Question

140 litres of an acid contains 90% of acid and rest water. The amount of water added to make the water 12.5% of the resulting mixture is:
(a) 5 litres
(b) 4 litres
(c) 3 litres
(d) none

Answer 1

Hint: To solve this problem, we will assume that x litres of water is added to the mixture. Now, in the final solution there is 87.5% acid $\left( 100-12.5=87.5\% \right)$. Thus, since the amount of acid remains conserved, we can simply balance the amount of acid in the initial and final solution to get the value of x.

Complete step-by-step answer:
A percentage is a number or ratio that can be expressed as a fraction of 100, which means, a part per hundred. The word percent means per 100. We can easily find any percentage using the formula of percentage which is:
$\text{Percentage}=\left( \dfrac{\text{Percentage of quantity}}{\text{Total quantity}} \right)\times 100$
It is represented by the symbol “%”. Percentages have no dimension, hence are dimensionless numbers. If we say, 50% of a number, then it means 50 percent of its whole.
Percentage Formula- To determine the percentage, we have to divide the numerator by denominator and then multiply the resultant to 100.
$\text{Percentage}=\left( \dfrac{\text{Percentage of quantity}}{\text{Total quantity}} \right)\times 100$
Example: $\dfrac{2}{5}\times 100=0.4\times 100=40\text{ percent}$
To calculate the percentage of a number, we need to use a different formula such as:
$\text{P }\!\!\%\!\!\text{ of number}=\text{X}$
where X is the required percentage.
If we remove the % sign, then we need to express the above formulas as;
$\dfrac{\text{P}}{100}\left( \text{Number} \right)=X$
Let us now consider the given question,
Let the amount of water required be x.
 When the water amount is increased to 12.5%, the acid amount
$100-12.5=87.5\%$
$\begin{align}
  & \left( \dfrac{90}{100} \right)\times 140=\left( \dfrac{87.5}{100} \right)\times \left( x+140 \right) \\
 & \Rightarrow 126=0.875x+122.5 \\
 & \Rightarrow 126-122.5=0.875x \\
 & \Rightarrow 3.5=0.875x \\
 & \Rightarrow x=4 \\
\end{align}$
$x=4$ litres of water added.

Hence, the answer is 4 litres.

Therefore, the final answer is (b).

Note: Another way to solve this problem is by assuming it analogous to conservation of species. According to this, in our case, since there is no change to acid amount (there is only change to acid percentage not amount), we can balance the initial acid amount with the final amount. This principle is not directly applicable for water since; some amount of water is added to the initial solution afterwards.