Question

The temperature at $12$ noon was ${10}^{o}C$ above zero. If it decreases at the rate of $2^{o}C$ per hour until midnight, at what time would the temperature be $8^{o}C$ below zero? What would be the temperature at midnight?

• A. ${14}^{o}C$
• B. ${-14}^{o}C$
• C. ${16}^{o}C$
• D. ${-16}^{o}C$

Answer 1

The correct option is B ${-14}^{o}C$

At $12$ noon, the temperature $=10°C$ above zero

The temperature is decreasing at $2°C$ per hour

$8°C$ below zero $=-8°C$

So, total fall in temperature from $10°C$ to $0°C$ and from $0°C$ to $-8°C=18°C$

Since the temperature falls $2°C$ in every one hour.

Therefore, to decrease $18°C$, time taken = $18/2$

= $9$ hours

Present time is $12$ noon so, the time when the temperature is $-8°C$

$=12noon+9hours$

So, The time at which the temperature will be $-8°C=9PM$

At 9 PM, the temperature is $-8°C$, the temperature at $12$ midnight will be =

$(-8°C)+(-2°C\times 3hours)$

$=(-8°C)+(-6°C)$

$=-14°C$

So, at 12 midnight the temperature will be$-14°C.$