if there are 500 students.

──────────────

Here, As it increases in number of students,

The number of days food will last decreases

So, They are in inverse proportion,⠀

\sf\bold{⟹300 \times 30 = 500 \times x}⟹300×30=500×x

\sf\bold{⟹9000 = 500 \times x}⟹9000=500×x

\sf\bold{⟹ \cancel{\dfrac{9000}{500} }= x}⟹

500

9000

=x

\implies\boxed{ \purple{ \bf 18 = x}}⟹

18=x

Hence, The food will last in 18 days for 500 students

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