Question

One litre of water is evaporated from $ 6 $ litres of a solution containing 5% salt. The percentage of salt in the remaining solution is:
A. $ 4\% $
B. $ 5\% $
C. $ 6\% $
D.None of these

Answer 1

Hint: Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from a certain size whereas percentage is the number or ratio expressed as a fraction of a hundred. Know the difference between the fraction and the percentage and apply accordingly.

Complete step-by-step answer:
Given that - One litre of water is evaporated from $ 6 $ litres of a solution containing salt
Therefore, salt in $ 6 $ litres $ = 5\% $ of $ 6 $ litres.
It can be expressed as –
 $ = \left( {\dfrac{5}{{100}} \times 6} \right) $
Simplify the above equation –
 $ = \left( {\dfrac{{30}}{{100}}} \right) $
Convert the above fraction in the decimal form-
 $ = 0.03 $
Now, Salt in new solution is
 $ = \left( {\dfrac{{0.03}}{5} \times 100} \right) $
Simplify the above equation-
 $ = \left( {\dfrac{{0.03 \times 20 \times 5}}{5}} \right) $
Common multiple from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
 $ = \left( {0.03 \times 20} \right) $
 $ = 6\% $
So, the correct answer is “Option C”.

Note: Be very good in multiples and simplification of the numbers. Always remember that the common multiples from the numerator and the denominator cancel each other. Multiples of the numbers are infinite; there is no end for the multiples of any number. Always remember that the first twenty multiples of the numbers till $ 20 $ at least. In the fraction, in denominator if we have ten then while converting into decimal point shift one point from right and similarly if there is hundred then shift two points from the right.