Question

The price of a second hand car is $\$6975$ . Which of the three offers below is the best offer? Give a reason for your answer.
(a) $\$900$ reduction.
(b) $15\%$ discount.
(c) Pay just seven-eighths.

Answer 1

Hint: In this problem we need to choose the one best offer from the given three offers to buy a second hand car of cost $\$6975$. For this we will consider each option individually and calculate the final price of the car by reducing the discount offer price in each offer. In the first offer we can observe a $\$900$ reduction in the price, so we will directly subtract $\$900$ from the price of the car which is $\$6975$. In the second offer we can observe $15\%$ discount. So we will first calculate how much amount if $15\%$ of the car price $\$6975$and reduce it from the car price $\$6975$. In the third offer we have to pay just seven-eighths. That means we need to pay seven parts from the eight parts of the total price. For this we will simply multiply the given price $\$6975$ with $\dfrac{7}{8}$ to get the final price in the third offer. After having final prices in each offer we can compare the three values and choose the offer which has the least final price.

Complete step by step answer:
Given that, the price of a second hand car is $\$6975$.
Considering the offer $\$900$ reduction.
The final price of the car after reducing $\$900$from actual price is given by
$\begin{align}
  & \text{price}=\$6975-\$900\\&\Rightarrow\text{price}=\$6075\\\end{align}$
Final price of the car after applying for the first offer is $\$6075$ .
Considering the second offer which is $15\%$ discount.
For this we are going to calculate the what amount is $15\%$of $\$6975$ by multiplying both the values, then we will have
$\begin{align}
  & \text{discount}=15\%\times \$6975\\&\Rightarrow\text{discount}=\dfrac{15}{100}\times\$6975\\&\Rightarrow\text{discount}=\$1046.25\\\end{align}$
Now the final price of the car after applying second offer is given by subtracting the discount price from the actual price, then we will get
$\begin{align}
  & \text{price}=\$6975-\$1046.25\\&\Rightarrow\text{price}=\$5928.75\\\end{align}$
So, the final price after applying $15\%$discount offer is $\$5928.75$ .
Considering the offer, Pay just seven-eighths.
In this case the final price of the car is obtained by multiplying the price $\$6975$with $\dfrac{7}{8}$, then we will have
$\begin{align}
  & \text{price}=\dfrac{7}{8}\times \$6975\\&\Rightarrow\text{price}=\$6103.13\\\end{align}$
The final price of the car after applying for the third offer is $\$6103.13$ .
On observing the final price of the car in all three offers we can say that the second offer which is $15\%$ discount is best. Because by applying this offer we can buy the car at low cost which is $\$5928.75$.

Note: While calculating the final price of the car in each offer don’t consider the cost price of the car as the final price of the car from the previous offer. That means when you are calculating the final price of the second offer don’t consider the value $\$6075$as the price of the car because it is the final price of the car after applying for the first offer.