# Radha earns $ 22\% $ of her investment. If she earns Rs. $ 187 $ , then how much did she invest?

Answer

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**Hint**: First of all we will assume the unknown investment be “x” then will frame the equation with $ 22\% $ of her investment which is equal to Rs. $ 187 $ then will make subject “x” and simplify for the required resultant value.

**:**

__Complete step-by-step answer__Let us assume that Radha invested Rs. “x”

Given that: Radha earns $ 22\% $ of her investment which is equal to Rs. $ 187 $ ,

Frame the mathematical equation with reference to the above word statement.

$ 22\% $ of “x” $ = 187 $

Here is a suggested multiplication operator.

$ 22\% \times x = 187 $

Percentage is expressed as the fraction where the denominator is hundred.

\[\dfrac{{22x}}{{100}} = 187\]

Make “x” the subject and perform cross multiplication where the denominator is multiplied with the numerator of the opposite side and the numerator is multiplied with the denominator of the opposite side.

$ x = \dfrac{{187 \times 100}}{{22}} $

Find the common factors from the numerator and the denominator and remove them.

$ x = \dfrac{{17 \times 11 \times 2 \times 50}}{{2 \times 11}} $

Common factors from the numerator and the denominator cancels each other.

$ x = 17 \times 50 $

Simplify the above expression finding the product of the term

$ x = 850 $ Rs.

Hence, the Radha had invested Rs. $ 850 $

**So, the correct answer is “ Rs. $ 850 $ ”.**

**Note**: lways read the word statement and frame the mathematical expression correctly. Remember and note that “of'' operator means multiplication. Also note that sometimes the language of the question is the given percent and thus used the “of” operator. Here suggests multiplication. Fractions are defined as the part of the whole. Generally, it represents any number of equal parts and it describes the part from a certain size and expressed as the numerator upon the denominator. Know the difference between the fraction and the percentage and apply accordingly.

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