Question

Sahil purchased an almirah for Rs 5200 and paid Rs 180 for its transportation. He also spent Rs 120 or painting and then sold it at a gain of 10%. Find the amount for which he sold the almirah if the selling price of 16 watches is equal to the cost price of 17 watches, find the gain percent.

Answer 1

Hint: First calculate the total cost price of an object and then apply the suitable condition to evaluate the different specified things.

Complete step-by-step answer:
As given in the question the cost of purchasing an almirah = Rs 5200.
The cost of transportation of almirah from shop to Sahil’s store = Rs 180.
The cost of painting of almirah with a colour to make it attractive = Rs 120.
Therefore, the total cost price after all the processing activities = 5200 + 180 + 120
                                                                                                                  = 5500.
Now to find the selling price we use the given gain percent.
$\begin{align}
  & Gain\%=\left( \dfrac{S.P}{C.P}-1 \right)\times 100 \\
  & \therefore 10=\dfrac{S.P-5500}{5500}\times 100 \\
 & S.P=\dfrac{1}{10}\times 5500+5500 \\
 & S.P=6050 \\
\end{align}$
Therefore, since the almirah is sold at a profit of 10%, the selling price of almirah is Rs 6050.
In the next part, we are required to calculate the gain percent for selling 16 watches at the price of purchasing 17 watches.
So, the ratio of selling price to cost price of watch can be expressed as:
$\dfrac{S.P}{C.P}=\dfrac{17}{16}$
The gain percent can be elaborated as $Gain%=\dfrac{S.P-C.P}{C.P}\times 100$
\[\begin{align}
  & Gain\%=\left( \dfrac{S.P}{C.P}-1 \right)\times 100 \\
 & =\left( \dfrac{17}{16}-1 \right)\times 100 \\
 & =\dfrac{100}{16} \\
 & =6.25\% \\
\end{align}\]
Therefore, the gain percent is 6.25.
So, Sahil sold the almirah for a price of Rs 6050 and for watches his gain percent is 6.25.

Note: The key concept involved in solving this problem is the knowledge of gain percent associated with the cost and selling price of an article. Concept clarity with a directive approach is required to simplify the problem statement into equations.