Plz solve it..... Plz

Dear Student,

i n f i r s t c a s e, i n i t i a l t e m p e r a t u r e, T_{i} = 80 ° C f i n a l t e m p e r a t u r e, T_{f} = 70 ° C t e m p e r a t u r e o f s u r r o u n d i n g, T_{0} = 25 ° C t = 12 m i n a c c o r d i n g t o N e w t o n' s l a w o f c o o l i n g, r a t e o f c o o l i n g, \frac{d T}{d t} = k [\frac{T_{i} + T_{f}}{2} - T_{0_{}}] \Rightarrow \frac{T_{i} - T_{f}}{t} = k [\frac{T_{i} + T_{f}}{2} - T_{0_{}}] \Rightarrow \frac{80 - 70}{12} = k [\frac{80 + 70}{2} - 25] \Rightarrow \frac{10}{12} = k [75 - 25] \Rightarrow \frac{10}{12} = k \times 50 \Rightarrow k = \frac{10}{12 \times 50} = \frac{1}{60} i n s e c o n d c a s e, i n i t i a l t e m p e r a t u r e, T_{i} = 70 ° C f i n a l t e m p e r a t u r e, T_{f} = 60 ° C l e t t_{1} b e t h e r e q u i r e d t i m e . a c c o r d i n g t o N e w t o n' s l a w o f c o o l i n g, r a t e o f c o o l i n g, \frac{d T}{d t} = k [\frac{T_{i} + T_{f}}{2} - T_{0}] \Rightarrow \frac{70 - 60}{t_{1}} = \frac{1}{60} [\frac{70 + 60}{2} - 25] \Rightarrow \frac{10}{t_{1}} = \frac{1}{60} [65 - 25] \Rightarrow \frac{10}{t_{1}} = \frac{1}{60} \times 40 = \frac{2}{3} \Rightarrow 2 t_{1} = 30 \Rightarrow t_{1} = 15 m i n

option(1) is correct.

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