Question

$ 3\,kg $ of rice can be served to $ 20 $ people. How much rice is required to serve $ 50 $ such people?
 $
  A.\,\,6.5\,kg \\
  B.\,\,4.5\,kg \\
  C.\,\,5.5\,kg \\
  D.\,7.5\,kg \\
  $

Answer 1

Hint: For this type of problems we use unitary methods. In this we first find the number of kg of rice is required for one person from given that $ 3\,kg $ of rice can serve to $ 20 $ people and then multiplying the result so obtained by number $ 50 $ to get required kg of rice is required to $ 50 $ such people.

Complete step-by-step answer:
Given,
 $ 3\,kg $ Of rice can be served to $ 20 $ people
To find the required solution to a given problem. We will use a unitary method.
In this method we first calculate how much kg of rice is required for $ 1 $ people.
For this we divide given $ 3\,kg $ of rice by number $ 20. $
Or we write it as:
 $ 20 $ people will be satisfied with $ 3\,kg $ of rice.
 $ 1 $ people will be satisfied in $ \dfrac{3}{{20}}\,kg $ of rice.
And hence for $ 50 $ such a person, how much rice is required. We can calculate the above equation by the number $ 50 $ .
Therefore, rice required for $ 50 $ people given as:
 $
\Rightarrow \dfrac{3}{{20}} \times 50 \\
   = \dfrac{{15}}{2} \\
   = 7.5 \;
  $
Therefore, from above we see that to serve $ 50 $ people it requires $ 7.5\,kg $ of rice.
So, the correct answer is “Option D”.

Note: We can also find the solution of a given problem in a ratio method. In this we first find the ratio of the number of people and equate it to the ratio of kg of rice by taking let ‘x’ kg of rice required for $ 20 $ such people and then on cross multiplying we can get the value of ‘x’ and so solve the given problem.