Question

Three items are purchased at Rs. 450 each. One of them is sold at a loss of \[10\% \] . The other two are sold as to gain \[20\% \] on the whole transaction. What is the gain \[\% \] on these two items?
A. \[30\% \]
B. \[35\% \]
C. \[25\% \]
D. \[20\% \]

Answer 1

Hint:
First of we will try to find the loss in that one product, then we will take a new variable let us say k and we will assume it to be the profit amount on the other two items needed to gain an overall profit of \[20 \% \], then we will solve for the variable k and then we will try to find the profit over those two items separately.

Complete step by step solution:
First, we will find the loss amount occurred in that one product
 \[10\% \] of Rs.450
 Loss amount $ = \dfrac{{10}}{{100}}(450) = 45$
Now the amount in which the first item was sold is price of first item – loss amount
Selling price of first item $ = 450 - 45 = 405$
Now let the profit in which the other two items are sold be Rs. k , so according to the question, the selling price of the other two items is such that the overall profit is maintained as \[20\% \] .
So overall selling price of all the three items is Rs. \[(450 + 450 + 405 + k)\; = \,Rs.\,1305 + k\]
Total purchased price of the three items is Rs. \[(450 + 450 + 450) = \] Rs.1350
So, profit $\% = \left( {\dfrac{{selling\,\,price - purchased\,price}}{{purchased\,\,price}}} \right)100$
On substituting the values, we get,
 $ \Rightarrow profit\% = \left( {\dfrac{{1305 + k - 1350}}{{1350}}} \right)100$
Now according to question overall profit is \[20\% \] so
 $ \Rightarrow \left( {\dfrac{{1305 + k - 1350}}{{1350}}} \right)100 = \left( {\dfrac{{20}}{{100}}} \right)100$
On simplification we get,
 $ \Rightarrow \left( {\dfrac{{k - 45}}{{1350}}} \right)100 = 20$
On dividing the equation by 100 we get,
 $ \Rightarrow \left( {\dfrac{{k - 45}}{{1350}}} \right) = \dfrac{2}{{10}}$
On multiplying the equation by 1350 we get,
 $ \Rightarrow k - 45 = 2 \times 135$
On simplification we get,
  $ \Rightarrow k - 45 = 270$
On adding 45 on both sides we get,
 $ \Rightarrow k = 270 + 45$
Hence, we have,
 $ \Rightarrow k = 315$
Now gain \[\% \] over the two items sold is $\dfrac{{profit\,\,amount\,\,of\,\,sold\,\,two\,\,items}}{{purchased\,\,amount\,\,of\,\,the\,\,two\,\,items}} \times 100$
Profit amount of sold two items is 315
Purchased amount of the two items \[ = 450 + 450 = 900\]
So, gain \[\% \] is $\dfrac{{315}}{{900}} \times 100 = 25\% $

So, the correct option is C.

Note:
First of all, find the loss amount or the profit amount mentioned in these types of questions.
Then find the selling price of the items, then follow the instructions given in the question that is if the amount that is to be found is of any particular item or overall price and then finally do the calculations to get the answer.