Question

There is enough food to feed 360 students for 60 days. for how long will the food take them if they are 400 students?

Answer 1

Answer:

• The food will exhaust in 54 days if there are 400 students.

Step-by-step explanation:

Given that:

• There is enough food to feed 360 students for 60 days.

To Find:

• For how long will the food take them if there are 400 students?

Let us assume:

• The food will exhaust in x days if there are 400 students.

Formula used:

• S₁ × D₁= S₂ × D₂

Where,

• S₁ = Number of students = 360
• D₁ = Number of days = 60
• S₂ = Number of students = 400
• D₂ = Number of days = x

Finding the value of x:

⟶ 360 × 60 = 400 × x

⟶ 21600 = 40x

⟶ x = 21600/400

⟶ x = 54

Hence,

• The food will exhaust in 54 days if there are 400 students.

Answer 2

Answer:

Given :-

• There is enough food to feed 360 students for 60 days.

To Find :-

• How long will the food take them if they are 400 students.

Solution :-

Let,

$\mapsto$ The food take them for 400 students be y days.

Given :

• Number of students (S₁) = 360 students
• Number of students (S₂) = 400
• Number of days (d₁) = 60 days
• Number of days (d₂) = x days

Then, by according to the question we can write the formula as :

$\longmapsto \sf\boxed{\bold{\pink{S_1 \times d_1 =\: S_2 \times d_2}}}$

where,

• S₁ = Number of students in first case
• S₂ = Number of students in second case
• d₁ = Number of days in first case
• d₂ = Number of students in second case

Given :

• S₁ = 360 students
• S₂ = 400 students
• d₁ = 60 days
• d₂ = x days

According to the question by using the formula we get,

$\implies \sf 360 \times 60 =\: 400 \times x$

$\implies \sf 21600 =\: 400x$

$\implies \sf \dfrac{216\cancel{00}}{4\cancel{00}} =\: x$

$\implies \sf \dfrac{\cancel{216}}{\cancel{4}} =\: x$

$\implies \sf \dfrac{54}{1} =\: x$

$\implies \sf 54 =\: x$

$\implies \sf\bold{\red{x =\: 54\: days}}$

$\therefore$ The food take them for 400 students is 54 days .

$\rule{150}{2}$

VERIFICATION :

$\dashrightarrow \sf 360 \times 60 =\: 400 \times x$

By putting x = 54 we get,

$\dashrightarrow \sf 360 \times 60 =\: 400 \times 54$

$\dashrightarrow \sf 21600 =\: 21600$

$\dashrightarrow\sf\bold{\green{21600 =\: 21600}}$

Hence, Verified .