Question

A man has Rs. 480 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?
A.45
B.60
C.75
D.90

Answer 1

Hint: Equality is the general relationship between two or more quantities. It basically tells the changes occurred when any of the quantity is changed.
In the question, the total values of the notes are dependent upon the number of notes of each denomination and if any of the numbers of the notes are changed then the total values of the coin will change accordingly. Here, we need to calculate the total number of notes the man has for which we need to calculate the number of notes of each denomination and add them to get the result.


Complete step by step solution:
The total amount that man has is Rs. 480 which is the total sum of values of one-rupee notes, five-rupee notes, and ten-rupee notes.
According to the question, the number of notes of each denomination is equal. So, let us assume the number of each note to \[x\].
Product of the value of the note with the number of the notes gives the total currency value. So, we can express this as \[1x + 5x + 10x = 480\].
Where \[x\]is the number of notes and 1, 5, 10 being their values, hence the number of notes will be:
\[
  1x + 5x + 10x = 480 \\
  16x = 480 \\
  x = \dfrac{{480}}{{16}} \\
  x = 30 \\
 \]
Hence, we can say there are a total of 90 notes as 30 being each.


Note: Total value of the sum is dependent on the number of each note if the number of notes is changed then the total value of the sum will change. Alternatively, we can check our answer as:
One-rupee note\[ = 1 \times x = 1 \times 30 = Rs.30\],
Five-rupee note \[ = 5 \times x = 5 \times 30 = Rs.150\]
Ten-rupee note \[ = 10 \times x = 10 \times 30 = Rs.300\]
Total \[ = 1x + 5x + 10x = 30 + 150 + 300 = Rs.480\]