Question

A man has 480 rupees in the denominations of one rupee notes, five rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
 $
  {\text{A}}{\text{. 90}} \\
  {\text{B}}{\text{. 75}} \\
  {\text{C}}{\text{. 45}} \\
  {\text{D}}{\text{. 60}} \\
 $

Answer 1

Hint: In order to find the total number of notes he has, we consider the number of one, five and ten rupee notes to be variable x, as it is given all three notes are equal in number. Now we form a relation using the total amount the man has and the variable and solve it for an answer.

Complete step-by-step answer:
Given Data,
The total amount is 480 rupees in terms of one, five and ten rupee notes.
Also the number of notes of each denomination is equal.

Let us consider the number of notes the man has be a variable ‘x’.
So according to the question the man has x one rupee notes, x five rupee notes and x ten rupee notes.

Also it is said that the total value of money the man has is 480 rupees.
Therefore we make a relation between this, it is given by
⟹ x (1) + x (5) + x (10) = 480
⟹ x + 5x + 10x = 480
⟹ 16x = 480
 $
   \Rightarrow {\text{x = }}\dfrac{{480}}{{16}} \\
   \Rightarrow {\text{x = 30}} \\
 $

Therefore the man has 30 one rupee notes, 30 five rupee notes and 30 ten rupee notes.
So the total number of notes the man has is equal to 30 + 30 + 30 = 90 Notes.

Option A is the correct answer.

Note: In order to solve this type of question the key is to know how to relate the two given conditions in the question, i.e. the total amount of money and equal number of notes of each denomination.
Once we make this relation, we just solve for the variable to determine the answer.
We can also check the answer obtained by just substituting the value obtained in the given relation. We got the number of notes to be 30, so let’s check if it makes a sum of 480 rupees.
30 × 1 rupee notes = 30 rupees.
30 × 5 rupee notes = 150 rupees.
30 × 10 rupee notes = 300 rupees.
So that’s a total of 30 + 150 + 300 = 480 rupees.
Hence proved.