Question

If $ 60\% $ of a sum of money is $ Rs\,420 $ , what is the total sum of money?

Answer 1

Hint: In the given question, we are required to calculate the total amount of money whose $ 60\% $ corresponds to $ Rs\,420 $ . We must remember the formula for finding the percentage of a number as: $ Percentage = \dfrac{{Part}}{{Whole\,Sum}} \times 100\% $ . So, we first figure out the part and the percentage and then substitute the known values in the formula so as to find the missing amount.

Complete step-by-step answer:
In this specific question, we are given that $ 60\% $ of a sum of money is $ Rs\,420 $ .
So, let us assume that the whole sum of money is equal to $ Rs\,x $ . Then, we will calculate $ 60\% $ of this sum of money and equate it to the amount given to us as $ Rs\,420 $ so as to find the value of x.
Now, we will use the formula of percentage $ Percentage = \dfrac{{Part}}{{Whole\,Sum}} \times 100\% $ to form an equation for the situation in the variable x.
So, we get,
 $ \Rightarrow 60\% = \dfrac{{Rs\,420}}{{Rs\,x}} \times 100\% $
Now, we will use the method of transposition in order to shift the terms from one side of the equation to another. So, we isolate the variable x to find the value.
 Multiplying both sides of equation by x, we get,
 $ \Rightarrow 60x = 420 \times 100 $
Dividing both sides of equation by $ 60 $ , we get,
 $ \Rightarrow x = \dfrac{{420 \times 100}}{{60}} $
Cancelling the common factors in numerator and denominator, we get,
 $ \Rightarrow x = 7 \times 100 $
Simplifying the calculations,
 $ \Rightarrow x = 700 $
So, we get the total amount of money as $ Rs\,700 $ .
This is our required final answer for the given problem.
So, the correct answer is “$ Rs\,700 $”.

Note: We must know the formula for finding the percentage of a number to attempt the given question. Work as many problems as possible to crack these types of problems in a limited time period. Take care of the calculations in order to be sure of the final answer.