# The value of $ 0.15\% $ of $ 33\dfrac{1}{3}\% $ of $ Rs\,10,000 $ is ?

(A) $ Rs\,0.05 $

(B) $ Rs\,5 $

(C) $ Rs\,105 $

(D) $ Rs\,150 $

Last updated date: 20th Mar 2023

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**Hint**: The given question requires us to find a specific percentage of a given number. To solve this problem, we need to know how to write a number in percentage. We have to follow the method to find the percentage of the given number two times in order to get to the final answer. Such questions require accuracy in arithmetic.

**:**

__Complete step-by-step answer__Let’s consider the given problem. We have to find $ 0.15\% $ of $ 33\dfrac{1}{3}\% $ of $ Rs\,10,000 $ .

First let us assume $ 33\dfrac{1}{3}\% $ of $ Rs\,10,000 $ to be x.

So, we will have to first convert the mixed fraction percentage to improper fraction percentage in order to find the value of x.

Mixed fractions are those fractions that have an integral value along with the fraction consisting of the numerator and denominator.

The fraction \[\left( {33\dfrac{1}{3}} \right)\] is a mixed fraction.

A mixed fraction $ \left( {x\dfrac{a}{b}} \right) $ can also be represented as $ \left( {\dfrac{{xb + a}}{b}} \right) $ .

So, we can convert the mixed fraction \[\left( {33\dfrac{1}{3}} \right)\] into improper fraction as \[\left( {\dfrac{{33 \times 3 + 1}}{3}} \right) = \dfrac{{100}}{3}\].

So, now we have to calculate $ \dfrac{{100}}{3}\% $ of $ Rs\,10,000 $ in order to find the value of x.

So, we get, $ x = \dfrac{{100}}{3}\% $ of $ Rs\,10,000 $

Then, $ x = \dfrac{{100}}{{300}} \times Rs\,10,000 $ .

Now, cancelling the common factors in numerator and denominator, we get,

$ \Rightarrow x = \dfrac{1}{3} \times Rs\,10,000 = Rs\dfrac{{\,10,000}}{3} $

So, we get the value of x as $ Rs\dfrac{{\,10,000}}{3} $ .

Now, we have to find $ 0.15\% $ of $ x = Rs\dfrac{{\,10,000}}{3} $ .

Let us assume y to be $ 0.15\% $ of $ Rs\dfrac{{\,10,000}}{3} $

So, we get, $ y = 0.15\% $ of $ Rs\dfrac{{\,10,000}}{3} $ .

$ \Rightarrow y = \dfrac{{0.15}}{{100}} \times Rs\,\dfrac{{10,000}}{3} $

Simplifying the expression, we get,

$ \Rightarrow y = \dfrac{{15}}{{10,000}} \times Rs\,\dfrac{{10,000}}{3} $

Cancelling the common factors in numerator and denominator, we get,

$ \Rightarrow y = Rs\,5 $

Hence, we get the value of $ 0.15\% $ of $ 33\dfrac{1}{3}\% $ of $ Rs\,10,000 $ as $ Rs\,5 $ .

Hence, option (B) is correct.

**So, the correct answer is “Option B”.**

**Note**: It is better to workout with the above-mentioned method and after solving a number of problems in this model, one can consider the method involving the unitary method. Solving problems by the unitary method needs better understanding in the concept of percentage. While solving such a problem using a unitary method, we consider the given number as $ 100\% $ of itself and then find out the desired percentage of the number. Work as many problems as possible to crack these types of problems in a limited time period.

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