Question

Which is greater, \[15\% \] of Rs 6,000 or \[10\% \] of Rs 7,000 and by how much?

Answer 1

Hint: Here, we have to find a comparison between the given two quantities. We will find the value for the given two quantities by using the percentage formula. Then by the arithmetic operation of subtraction, we will find the difference between these two quantities. Subtraction is defined as the removing a particular from the collection of a larger number of objects.

Formula Used:
If we are given the percentage \[P\] % of the total \[x\] , then the quantity for the percentage \[y\] is given by \[y = P\% \times x\]

Complete step-by-step answer:
First, We will find \[15\% \] of Rs 6,000.
Let \[x\] be the value of \[15\% \] of Rs 6,000.
\[x = 15\% \] of Rs. 6,000
\[ \Rightarrow x = \dfrac{{15}}{{100}} \times {\rm{Rs}}.6000\]
By dividing the terms, we get
\[ \Rightarrow x = 15 \times {\rm{Rs}}.60\]
\[ \Rightarrow x = {\rm{Rs}}.900\]
So, the value of \[15\% \] of Rs 6,000 is \[Rs.900\]
Now, we will find the value of \[10\% \] of Rs. 7,000.
Let \[y\] be the value of \[10\% \] of Rs 7,000.
\[y = 10\% \] of Rs 7,000
\[ \Rightarrow y = \dfrac{{10}}{{100}} \times {\rm{Rs}}.7000\]
By dividing the term, we get
\[ \Rightarrow y = 10 \times {\rm{Rs}}.70\]
Multiplying the terms, we get
\[ \Rightarrow y = {\rm{Rs}}.700\]
So, the value of \[10\% \] of Rs 7,000 is Rs 700.
Now, we will find the greater of \[15\% \] of Rs 6,000 or \[10\% \] of Rs 7,000.
So, by comparison, we get
\[{\rm{Rs}}.900 > {\rm{Rs}}.700\]
\[ \Rightarrow 15\% \] of Rs 6000 \[ > 10\% \] of Rs 7000
Now, we will find the difference between these two expressions by subtracting the lesser number from the greater number.
 \[ \Rightarrow 15\% \] of Rs 6000 \[ - 10\% \] of Rs 7000 \[ = {\rm{Rs}}.900 - {\rm{Rs}}.700\]
 \[ \Rightarrow 15\% \] of Rs 6000 \[ - 10\% \] of Rs 7000 \[ = {\rm{Rs}}.200\]
Therefore, the \[15\% \] of Rs 6,000 is greater than \[10\% \] of Rs 7,000 and by Rs 200.


Note: The comparison of two quantities can be represented by the greater than or lesser than symbols. We often get confused with the symbols of these comparisons. Greater than (\[ > \]) can be remembered by the alligator method. We know that the crocodiles always eat the larger number of fishes, so that the symbol would be the crocodile’s opening of its mouth. Less than \[ < \] is remembered by the L- method, since the less than starts with the letter L. We should find the difference between these comparisons too.