Math Problem Statement

A person has Rs.640 worth of Rs.1, Rs.5 and Rs.10 notes. The number of each type of note is equal. What is the total number of notes to him?

Solution

To solve this, let the number of each type of note be xx. Then:

  • The total value of xx notes of Rs.1 is 1x=x1 \cdot x = x.
  • The total value of xx notes of Rs.5 is 5x=5x5 \cdot x = 5x.
  • The total value of xx notes of Rs.10 is 10x=10x10 \cdot x = 10x.

The total value of all the notes is given as Rs.640. Therefore, we can write:

x+5x+10x=640x + 5x + 10x = 640

Simplify the equation:

16x=64016x = 640

Solve for xx:

x=64016=40x = \frac{640}{16} = 40

Thus, the total number of notes is:

3x=340=1203x = 3 \cdot 40 = 120

Final Answer:

The total number of notes is 120.


Would you like me to provide a breakdown of related concepts or solve variations of this problem? Here are some related questions for practice:

  1. If the number of Rs.5 notes was doubled, what would the new total value be?
  2. What is the total value if the number of Rs.1 notes is halved?
  3. If the total value of Rs.1 notes is Rs.50, how many Rs.5 and Rs.10 notes are there?
  4. What would the total number of notes be if the total value increased to Rs.960 while keeping the number of each type of note equal?
  5. How would the calculation change if there were twice as many Rs.10 notes as Rs.1 and Rs.5 notes?

Tip:

When dealing with equal proportions or uniform distribution, always start by representing each category with a variable and express the problem mathematically.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Arithmetic

Formulas

Total value = Sum of individual values
x + 5x + 10x = Total value

Theorems

Basic Arithmetic and Linear Equation Solving

Suitable Grade Level

Grades 6-8