Question

A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

• A. \(60\)
• B. \(40\)
• C. \(50\)
• D. \(30\)

Hint:

Temperature difference from the surroundings decays exponentially.

Answer 1

The Correct Option is B

Step 1: Spot the halving:
The excess falls $80 \to 40$ in $20$ min, so the excess halves every $20$ min.

Step 2: Count halvings:
To reach $40$ C the excess must drop from $80$ to $20$, which is two halvings, so $2 \times 20 = 40$ min.

Final Answer:
The total time is $40$ minutes, option (B). \[ \boxed{40} \]