Question

The cost of 3 televisions and 2 VCR’s is $Rs.35000$. The shop – keeper wants a profit of $Rs.1000$ per television and $Rs.500$ per VCR. He can sell 2 televisions and 1 VCR and he gets the total revenue as $Rs.21500$. Find the cost and the selling price of a television and a VCR.

Answer 1

Hint: Assume that the cost of television and VCR is ‘x’ and ‘y’ respectively. To find the selling price of television and VCR, add the profit to the cost price of VCR. Write equations relating them based on the data given in the question. Solve the equations to calculate the cost price of both the items and then calculate the selling price of both the items.

Complete step-by-step answer:
We have data regarding the cost price and selling price of television and VCR. We have to calculate their cost price and selling price.
Let’s assume that the cost price of television and VCR is Rs.x and Rs.y.
We know that the cost of 3 televisions and 2 VCR’s is Rs.35000. thus, we have $3x+2y=35000.....\left( 1 \right)$.
We will now calculate the selling price of both the items. We know that selling price is the sum of cost price and profit gained on the item.
We know that the profit gained on television is Rs.1000 and its cost price is Rs.x. Thus, the selling price of the television is $Rs.\left( 1000+x \right)$.
Similarly, we know that the profit gained on VCR is Rs.500 and its cost price is Rs.y. Thus, the selling price of VCR is $Rs.\left( 500+y \right)$.
We know that the price of selling 2 televisions and 1 VCR is Rs.21500. Thus, we have $2\left( 1000+x \right)+\left( 500+y \right)=21500$.
Simplifying the above equation, we have $2000+2x+500+y=21500$.
Thus, we have $2x+y=21500-2500=19000.....\left( 2 \right)$.
We will now solve equation (1) and (2) by the elimination method. Multiplying equation (2) by 2 and subtracting it from equation (1), we have$\left( 3x+2y \right)-2\left( 2x+y \right)=35000-2\times 19000$.
Simplifying the above equation, we have $3x+2y-4x-2y=35000-38000$.
Thus, we have $x=Rs.3000......\left( 3 \right)$.
Substituting equation (3) in equation (2), we have $2\times 3000+y=19000$.
Simplifying the above equation, we have $6000+y=19000$.
Thus, we have $y=19000-6000=Rs.13000......\left( 4 \right)$.
We will now calculate the selling price of television and VCR.
We know that the selling price of the television is $Rs.\left( 1000+x \right)$. Using equation (4), the selling price of the television is $=Rs.1000+Rs.3000=Rs.4000$.
Similarly, we know that the selling price of VCR is $Rs.\left( 500+y \right)$. Using equation (3), the selling price of VCR is $=Rs.13000+Rs.500=Rs.13500$.
Hence, the cost price of television and VCR is Rs.3000 and Rs.13000 respectively. While the selling price of television and VCR is Rs.4000 and Rs.13500 respectively.

Note: We must keep in mind that the selling price is calculated by adding profit to the cost price. Otherwise, we won’t be able to solve this question. We observe that we have solved this question using linear equations in two variables. We can solve the equations for x and y using the substitution method also, but that would be time consuming. Also, we must not forget to compute the selling price after finding the cost price, as in the question, we have been asked to compute both cost price and selling price.