Question

Mr. Pankaj took Health Insurance Policy for his family and paid Rs. $ 900 $ as SGST. Find the total annual premium paid by him for this policy, rate of GST being $ 18\% . $

Answer 1

Hint: Here first of all we will find the rate of percentage for GST from SGST. Then the given data will find the amount of the policy and then will find the total annual premium from it. We will simply equate using the concepts of percentage.

Complete step-by-step answer:
Let us say that the basic amount without GST is $ = Rs.P $
Given that GST $ = 18\% $
SGST is half of the GST rate.
SGST $ = \dfrac{{18}}{2} $
Common factors from the numerator and the denominator cancel each other.
SGST $ = 9\% $
SGST in terms of amount –
SGST $ = \left( {\dfrac{9}{{100}}} \right)P $
Given that SGST $ = 900Rs. $ Place value in the above equation –
  $ 900 = \left( {\dfrac{9}{{100}}} \right)P $
Do-cross multiplication, where numerator of one side is multiplied with the denominator on the opposite side.
 $ \Rightarrow 900 \times 100 = 9P $
Simplify and make required value for “P” as the subject. When the term multiplicative at one side is moved to the opposite side then it goes to the denominator.
 $ \Rightarrow \dfrac{{900 \times 100}}{9} = P $
Simplify for the terms in the numerator of the equation –
 $ \Rightarrow \dfrac{{9 \times 100 \times 100}}{9} = P $
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
  $ \Rightarrow 100 \times 100 = P $
Simplify the above equation –
 $ \Rightarrow P = 10000\;Rs. $ .... (A)
Now, the basic policy amount is $ = Rs.\;{\text{10000}} $
GST paid $ = 18\% $
So, GST percentage of the amount
GST paid $ = \left( {\dfrac{{18}}{{100}}} \right) \times 10000 $
Common factors from the numerator and the denominator cancel each other.
GST paid $ = 18 \times 100 $
Simplify –
GST paid $ = 1800{\text{ Rs}}{\text{.}} $ .... (B)
From equation (A) and (B) –
Total Amount Paid $ = 10000 + 1800 $
Simplify by doing addition –
Total Amount Paid $ = Rs.\;11800 $
So, the correct answer is “ $ = Rs.\;11800 $ ”.

Note: Be good in multiples and simplify the equations using the basic concepts of mathematics. Percentage is the number or ratio expressed as a fraction of hundred. Know the difference between the fraction and the percentage and apply accordingly.