a hostel has enough food to feed 1500 students for 100 days.

For how many students would the food last if 120 more students were to join the hostel

Given, 1500 students have food for 100 days.

now for 1 student, food available = 100*1500

Given, 120 more students joined.

So, for 1620 student, food available = (100*1500)/1620

                                                          = (10*1500)/162

                                                          = (10*500)/54          (1500 and 162 is divided by 3)

                                                          = (10*250)/27          (500 and 54 is divided by 2)

                                                          = 2500/27

                                                          = 92.59

                                                          ≅ 93

So, the food is available for 1620 students for 93 days.