Question

A salesman is allowed $5\dfrac{1}{2}\% $discount on the total sales made by him plus a bonus of $\dfrac{1}{2}\% $on the sales over Rs. $10,000$. If his total earnings were Rs. $1990$, then his total sales (in Rs.) were:
A) $30,000$
B) $32,000$
C) $34,000$
D) $35,000$

Answer 1

Hint:Evaluate the total sales by calculating the given discount on the total sales and then add it to the bonus amount which is given on the sales over Rs. $10,000$.
Bonus amount is calculated over the sales of Rs. $10,000$.

Complete step-by-step solution:
We are given that $5\dfrac{1}{2}\% $discount is offered on the total sales and he also gets the bonus of $\dfrac{1}{2}\% $ on the sales over Rs. $10,000$.
First, we assume the total sales.
Let the total sales be Rs. $x$
Now, evaluate the $5\dfrac{1}{2}\% $discount which is given on the total sales.
That is, $5\dfrac{1}{2}\% $of $x$.
The percentage sign can be removed by dividing the quantity by $100$
$5\dfrac{1}{2}\% \times x = \dfrac{{11}}{{2 \times 100}} \times x = \dfrac{{11x}}{{200}}$
Now, we evaluate the bonus earned by him.
He gets the bonus of $\dfrac{1}{2}\% $ on the sales over Rs. $10,000$.
The sales over Rs. $10,000$will be $x - 10,000$
Write the $\dfrac{1}{2}\% $ of $x - 10,000$
The percentage sign can be removed by dividing the quantity by $100$
$\dfrac{1}{2}\% \times (x - 10000) = \dfrac{{x - 10000}}{{200}}$
The total earnings were Rs. $1990$ and it is the sum of bonus amount and discount offered on the total sales.
Write the mathematical condition for the total earning.
$\dfrac{{11x}}{{200}} + \dfrac{{x - 10000}}{{200}} = 1990$
Solve the equation and evaluate the value of $x$.
$
  \dfrac{{12x - 10000}}{{200}} = 1990 \\
  12x = 398000 + 10000 \\
  x = 34000 \\
 $

Therefore, the total sales were Rs. $34,000$
Hence, option (C) is correct.

Note:
The total earning of any salesman includes bonus amount which he is getting on the excessive sales, profit earned by him by selling the things more than its cost price and the discount earned by him.