Question

If p lb. of salt is dissolved in q lb. of water, the percent of salt in the resulting solution is
 (a) $\dfrac{100p}{p+q}$
(b) $\dfrac{p}{p+q}$
(c) $\dfrac{100q}{p+q}$
(d) none of these

Answer 1

Hint: In order to solve this question, we need to find the ratio of the amount of salt present after the mixing process to the total amount of the solution. Then, in order to find the percentage, we need to multiply the final ratio by 100.

Complete step by step answer:
In this problem, we are mixing salt in water.
We are given that p lb. of salt is mixed in q lb. of water.
In short, we are adding p lb. of salt in q lb. of water.
Hence, the total mixture of water becomes (p + q) lb. of water.
Now we need to find the percent of salt in the solution.
For this, we need to take the ratio of the current weight of salt to the total weight of the current solution.
The ratio comes out to be $\dfrac{p}{p+q}$ .
This ratio gives how many parts of the solution contains salt.
Now, we need to find the percentage of the ratio.
Percentage of the ratio gives the ratio out of 100.
We do not use any information; it becomes easier to keep the reference as 100.
Now, by taking the reference we get,
Percentage of salt in the current solution = $\dfrac{p}{p+q}\times 100$ .
Rearranging the terms, we get,
The percentage of salt in the current solution = $\dfrac{100p}{p+q}$ .

So, the correct answer is “Option a”.

Note: In this option, we need to find the ratio of the salt to the current solution. Hence, there will always be p in the numerator because it represents the quantity of the salt. So, we can eliminate the option (c). Also, we are asked to find the percentage of salt. So, we need to multiply by 100 and hence, there will be 100 in the numerator. This eliminates the option (b).