The temperature of equal masses of three different liquids A, B and Care 12°C 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C and when B and C are mixed is 23°C. The temperature when A and C are mixed is :

Options

A. ` 18 . 2 ^(@) C `
B. ` 22 ^(@) C `
C. ` 20 . 2 ^(@)C `
D. ` 24.2 ^(@)C `

Answer

C

Explanation

Ist case
` " " ms_(A) (t-t_A) = ms_B (t_B -t)`
` S_A (16-12) =s_B (19-16)`
` " " 4s_A = 3s_B`
Iind case:
` " " ms_B (t-t_B) = ms_C (t_C- t)`
` s_B (23-19) = s_C (28-23)`
` " " 4s_B = 5s_C `
` 3s_B = (15)/(4)s_c`
` therefore " " 4s_A = 3s_B= (15)/(4 )s_C`
`rArr " " 16s_A = 12s_B= 15s_C =k`
` " " s_A : s_B : s_C = (1)/(16) : (1)/(12) : (1)/(15) `
` s_A =(k)/(16) ,s_C = (k)/(15)`
When A and C are mixed
` ms_A (t-t_A) = ms_C (t_C - t)`
` (k)/(16) (t-12) = (k)/(15) (28-t)`
` 15 t - 180 = 448- 16t`
` 31 t = 628`
` rArr " " t= 20 .2^(@) C `