A sum of money is to be distributed among P, Q, R, and S in the proportion 5 ∶ 2 ∶ 4 ∶ 3, respectively. If R gets Rs. 1000 more than S, what is the share of Q (in Rs.)?
2000
Money Distribution Problem: Understanding Ratios
This problem focuses on the distribution of a sum of money among four individuals—P, Q, R, and S—according to a specified ratio. We are given a condition about the difference in shares between R and S, which is key to finding the value of each part of the ratio and subsequently, the specific share of Q.
Ratio of Money Distribution
The shares of P, Q, R, and S are in the proportion 5 ∶ 2 ∶ 4 ∶ 3, respectively. This means that if the total money is divided into parts, P gets 5 parts, Q gets 2 parts, R gets 4 parts, and S gets 3 parts.
- P's share ∶ Q's share ∶ R's share ∶ S's share = 5 ∶ 2 ∶ 4 ∶ 3
Representing Individual Shares Algebraically
To calculate the actual money distributed, we can introduce a common multiplier, often denoted as \(x\), for each part of the ratio. This allows us to express each person's share as an algebraic term:
- Share of P \( = 5x \)
- Share of Q \( = 2x \)
- Share of R \( = 4x \)
- Share of S \( = 3x \)
Calculating the Value of Each Share Part (\(x\))
The problem states a critical piece of information: "R gets Rs. 1000 more than S". We can translate this into an equation using our algebraic representations of the shares:
R's share \( - \) S's share \( = \) Rs. 1000
Substitute the expressions for R's and S's shares into the equation:
\( 4x - 3x = 1000 \)
Simplifying the equation gives us the value of \(x\):
\( x = 1000 \)
This means that each 'part' in our ratio corresponds to Rs. 1000.
Determining Q's Share
Now that we have found the value of \(x\), we can easily calculate Q's share. From our initial representation:
Q's share \( = 2x \)
Substitute the value of \(x = 1000\):
Q's share \( = 2 \times 1000 \)
Q's share \( = 2000 \)
Therefore, the share of Q is Rs. 2000.
Verification of Money Distribution
Let's quickly verify the shares for all individuals using \(x = 1000\):
| Individual | Ratio Expression | Calculated Share (in Rs.) |
|---|---|---|
| P | \(5x\) | \(5 \times 1000 = 5000\) |
| Q | \(2x\) | \(2 \times 1000 = 2000\) |
| R | \(4x\) | \(4 \times 1000 = 4000\) |
| S | \(3x\) | \(3 \times 1000 = 3000\) |
We can see that R's share (Rs. 4000) is indeed Rs. 1000 more than S's share (Rs. 3000), which matches the condition given in the problem statement.
Important Questions from Ratio and Proportion
If the ratio of three numbers A, B and C is 2 ∶ 3 ∶ 5, and the sum of the squares of these numbers is 3800, then the value of C is:
A bag contains ₹310 in the form of 5 rupee, 2 rupee and 1 rupee coins in the ratio 4 ∶ 3 ∶ 5. What is the number of 5 rupee coins?
The ratio of three numbers is 3 ∶ 5 ∶ 4 and the sum of their squares is 11250. Find the sum of the numbers.
When 'x' is subtracted from each of the numbers 22, 39, 56 and 107, then the resulting numbers, in this order, are in proportion. What is the mean proportional between (x + 3) and (3x - 7)?
The salaries of Ravi and Sumit are in the ratio 4 ∶ 5. If the salary of each is increased by Rs. 6,000 the new ratio becomes 35 ∶ 40. What will be Sumit's increased salary?
