Question

By selling a pen for Rs. 15, a man loses one-sixteenth of what it costs him. Find the cost price of one pen.
A.Rs 16
B.Rs 18
C.Rs 20
D.Rs 21

Answer 1

Hint: We can take the cost price as a variable x. Then the loss is $\dfrac{1}{{16}}x$ . The selling price is given by reducing the loss from the cost price. So, we get an equation in x and equate it to the given selling price. On simplification and solving for x, we will get the required cost price.

Complete step-by-step answer:
Let x be the cost price of the pen.
It is given that the selling price is Rs. 15 and the loss is one-sixteenth of the cost price.
Therefore, the cost price is $\dfrac{1}{{16}}x$ .
We know that the selling price is given by subtracting the loss from the cost price.
 $ \Rightarrow S.P. = C.P. - loss$
On substituting the values, we get,
 $ \Rightarrow 15 = x - \dfrac{1}{{16}}x$
We can take the LCM of the RHS.
 $ \Rightarrow 15 = \dfrac{{16x - x}}{{16}}$
After the subtraction, we get,
 $ \Rightarrow 15 = \dfrac{{15x}}{{16}}$
Now we can cancel 15 from both sides,
 $ \Rightarrow 1 = \dfrac{x}{{16}}$
On cross multiplying, we get,
 $ \Rightarrow x = 16$
Therefore, the cost price of the pen is Rs 16
So, the correct answer is option A.
Note: Alternate method to solve the problem is,
It is given that the loss is $\dfrac{1}{{16}}$ of the cost price.
Then the other part of the cost price will give the selling price.
Therefore, $\dfrac{{15}}{{16}}$ of the cost price is the selling price.
$ \Rightarrow S.P. = \dfrac{{15}}{{16}} \times C.P.$
We can write the equation in terms of the cost price,
$ \Rightarrow C.P. = \dfrac{{16}}{{15}} \times S.P.$
It is given that the selling price is Rs. 15.
$ \Rightarrow C.P. = \dfrac{{16}}{{15}} \times 15$
On simplification, we get,
$ \Rightarrow C.P. = 16$
Therefore, the cost price of the pen is Rs 16