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
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
