Question

On selling an almirah for $Rs\,20350$ , a man gains $10\% $ . what percent does he gain on selling same for Rs $19610?$

Answer 1

Hint: In the above question we have been given the selling price of the almirah and the gain percent. We can find the cost price from this. After that, we will use the formula of the gain percent to calculate the value. We can calculate the profit by subtracting the value of the cost price of almirah from the selling price of the almirah.

Formula used:
$gain\% = \dfrac{{profit}}{{C.P}} \times 100$

Complete step-by-step answer:
Here we have been given the selling price of almirah $Rs20350$ .
We also have the gain percent i.e.
$10\% $
So this gain can be written as
$ \Rightarrow (100 + 10)\% = 110\% $
We can write the expression as
$ \Rightarrow 110\% $ of C.P is $Rs\,20350$
We know that in mathematical terms “of” means to multiply.
So we will now simplify the above equation and find the value of cost price i.e.
$ \Rightarrow \dfrac{{110}}{{100}} \times C.P = 20350$
It can be simplified as:
$ \Rightarrow C.P = \dfrac{{20350 \times 100}}{{110}}$
It gives us the value of cost price of the almirah i.e.
$C.P = 18500$
Now we have the selling price and the cost price.
We can calculate the profit by subtracting the cost price of almirah from the selling price.
Therefore we have profit as:
$19610 - 18500$
It gives us the value of profit on selling the almirah i.e.
$Rs\,1110$
Now we will substitute the value in the formula of the gain percent and it gives us:
$ \Rightarrow gain\% = \dfrac{{1110}}{{18500}} \times 100$
On simplifying the value it gives us
$ \Rightarrow gain\% = 6$
Hence on selling the same almirah for $Rs\,19610$ , the gain percent will be $6\% $ .

Note: We should note that in these types of questions, we should always remember the basic formulas to solve. If we have to calculate the loss then we can subtract the selling price of the product from the cost price.
Its formula can be written as
$Loss = C.P - S.P$ .
Similarly, if we have to find the value of loss percentage then its formula can be written as;
$Loss\% = \dfrac{{loss}}{{C.P}} \times 100$