Question

An electrician sells a room heater for Rs $$3220$$, gaining $${\displaystyle \frac{1}{6}}$$ of its cost price. Find his gain percentage?

Answer 1

Hint: If the gain and Cost Price of an object is given, we can find the gain percentage easily. Here we are provided with both gain and cost price hence we find the gain percentage using the following formula.

Formula used: The percentage of gain of the object will be = $$\left(Gain\times {\displaystyle \frac{100}{CP}}\right)\mathrm{\%}$$

Complete step-by-step answer:
It is given that an electrician sells a room heater for Rs $$3220$$ and he gains $${\displaystyle \frac{1}{6}}$$ of its cost price.
We have to find his gain percent.
Cost of the room heater is Rs. $$3220$$.
Gain in room heater is $${\displaystyle \frac{1}{6}}$$ of its cost price.
Which is nothing but the multiplication of cost price and $${\displaystyle \frac{1}{6}}$$.
Hence, the gain amount is calculated as Rs. $${\displaystyle \frac{1}{6}}\times 3220$$
Let us solve the above term so that we get, the gain amount as Rs. $$536.66$$
Now, the percentage of gain is found using the formula$$\left(Gain\times {\displaystyle \frac{100}{CP}}\right)\mathrm{\%}$$
Where cost price is given as Rs. $$3220$$ and gain is found as $$536.66$$
Let us now substitute the gain and Cost Price we have found in the given formula, we get,
The gain percentage is $$536.66\times {\displaystyle \frac{100}{3220}}$$
Let us simplify the above equation so that we can get the gain percentage,
The gain percentage is found as $$16.67\mathrm{\%}$$.
Hence, the gain percentage is $$16.67\mathrm{\%}$$.

Note: When the selling price of an object is more than the cost price, there will be gain else it will be loss. Gain is also known as profit. The percentage of profit is useful in finding the gain of the merchant.