A sum of Rs 8400 is made up of 50,20,10 and 5 rupee notes.The number of 10 rupee notes is five times the number of 5 rupee notes, four times the number of 20 rupee notes and ten times the number of 50 rupee notes.What is the number of notes in each denominator?
Homework Posting Tips
Please show your work. Tutors will not do your homework for you. Please show your work for any question that you are posting.
To solve this problem, we can assign variables to represent the number of each type of note. Let's say:
Let x = number of 50-rupee notes
Let y = number of 20-rupee notes
Let z = number of 10-rupee notes
Let w = number of 5-rupee notes
According to the given information, we can form the following equations:
Equation 1: x + y + z + w = total number of notes
Equation 2: 50x + 20y + 10z + 5w = 8400
Equation 3: z = 10w (the number of 10 rupee notes is ten times the number of 50 rupee notes)
Equation 4: z = 4y (the number of 10 rupee notes is four times the number of 20 rupee notes)
Equation 5: z = 5w (the number of 10 rupee notes is five times the number of 5 rupee notes)
Now we can solve these equations simultaneously. Let's substitute equations 3, 4, and 5 into equation 1:
x + y + (10w) + w = total number of notes
x + y + 11w = total number of notes
We can further simplify this equation to:
x + y + 11w = total number of notes --> Equation 6
Substituting equations 3, 4, and 5 into equation 2:
50x + 20y + (10z) + 5w = 8400
50x + 20y + (10 * 4y) + 5w = 8400 --> Equation 7
Now let's solve this system of equations (equations 6 and 7) using substitution or elimination method to find the values of x, y, z, and w.