Question

Question is asked from - direct and inverse proportion

In the hostel there are 100 students and food is available for them is for 40 days . 10 days later, 20 student more join the hostel then find how long food will be last.

Answer 1

Step-by-step explanation:

Here is your Answer

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Answer 2

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✤ How to solve?

In the question it is given to us that in the hostel there are 100 students and availability of food for them is for 40 days , After 10 days 20 students more join the hostel and we need to find for how many days the food will be last long.

So after 10 days there will be 120 students and we need to find the number of days in which the food will be last long by assuming the value of food as x .

This is the question of chapter - direct and inverse proportion, so first let's find that our question is of direct proportion or inverse proportion?

We know that if the student will be increase then the availability of food will be decrease. therefore, it is not balance . hence , it is a inverse proportion.

Let's find the solution !

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✤ Step by step solution !

Given :-

• In the hostel there are = 100 students
• Food is available for them is for = 40 days

10 days later,

• number of increasement in students = 20 [ now total students = 120]

To find :-

• How long food will be last ?

⠀

Lets solve it !

⠀

| Student⠀|⠀Days |

| 100⠀⠀⠀⠀|⠀⠀40 |

|⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀|

| ↓After 10 days↓⠀|

| 100⠀⠀⠀⠀|⠀⠀30⠀|

⠀

Now ,

⠀

| Student⠀|⠀Days |

| 100⠀⠀⠀⠀|⠀⠀30 |

| 120⠀⠀⠀⠀|⠀⠀x ⠀|

⠀

⠀

Let do it direct

⠀

| Student⠀|⠀Days |

| 100⠀⠀⠀⠀|⠀⠀⠀x |

| 120⠀⠀⠀⠀|⠀⠀30⠀|

⠀

let's find number of days!

$\Longrightarrow \sf\dfrac{100}{120} = \dfrac{ x}{30}$

$: \Longrightarrow \sf 100 \times 30 = 120 \times x$

$: \Longrightarrow \sf 3000 = 120 x$

$: \Longrightarrow \sf x = \dfrac{ \cancel{300} \cancel{0}}{ \cancel{12} \cancel{0}}$

$: \Longrightarrow \sf x = \blue{25 \: days}$

⠀

Hence , solved !!

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