Question

The average temperature for the the first 5 day of the year is ${40}^{\circ }$ and the average temperature from second to sixth day is ${42}^{\circ }$ and the ratio between the temperature of $1^{st}$ day and the $6^{th}$ day is $3:4$, find the temperature of the sixth day.

Answer 1

The average temperature of first $5$ days $={40}^o$C

$\therefore$ Total temperature of $1^{st}$ day to $5^{th}$ day $=5\times {40}^{\circ }\text{C}={200}^{\circ }\text{C}$

The average temperature of $2^{nd}$ to $6^{th}$ days $={42}^{\circ }\text{C}$

$\therefore$ Total temperature of $2^{nd}$ day to $6^{th}$ day $=5\times {42}^{\circ }\text{C}={210}^{\circ }\text{C}$

Difference between the temperature $=({210}^{\circ }-{200}^{\circ })\text{C}={10}^{\circ }\text{C}$

Let, $3x$ be first day temperature and $4x$ be sixth day temperature.

$⟹4x-3x={10}^{\circ }\text{C}$

$\therefore$ $x={10}^{\circ }\text{C}$

$\Rightarrow$ $6th$ day temperature $=4\times {10}^{\circ }\text{C}={40}^{\circ }\text{C}$