Question
Download Solution PDFIf 2P = 3Q = 5R and P + Q + R = 6200, then the difference between P and R is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
2P = 3Q = 5R
P + Q + R = 6200
Concept or Formula:
Use the given equations to express P, Q, and R in terms of a common variable.
Substitute these expressions into the second given equation to solve for the common variable.
Then calculate the values of P and R using the common variable.
The difference between P and R can be found by subtracting the smaller value from the larger one.
Solution:
Let 2P = 3Q = 5R = k (some constant)
⇒ P = k/2, Q = k/3, and R = k/5
Substitute P, Q, R in P + Q + R = 6200
⇒ k/2 + k/3 + k/5 = 6200
Solve the above equation for k,
⇒ k (1/2 + 1/3 + 1/5) = 6200
⇒ k (15/30 + 10/30 + 6/30) = 6200
⇒ k × 31/30 = 6200
⇒ k = 6200 × 30/31
⇒ k = 6000
Substitute k = 6000 in P = k/2 and R = k/5
⇒ P = 6000/2 = 3000 and R = 6000/5 = 1200
Find the difference between P and R
⇒ P - R = 3000 - 1200 = 1800
Therefore, the difference between P and R is 1800.
Last updated on Jul 8, 2025
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