Question

A large watermelon weighs 20 kg with 96% of its weight being water. It is allowed to stand in the sun and some of the water evaporates, so that now only 95% of its weight is water. Its reduced weight will be:
a. $ 18 $ kg
b. $ 17 $ kg
c. $ 16.5 $ kg
d. $ 16 $ kg

Answer 1

Hint: We will use the unitary method for calculating the non-water content of the watermelon (what is left after $ 96\% $ of the content ) of $ 20 $ kg and then use the obtained result to calculate the non-water content of the watermelon (what is left after $ 95\% $ of the content ) of the unknown value to get our desired answer.
The unitary method involves the use of direct relation between two different quantities in which the increase and decrease of one unit affects the variation of the other unit.
 $ x\% $ of $ y $ is given by $ \dfrac{x}{{100}} \times y $ where $ x $ and $ y $ are known parameters.

Complete step-by-step answer:
Here we are given with the data that $ 20 $ kg watermelon contains $ 96\% $ of water in it.
So, the presence of non-water content in the watermelon is the remaining, that is $ (100 - 96)\% = 4\% $ of $ 20 $ kg.
So, by applying the the unitary method we can find out the weight of non-water content of the Watermelon as:
 $ 4\% $ of $ 20 $ kg , which is given by $ \dfrac{4}{{100}} \times 20 = 0.8 $ kg
As the watermelon is exposed to the sun, the water content inside the watermelon is reduced from the initial $ 96\% $ to $ 95\% $ of the total content.
So the left out or evaporated part of the watermelon must be the water content inside the watermelon.
The remaining portion now, that is $ (100 - 95)\% = 5\% $ must be composed of the $ 0.8 $ kg non-water content which we found earlier.
Assume it to be a finite quantity $ y $ kg.
Now 5% of $ y $ is equal to $ 0.8 $ kg, which mathematically means:
 $ \dfrac{5}{{100}} \times y = 0.8 $ kg
On cross multiplication of the above equation we get:
 $ y = 0.8 \times \dfrac{{100}}{5} $ kg
 $ \Rightarrow y = \dfrac{{80}}{5} = 16 $ kg
So, the reduced weight of the watermelon will be $ 16 $ kg.
So, the correct answer is “Option D”.

Note: There are 4 choices to address so, an alternative method is to use the hit and trial method which can be used to check individually all the four options to find option ‘d’ is correct.