Question

Is the following statement true?
40 persons : 200 persons = Rs. 15: Rs.75
A) True
B) False

Answer 1

Hint: To solve the question, we have to calculate the given ratios separately in order to reach the right answer. Factorize the larger number of ratios in terms of the smaller number, to ease the procedure of solving.

Complete step-by-step answer:
The LHS of the given expression is 40 persons : 200 persons
 The factorization of 200
\[\begin{align}
  & =2\times 100 \\
 & =2\times 4\times 25 \\
 & =2\times 4\times 5\times 5 \\
 & =10\times 4\times 5 \\
 & =40\times 5 \\
\end{align}\]
By substituting the value of 200 in the LHS of the given expression, we get
 40 persons : 200 persons \[=40:200=40:(40\times 5)\]
The expression can also be written as the following
\[40:(40\times 5)=\dfrac{40}{40\times 5}\]
\[=\dfrac{1}{5}\]
= 1 : 5
Thus, the LHS of the given expression 40 persons : 200 persons is equal to 1 : 5
The RHS of the given expression is Rs. 15: Rs.75
 The factorization of 75 \[=5\times 15\]
By substituting the value of 75 in the RHS of the given expression, we get
 Rs. 15: Rs.75 \[=15:75=15:(15\times 5)\]
The expression can also be written as the following
\[15:(15\times 5)=\dfrac{15}{15\times 5}\]
\[=\dfrac{1}{5}\]
= 1 : 5
Thus, the RHS of the given expression Rs. 15: Rs.75 is equal to 1 : 5
LHS of the given expression = RHS of the given expression
\[\therefore \] 40 persons : 200 persons = Rs. 15: Rs.75
The given statement is true.
Hence, option (a) is the right choice.

Note: The possibility of mistake can be stating the given statement is false considering that 15 is not a factor of 40 and 75 is not a factor of 200. The other possibility of mistake can be not factorizing the numbers, which ease the procedure of solving.