A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
33
Understanding the Problem: Finding the Total Number of Notes
The question asks us to find the total number of notes a man has, given that he has an equal number of five, ten, and twenty rupee notes, and their total value is Rs. 385.
Let's break down the information given:
- Denominations of notes: Rs. 5, Rs. 10, and Rs. 20.
- Number of notes of each denomination is equal.
- Total value of all notes: Rs. 385.
We need to determine the count for each type of note first, and then sum them up to find the total number of notes.
Step-by-Step Solution to Find the Number of Notes
Let's assume the man has 'x' notes of each denomination. Since the number of notes for five, ten, and twenty rupee notes is equal, he has:
- x number of Rs. 5 notes
- x number of Rs. 10 notes
- x number of Rs. 20 notes
Now, let's calculate the total value contributed by each denomination:
- Value from Rs. 5 notes = Number of Rs. 5 notes × Value per note = \(x \times 5 = 5x\) rupees
- Value from Rs. 10 notes = Number of Rs. 10 notes × Value per note = \(x \times 10 = 10x\) rupees
- Value from Rs. 20 notes = Number of Rs. 20 notes × Value per note = \(x \times 20 = 20x\) rupees
The total value of all the notes is the sum of the values from each denomination. We are given that the total value is Rs. 385.
So, we can write an equation:
\(\text{Value from Rs. 5 notes} + \text{Value from Rs. 10 notes} + \text{Value from Rs. 20 notes} = \text{Total Value}\)
\(5x + 10x + 20x = 385\)
Now, let's combine the terms on the left side:
\((5 + 10 + 20)x = 385\)
\(35x = 385\)
To find the value of 'x', we need to divide the total value by the sum of the values of one note of each denomination:
\(x = \frac{385}{35}\)
Let's perform the division:
\(x = 11\)
So, the man has 11 notes of each denomination.
- Number of Rs. 5 notes = 11
- Number of Rs. 10 notes = 11
- Number of Rs. 20 notes = 11
The question asks for the total number of notes. The total number of notes is the sum of the number of notes of each denomination:
\(\text{Total number of notes} = \text{Number of Rs. 5 notes} + \text{Number of Rs. 10 notes} + \text{Number of Rs. 20 notes}\)
\(\text{Total number of notes} = x + x + x = 3x\)
Substituting the value of x = 11:
\(\text{Total number of notes} = 3 \times 11 = 33\)
Thus, the total number of notes the man has is 33.
Summary of the Calculation
| Denomination | Number of Notes (x) | Value (in Rs.) |
|---|---|---|
| Rs. 5 | x | 5x |
| Rs. 10 | x | 10x |
| Rs. 20 | x | 20x |
| Total | 3x | 35x |
We found that \(35x = 385\), which gave \(x = 11\). The total number of notes is \(3x = 3 \times 11 = 33\).
Revision Table - Understanding Note Problems
| Concept | Explanation | Example |
|---|---|---|
| Representing unknowns | Use variables (like 'x') for quantities you need to find, especially when they are equal or related. | If there are equal numbers of Rs. 5, Rs. 10, Rs. 20 notes, let the number of each be 'x'. |
| Calculating total value | Multiply the number of items by the value of each item for each category, then sum them up. | Total value = (Number of Rs. 5 notes × 5) + (Number of Rs. 10 notes × 10) + ... |
| Forming equations | Set the total calculated value equal to the given total value. | If total value is Rs. 385, then \(5x + 10x + 20x = 385\). |
| Solving linear equations | Combine like terms and isolate the variable using inverse operations. | \(35x = 385 \implies x = 385/35\). |
| Answering the specific question | Make sure to calculate exactly what the question asks for (e.g., total notes, not just the number of each type). | Question asks for total notes (3x), not just 'x'. |
Additional Information - Related Concepts
Problems involving different denominations of currency notes or coins are common in arithmetic and algebra. They often require setting up and solving linear equations based on the total number of items, their total value, or relationships between the quantities of different items.
- Coin Problems: Similar to note problems, these involve calculating the total value based on the number of coins of different denominations (e.g., 1 rupee coins, 2 rupee coins, 5 rupee coins).
- Age Problems: Another type of word problem where variables are used to represent unknown ages, and equations are formed based on given relationships between ages at different times (past, present, future).
- Mixture Problems: Involve combining different quantities with different properties (like price or concentration) and calculating the properties of the resulting mixture. Equations are formed based on the total quantity and the total value/property.
Practicing these types of problems helps in building skills in translating word problems into mathematical equations and solving them systematically.
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