Question

By selling a machine for Rs. 27000, Juhi lost 10 on it. At what price should she sell to gain 5%?

Answer 1

Hint: We need to remember that the cost price is the main junction between two types of selling values. From the given values of selling price and lost percentage, we find the cost price. Then we find the selling price of the machine with a $5\%$ gain to find the solution to the problem.

Complete step-by-step solution:
Let’s assume Juhi bought the machine for Rs. x. She lost $10\%$ when she sold the machine for Rs. 27000.
Based on the cost price and the loss percentage we can find the selling price which is
$x\left( 1-\dfrac{10}{100} \right)=\dfrac{9x}{10}$. This will be equal to 27000. We equate them and get
$\dfrac{9x}{10}=27000\Rightarrow x=\dfrac{27000\times 10}{9}=30000$.
So, the price of the machine is Rs. 30000.
Now we need to sell it at such a price that she gains $5\%$ on it.
She gains 5% on the actual price of Rs. 30000.
So, the selling price will be $30000\left( 1+\dfrac{5}{100} \right)=\dfrac{30000\times 105}{100}=31500$.
Therefore, Juhi needs to sell the machine at Rs. 31500.

Note: We can use another variable to form a two-variable equation to solve the problem. We would have taken that the selling price to gain $5\%$ is y. Then we have used the formula to find the gain percentage to equate with 5. Also, we could have used a formula of 100 instead of a variable to find the solution.