A cup of coffee cools from `90^0 C` to `80^0 C` in t minutes when the room temperature is `20^0 C`. The time taken by a similar cup of coffee to cool from `80^0 C` to `60^0 C` at a room temperature same at `20^0 C` is

Options

A. `(13)/(5)` t
B. `(10)/(13)` t
C. `(5)/(13)` t
D. `(13)/(10) t`

Answer

A

Explanation

`(90-80)/(t) = k [ (90 + 80)/(2) -20]`....... (i)
`(80-60)/(t.) = k [ (80 + 60)/(2) - 20]` ..... (ii)
`(10)/(t) xx (t.)/(20) = (65)/(50) , t. = (2 xx 65)/(50) t = (13)/(5) t` .