Question

Two taps supply water to a container, one at the temperature of $20^{\circ}C$ at the rate of $2 \,$kg/minute and another at $80^{\circ}C$ at the rate of $1$ kg/minute. If the container gets water from the two taps simultaneously for $10$ minutes, then the temperature of water in the container is

• A. $35^{\circ}C$
• B. $30^{\circ}C$
• C. $50^{\circ}C$
• D. $40^{\circ}C$
• E. $ 45^{\circ}C$

Answer 1

Answer: (D)

Mass of water collected from tap $1\, cm \,\,10$ minutes,
$m_{1}=2 \times 10=20 \,kg$
$T_{1}=20^{\circ} C$
Mass of water collected from tap $2 \,cm\,\,\,10$ minutes
$m_{2}=1 \times 10=10\, kg$
$T_{2}=80^{\circ} C$
Final temperature
$T=\frac{M_{1} T_{1}+M_{2} T_{2}}{M_{1}+M_{2}}$
$=\frac{20 \times 20+10 \times 80}{30}=40^{\circ} C$