Question

The difference between two selling prices of a T-shirt with profits of 4% and 5% respectively is Rs. 6. Find S.P of each T-shirt.

Answer 1

Hint: In this question it is given that the difference between two selling prices of a T-shirt with profits of 4% and 5% respectively is Rs. 6. We have ro find the S.P of each T-shirt. So to find the solution we need to know that the selling price, S.P=(C.P+profit).....(1)
Where, C.P is the cost price.
So after finding the S.P for different profit percentages and by subtracting we are able to get our required solution, i,e the cost price.

Complete step-by-step solution:
Let the C.P of the given T-shirt be Rs.x .
Now, when the profit percentage is 4%,
Then, profit = 4% of C.P=$$\dfrac{4}{100} x =\dfrac{4x}{100}$$
$$\therefore \text{S.P}_{1} =\text{C.P} +\text{profit}$$
   $$=x+\dfrac{4x}{100}$$
   $$=\dfrac{100x+4x}{100}$$
   $$=\dfrac{104x}{100}$$
Now when the profit percentage is 5%,
Then, profit = 5% of C.P=$$\dfrac{5}{100} x =\dfrac{5x}{100}$$
$$\therefore \text{S.P}_{2} =\text{C.P} +\text{profit}$$
   $$=x+\dfrac{5x}{100}$$
   $$=\dfrac{100x+5x}{100}$$
   $$=\dfrac{105x}{100}$$
Since, it is given that the difference between the two selling price is Rs. 6.
Therefore, we can write,
$$\text{S.P}_{2} -\text{S.P}_{1} =6$$
$$\Rightarrow \dfrac{105x}{100} -\dfrac{104x}{100} =6$$
$$\Rightarrow \dfrac{105x-104x}{100} =6$$
$$\Rightarrow \dfrac{x}{100} =6$$
$$\Rightarrow x=6\times 100$$
$$\Rightarrow x=600$$
Therefore, the C.P of the T-shirt= Rs.600
Now we have to find the selling prices,
So when profit is 4%,then S.P=$$\dfrac{104}{100} \times 600=104\times 6=624$$
And when profit is 5%, then S.P=$$\dfrac{105}{100} \times 600=105\times 6=630$$
Therefore, the selling prices are Rs.624 and Rs.630.

Note: While solving this type of problem you need to keep in mind some basic rules, which are:
If the cost price (C.P.) of the article is equal to the selling price (S.P.), then there is no loss or gain.
When C.P and gain percentage is given then we have to add the gain with C.P.
When C.P and loss percentage is given then we have to subtract the loss from C.P in order to get S.P.
And if r% be the gain or loss percentage, then gain or loss is equals to $$\dfrac{r}{100} \times \text{C.P}$$