Question

In a hostel there is enough food for 300 students for 32 days. In how many days the food will last if 100 more students join in the hostel?
(a) 40 days
(b) 30 days
(c) 25 days
(d) 24 days​

Answer 1

Answer:

total no of students= 300+100=400

no. of days food last for 300 students=32 days

no of days food last for 1 student= 300×32

no of days food last for 400 students=

300×32 = 3×8=24 days

400

Answer 2

Given : In a hostel there is enough food for 300 students for 32 days .

Exigency To Find : How many days the food will last if 100 more students join in the hostel .

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⠀⠀⠀⠀⠀No . of Student when 100 more students join :

• Total number of Students = 300 + 100

• Total number of Students = 400 students

⠀⠀⠀⠀⠀We need to find how many days the food will lasts :

❍ Let's Consider the food lasts for a days when 100 more students join .

• Number of Students = 300 & 400
• Number of Days =⠀⠀⠀32 & a

Thus , It's looks a like ,

• When number of Students increase then the number of days will decrease [ Quantity of food is same ]

Therefore,

• They are in inverse Proportion .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: According \: to \: the \: Question \: \::}}$

$\qquad :\implies \sf{ 300 \times 32 = 400 \times a }\qquad \longrightarrow..(x_1 y_1 = x_2 y_2)$

$\qquad :\implies \sf{ \dfrac{3\cancel {00} \times 32}{4\cancel{00}} = a }$

$\qquad :\implies \sf{ \dfrac{3 \times32 }{4} = a }$

$\qquad :\implies \sf{ \dfrac{3\times \cancel {32} }{\cancel{4}} = a }$

$\qquad :\implies \sf{ 3 \times 8 = a }$

$\qquad :\implies \bf{ 24 = a }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\:The\:number \:of\:Days\:the\:food\:will\:last \:is\:\bf{24\: days}}}}$

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