Certain quantity of water cools from 70^(@)C to 60^(@)C in the first 5 minutes and to 54^(@)C in the next 5 minutes and to 54^(@)C in the next 5 minutes. The temperature of the surroundings is

Certain quantity of water cools from 70^(@)C to 60^(@)C in the first 5

1.	Certain quantity of water cools from 70^(@)C to 60^(@)C in the first 5 minutes and to 54^(@)C in the next 5 minutes and to 54^(@)C in the next 5 minutes. The temperature of the surroundings is
Answer» `45^(@)C` `20^(@)C` `42^(@)C` `10^(@)c` Solution :For the first 5 MINUTES, `(T_(2)-T_(1))/(t)=-k[(T_(1)+T_(2))/(2)-T]` `:.(60-70)/(5)=-k[(60+70)/(2)-T]` `:.-2=-k[65-T`. . .(1) For the NEXT 5 minutes, `(54-60)/(5)=-k((54+60)/(2)-T)` `:.-(6)/(5)=-k(57-T)`. . . (2) Dividing equation (1) by equation (2), `(10)/(6)=(65-T)/(57-T)` `:.570-10T=390-6T` `:.570-390=10T-6T` `:.180=4T` `:.T=(180)/(4)` `:.T=45^(@)C`