Question

If the average wages of a worker during a fortnight comprising $15$ consecutive working days was $90\$$ per day.
During the first $7$ days, his average wages was $87\$$ units per day and the average wages during the last $7$ days was $92\$$ per day. Then his wage on the $8^{th}$ day is

• A. $97~\$
• B. $90~\$
• C. $83~\$
• D. $92~\$

Answer 1

The correct option is A $97~\$

Let $x_1,x_2,x_3\dots x_{15}$ represent the $15$ working days
Average of first $7$ days is $87\$$
$\Rightarrow \frac{x_1+x_2+\cdots +x_7}{7}=87$
$\Rightarrow x_1+x_2+\cdots +x_7=7\times 87\dots \left(1\right)$

Average of last $7$ days is $92\$$
$\Rightarrow \frac{x_9+x_{10}+\cdots +x_{15}}{7}=92$
$\Rightarrow x_9+x_{10}+\cdots +x_{15}=7\times 92\dots \left(2\right)$

and average of $15$ days is $90\$$
$\Rightarrow \frac{(x_1+x_2+\cdots +x_7)+x_8+(x_9+\cdots +x_{15})}{15}=90$
From equation $\left(1\right)$ and $\left(2\right)$
$\Rightarrow \frac{7\times 87+x_8+7\times 92}{15}=90$
$\Rightarrow x_8=90\times 15-7\times 179=97\$$