Question

By selling a transistor for Rs 572, a shopkeeper earns a profit equivalent to \[30\% \] of the cost price of the transistor. What is the cost price of the transistor?
A.Rs 400
B.Rs 340
C.Rs 440
D.None of these

Answer 1

Hint: We will first express the profit earned in terms of the cost price. Then we will substitute the profit in terms of cost price and the value of selling price in the relation between profit, selling price and cost price. We will solve it further to find the cost price of the transistor.

Formula used:
We will use the following formulas:
1.\[{\rm{Profit}}\% = \dfrac{{{\rm{Profit}}}}{{{\rm{Cost Price}}}} \times 100\]
2.Profit earned \[ = \]Selling Price \[ - \] Cost Price.

Complete step-by-step answer:
We are given that the shopkeeper has earned a profit of \[30\% \] by selling the transistor for Rs 572.
Substituting value of profit percentage in the formula, we get
\[30 = \dfrac{{{\rm{Profit}}}}{{{\rm{Cost Price}}}} \times 100\]
Dividing both sides by 100, we get
\[ \Rightarrow \dfrac{{30}}{{100}} = \dfrac{{{\rm{Profit}}}}{{{\rm{Cost Price}}}} \times \dfrac{{100}}{{100}}\]
Simplifying the fraction, we get
\[ \Rightarrow \dfrac{3}{{10}} = \dfrac{{{\rm{Profit}}}}{{{\rm{Cost Price}}}}\]
Taking Cost Price from the denominator in RHS to the numerator in LHS, we get
\[ \Rightarrow {\rm{Profit}} = \dfrac{3}{{10}} \times {\rm{Cost Price}}\] ………..\[(1)\].
Now, let us take Cost Price \[ = x\].
So, equation \[(1)\] becomes
\[ \Rightarrow {\rm{Profit}} = \dfrac{3}{{10}}x\] …………\[(2)\]
It is given that Selling Price is Rs. 572.
Substituting 527 for selling price and \[x\] for cost price in the formula Profit earned \[ = \]Selling Price \[ - \] Cost Price, we get
\[{\rm{Profit = 572}} - x\] ……….\[(3)\]
Using equation\[(2)\] in equation \[(3)\], we have
\[ \Rightarrow \dfrac{3}{{10}}x = 572 - x\]
Collecting like terms on the LHS,
\[ \Rightarrow \dfrac{3}{{10}}x + x = 572\]
Taking LCM on LHS, we get
\[ \Rightarrow \dfrac{{3x + 10x}}{{10}} = 572\]
Adding the terms in the numerator, we get
\[ \Rightarrow \dfrac{{13x}}{{10}} = 572\]
On cross multiplication, we get
\[\begin{array}{l} \Rightarrow x = 572 \times \dfrac{{10}}{{13}}\\ \Rightarrow x = \dfrac{{5720}}{{13}}\end{array}\]
Therefore, we get the \[x = 440\]. Hence, the Cost Price of the transistor is Rs 440 .
So, the correct answer is option C.

Note: We know that cost price is the price at which a product is purchased. Selling price is the price at which the product is sold. A seller incurs profit when the selling price is greater than the cost price of the product. A seller incurs loss when the selling price is greater than the cost price of the product. We can find profit by subtracting the selling price from the cost price.