The ratio of salary of P, Q and R is 5 ∶ 6 ∶ 8. If R gets Rs. 2200 more than Q, then what is the salary of P?
Rs. 5500
Solving Salary Ratio Problems
This problem involves finding the salary of a person (P) given the ratio of salaries of three people (P, Q, R) and the difference in salary between two of them (R and Q).
Understanding the Salary Ratio
The ratio of the salaries of P, Q, and R is given as 5 ∶ 6 ∶ 8. This means that for some constant value, let's call it 'x', the salaries can be represented as:
- Salary of P = \(5x\)
- Salary of Q = \(6x\)
- Salary of R = \(8x\)
Here, 'x' represents a common multiplier for the ratio terms.
Using the Salary Difference to Find 'x'
We are told that R gets Rs. 2200 more than Q. We can write this as an equation using our expressions for their salaries:
Salary of R - Salary of Q = Rs. 2200
Substituting the expressions in terms of 'x':
\(8x - 6x = 2200\)
Calculating the Value of 'x'
Now, we solve the equation for 'x':
\(2x = 2200\)
To find 'x', divide both sides by 2:
\(x = \frac{2200}{2}\)
\(x = 1100\)
The value of the common multiplier 'x' is 1100.
Finding the Salary of P
The salary of P is given by \(5x\). Now that we know the value of 'x', we can calculate P's salary:
Salary of P = \(5 \times x\)
Salary of P = \(5 \times 1100\)
Salary of P = \(5500\)
So, the salary of P is Rs. 5500.
Verification
Let's quickly verify the salaries using \(x = 1100\):
- Salary of P = \(5 \times 1100 = 5500\)
- Salary of Q = \(6 \times 1100 = 6600\)
- Salary of R = \(8 \times 1100 = 8800\)
Is the difference between R and Q's salary Rs. 2200?
\(8800 - 6600 = 2200\)
Yes, the condition is satisfied. The calculated salaries are consistent with the given information.
| Person | Ratio Part | Calculated Salary (Rs.) |
|---|---|---|
| P | 5 | 5500 |
| Q | 6 | 6600 |
| R | 8 | 8800 |
Therefore, the salary of P is Rs. 5500.
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Ratio | A comparison of two or more quantities of the same kind. Represented as a:b or a:b:c. |
| Ratio Constant (x) | A common multiplier used to convert ratio parts into actual values. If the ratio is a:b, the values can be ax and bx. |
| Solving Ratio Problems | Represent the quantities using the ratio and a constant (x). Use the given conditions (sum, difference, etc.) to form an equation and solve for x. Substitute x back into the expressions to find the actual values. |
Additional Information: Ratio Applications
Ratios are widely used in many real-life situations and mathematical problems. Some common applications include:
- Mixing Ingredients: Recipes often use ratios to specify the amounts of different ingredients.
- Scaling Maps and Models: Ratios represent the scale, showing how a distance on the map relates to a real distance.
- Comparing Proportions: Used to compare quantities in finance, science, engineering, and daily life.
- Sharing Quantities: A total quantity can be divided among individuals or groups in a given ratio.
Understanding ratios is fundamental for solving problems involving proportions and comparative values.
Important Questions from Simple Ratios
If the value of \(\frac{{p - q}}{q} = \frac{4}{3}\) .find p : q
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
The two numbers are in the ratio of 9 ∶ 7 and the difference between of these two number is 6000. What is the sum of the two numbers?
A certain number is added to each of a pair of numbers which are in the ratio 4 ∶ 5. The sum of the resulting numbers is 39 and their ratio (taken in the same order as mentioned above) is 6 ∶ 7. What is the number added?
If (p + q) ∶ (q + r) ∶ (r + p) = 5 ∶ 6 ∶ 7 and p + q + r = 18, find the value of p ∶ q ∶ r
