Question

A shopkeeper purchased $200$ bulbs for Rs.$10$ each. However $5$ bulbs were fused and had to be thrown away. The remaining were sold at Rs.$12$ each. Find the gain or loss $\% $.

Answer 1

Hint: We will substitute the given values into the gain and loss % formulas to get the required answer.
You must know that the gain percent
${\text{gain}}\% = \left( {\dfrac{{{\text{Selling price}} - {\text{Cost price}}}}{{{\text{Cost price}}}} \times 100} \right)\% $
${\text{loss}}\% = \left( {\dfrac{{{\text{Cost price}} - {\text{Selling price}}}}{{{\text{Cost price}}}} \times 100} \right)\% $
Use this formula, we will get answer

Complete step-by-step solution:
So, according to the question, there is a shopkeeper who purchased \[200\]bulbs and the price of one bulb which he had to pay is Rs.$10$ for one bulb. Now, he found that out of \[200\], $5$ bulbs were fused and $195$ are working.
So, from the above information, we can find how much shopkeepers spend to buy \[200\] bulbs which is also called cost price.
As we know that he purchased bulb for Rs.$10$, so total amount of purchasing \[200\]bulb is equal to
$
   = 200 \times 10 \\
   = 2000
 $
So, the cost price is equal to Rs.$2000$.
Now he found that out of $200$ bulbs, $5$ bulbs were fused and he threw that $5$ bulbs.
And he sells the remaining for Rs.$12$ each.
That means, he sells one bulb for Rs.$12$
Now he has a total $ = \left( {200 - 5} \right)$ bulb which is working.
Total working bulbs$ = 195$
Now he sells one bulb for Rs.$12$
So, total selling price$ = 12 \times 195 = 2340$
We got selling price Rs.$2340$
As we know that if the selling price is greater than cost price, the shopkeeper will get profit.
Here also, the selling price is greater than cost price, so we have to calculate the net gain percent.
As we know that the
gain$\% = $ (selling price – cost price)$ \div $(cost price)$ \times 100$
putting all values that we had found in this formula
net gain percent is
$
   = \dfrac{{\left( {2340 - 2000} \right)}}{{2000}} \times 100 \\
   = \dfrac{{340}}{{2000}} \times 100 \\
   = 17\%
 $

So the shopkeeper had $17\% $profit in selling these bulbs for Rs.$12$.

Note: Alternative Method:
Cost price of bulb$ = 200 \times 10 = 2000$
Selling price of bulb$ = 12 \times \left( {200 - 5} \right) = 12 \times 195 = 2340$
Now as selling price $ > $cost price
Shopkeeper gets profit
${\text{gain}}\% = \left( {\dfrac{{{\text{Selling price}} - {\text{Cost price}}}}{{{\text{Cost price}}}} \times 100} \right)\% $
$
   = \dfrac{{\left( {2340 - 2000} \right)}}{{2000}} \times 100 \\
   = \dfrac{{340}}{{20}} = 17\%
 $