Question

Mr. Sinha sold two tape-recorders for \[Rs.{\text{ }}990\] each; gaining \[10\% \] on one and losing \[10\% \] on the other. Find his total loss or gain, as percent, on the whole transaction.

Answer 1

Hint: In this question we have to find the percentage of total loss or gain in this whole sales transaction. For this they give selling cost of the tape-recorders and percentage gain and loss respectively. To solve this problem, at first, we will find the cost price of both the tape-recorders separately.
Next, we will find the total CP and SP and we will compare the transaction. If SP is more than CP, there will be gain, otherwise loss. If both SP and CP are the same, there will be no gain or loss.

Complete step-by-step answer:
It is given that; the two tape-recorders for \[Rs.{\text{ }}990\] each; gaining \[10\% \] on one and losing \[10\% \] on the other.
We have to find the total loss or gain on the whole transaction.
Here, S.P. be the selling price and C.P. be the cost price.
We find the loss and gain amount for both the tape-recorder separately.
For the first tape-recorder there is \[10\% \] gain.
We know that,
\[{\text{Profit}}\% = \dfrac{{SP - CP}}{{CP}} \times 100\]
Substitute the values we get,
\[ \Rightarrow \dfrac{{990 - CP}}{{CP}} \times 100 = 10\]
Simplifying we get,
\[ \Rightarrow 99000 - 100CP = 10CP\]
Simplifying again we get,
\[ \Rightarrow 99000 = 110CP\]
Simplifying again we get,
\[ \Rightarrow CP = 900\]
For the second tape-recorder there is \[10\% \] loss.
We know that,
\[{\text{Loss}}\% = \dfrac{{CP - SP}}{{CP}} \times 100\]
Substitute the values we get,
\[ \Rightarrow \dfrac{{CP - 990}}{{900}} \times 100 = 10\]
Simplifying we get,
\[ \Rightarrow CP - 990 = 90\]
Simplifying again we get,
\[ \Rightarrow CP = 990 + 90\]
Simplifying again we get,
\[ \Rightarrow CP = 1080\]
So, the total cost price is \[{\text{Rs}}.{\text{ }}1080 + 900 = {\text{ Rs}}{\text{. 1980}}\]
Total selling price is \[{\text{Rs}}{\text{. }}990 + 990 = {\text{Rs}}.{\text{ 1980}}\]
Here, the cost price and the selling price are the same. So, there is no gain or no loss.

Note: The amount that a customer pays to buy a product is called a selling Price. It is abbreviated as S. P.
Cost Price is the price at which an article is purchased by the buyer. It is abbreviated as C. P.
If the cost price is less than the selling price, there will be gain or profit. Otherwise there will be loss.