The weekly expenses of a hostel are partly constant and partly vary directly as the number of inmates . If the expenses are rs 2000 when the number of inmates is 120 and rs 1700 when the number is 100 . Find the number of inmates when the expenses are rs 1880 .

The weekly expenses of a hostel are partly constant and partly vary di

1.	The weekly expenses of a hostel are partly constant and partly vary directly as the number of inmates . If the expenses are rs 2000 when the number of inmates is 120 and rs 1700 when the number is 100 . Find the number of inmates when the expenses are rs 1880 .
Answer» Let the expenses be rs y and the number of inmates = x. As per question , y =`k_1 +k_2x……..(1)` [where `k_1 =constant and k_2 ne 0= ` variation constant ] As per question, if x =120 , then y 2000. `therefore` from (1) we get , 2000 =`k_1 +k_2xx120` or, `k_1+120k_2=2000......(2)` Again , if x =100,then y =1700. `therefore` from (1) we get ,1700=`k_1+k_2xx100` or, `k_1+100k_2=1700........(3)` Now , subtracting (3) from (2) we get , `20k_2=300 or, k_2=15` . `therefore` from (2) we get ,` k_1 +120 xx15 =2000` `rArrk_1=2000-1800` `rArr k_1 =200` `therefore` from (1) we get ,y 200 +15x........(4) so, putting y = 1880 in (4) we get , 1880 =200 +15x or, 15x =1680 or, x=`(1680)/(15)=112` . Hence the required number of inmates =112.