Question

How much pure alcohol should be added to 400ml of strength 15% to make its strength 32%?
A) 50ml
B) 75ml
C) 100ml
D) 150ml

Answer 1

Hint:
Here, we have to find the amount of pure alcohol that should be added to the solution to make its strength greater than the older strength. First we have to find the amount of alcohol present in the solution at first with the strength at first. With the amount at first we have to find the amount of solution at last with the given strength. Percentage is the ratio or number expressed as a fraction of 100.

Formula Used:
Percentage can be calculated by the formula \[Percentage = \dfrac{x}{n} \times 100\% \] where \[x\] is the value to which the percentage is calculated and \[n\] is the total amount.

Complete step by step solution:
We are given a 400ml solution with strength 15%.
Percentage can be calculated by the formula \[Percentage = \dfrac{x}{n} \times 100\% \]
By using the formula and rewriting the formula, we get
\[ \Rightarrow \] The amount of alcohol in 400ml solution of 15% strength\[ = \dfrac{{15}}{{100}} \times 400ml\]
Dividing both the terms, we get
\[ \Rightarrow \] The amount of alcohol in 400ml solution of 15% strength\[ = 15 \times 4ml\]
Multiplying the numbers, we get
\[ \Rightarrow \] The amount of alcohol in 400ml solution of 15% strength\[ = 60ml\]
Let the required amount of alcohol be added to the solution to make its strength 32%\[ = x{\rm{ }}ml\].
It will increase the amount of the solution by \[x{\rm{ }}ml\].
So, the amount of alcohol now \[ = (60 + x)ml\]
and the amount of the solution\[ = (400 + x)ml\]
Then, the strength\[ = 32\% \]
Percentage can be calculated by the formula \[Percentage = \dfrac{x}{n} \times 100\% \]
By using the formula and rewriting the formula, we get
\[ \Rightarrow \dfrac{{(60 + x)}}{{(400 + x)}} = \dfrac{{32}}{{100}}\]

By cross multiplying, we get
\[ \Rightarrow 100(60 + x) = 32(400 + x)\]
Multiplying the terms, we get
\[ \Rightarrow 6000 + 100x = 12800 + 32x\]
Rewriting the equation, we get
\[ \Rightarrow 100x - 32x = 12800 - 6000\]
Subtracting the terms, we get
\[ \Rightarrow 68x = 6800\]
Dividing both the terms, we get
\[ \Rightarrow x = \dfrac{{6800}}{{68}}\]
\[ \Rightarrow x = 100ml\]

Therefore, the amount of solution that should be added to make its strength 32% is 100ml.

Note:
We should note that the increase or the decrease is always on the original quantity. If the increase or decrease is given in absolute and the percentage increase or decrease is to be calculated, then the following formula is applied to do so. \[\% {\rm{ }}increase{\rm{ }} = {\rm{ }}100{\rm{ }} \times {\rm{ }}\dfrac{{Quantity\,{\rm{ }}increase}}{{original\,{\rm{ }}quantity}}\] . But this can be applied only when the original quantity is also given in absolute.