Question

1. There are 120 students in a hostel. Food provision for them is
50 days. How long will these provisions last if 30 more join the
group.​

Answer 1

Step-by-step explanation:

the provision of 120 students for 50 days

the provision of 1 student for (50*120)days

if 30 men more joined

(120+30)=150 mens

then,

the provision last in 120*50/150 =40days

Answer 2

Given : ↴

$\sf \: For \: 120 \: students, \: food \: provision \: is \: 50 \: days.$

To find : ↴

$\sf \: How \: long \: the \: food \: will \: last,$

$\sf \: If \: 30 \: more \: students \: join \: the \: group.$

$\begin{gathered}\dag\: \purple{\underline{\textsf{\textbf{ \red{So, \: Let's \: Start : }}}}} \\ \end{gathered}$

$\sf \: If \: 30 \: more \: students \: join \: the \: group,$

$\sf \: Then \: total \: number \: of \: students \: = \: 120 + 30 = 150$

$\sf \underline{Let \: the \: food \: provision \: last \: for \: M \: days.}$

$\sf \: Then \: Our \: table \: looks \: like \: :$ ↴

$\boxed{ \purple{\begin{array} {c|c|c} \bf{ Number \: of } \\ { \bf{Students}}& \sf{120}& \sf{ 150} \\ \dfrac{\qquad\qquad \qquad}{} & \dfrac{\qquad}{} & \dfrac{\qquad}{} \\ \bf{Days } & \sf{50}& \sf{M} \\ \dfrac{\qquad \qquad\qquad}{} & \dfrac{\qquad}{}& \dfrac{\qquad}{} \end{array}}}$

$\sf \: As \: we \: increase \: the \: number \: of \: students,$

$\sf \: then \: number \: of \: days \: food \: will \: last \: decrease$

$\sf \: \green{\therefore \: \underline{They \: are \: in \: inverse \: proportion.}}$

$\sf \longrightarrow \: 120 \times 50 = 150 \times M$

$\sf \longrightarrow \: \dfrac{120 \times 50}{150} \: = \: M$

$\sf \longrightarrow \: \dfrac{120 \times 1}{3} \: = \: M$

$\sf \longrightarrow \: \dfrac{120 }{3} \: = \: M$

$\sf \longrightarrow \: \dfrac{120 }{3} \: = \: 40 \: days.$

$\sf \: \blue{\underline{Hence \: our \: answer \: is \: 40 \: days.} }$