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

Question

A cup of coffee cools from 90° C to 80° C in t minutes, when the room temperature is 20° C. The time taken by a similar cup of coffee to cool from 80° C to 60° C at a room temperature same at 20° C is : (A) (13/10) t (B) (13/5) t (C) (10/13) t (D) (5/13) t

Tardigrade Admin · Accepted Answer

(((80-60/t'))/((90-80)t))=(((80+60/2)-20)/((90+80)2-20)) ⇒ (20/t') × (t/10)=(50/65) ⇒ t=2 t × (65/50)=(13/5) t

Q. A cup of coffee cools from $9 0^{\circ} C$ to $8 0^{\circ} C$ in t minutes, when the room temperature is $2 0^{\circ} C$ . The time taken by a similar cup of coffee to cool from $8 0^{\circ} C$ to $6 0^{\circ} C$ at a room temperature same at $2 0^{\circ} C$ is :

$\frac{13}{10} t$

$\frac{13}{5} t$

$\frac{10}{13} t$

$\frac{5}{13} t$

$\frac{( \frac{80 - 60}{t ^{'}} )}{( \frac{90 - 80}{t} )} = \frac{( \frac{80 + 60}{2} - 20 )}{( \frac{90 + 80}{2} - 20 )}$
$\Rightarrow \frac{20}{t ^{'}} \times \frac{t}{10} = \frac{50}{65}$
$\Rightarrow t = 2 t \times \frac{65}{50} = \frac{13}{5} t$

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

1013​t

513​t

1310​t

135​t