Divide Rs. 8000 into two parts so that simple interest on first part for 3…
2024
Divide Rs. 8000 into two parts so that simple interest on first part for 3 years at 5% p.a. may be equal to simple interest on the second part for 5 years at 9% p.a.
Answer: A. Rs. 2,000, Rs. 6,000 — Step-by-Step SolutionTo divide Rs. 8000 into two parts such that the simple interest on both is equal, we can set up an equation based on the simple interest…
- A.
Rs. 2,000, Rs. 6,000
- B.
Rs. 2,500, Rs. 5,500
- C.
Rs. 3,000, Rs. 5,000
- D.
None of these
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Correct answer: A
Step-by-Step Solution
To divide Rs. 8000 into two parts such that the simple interest on both is equal, we can set up an equation based on the simple interest formula: S.I. = (P × R × T) / 100.
Define the parts:
Let the first part be x.
Let the second part be (8000 - x).
Set up the equation for equal interest:
Interest on first part = (x × 5 × 3) / 100
Interest on second part = ((8000 - x) × 9 × 5) / 100
Since the interests are equal: (15x) / 100 = (45 × (8000 - x)) / 100
Solve for x:
15x = 45(8000 - x)
Divide both sides by 15: x = 3(8000 - x)
x = 24000 - 3x
4x = 24000
x = 6000
Find the two parts:
First part (x) = Rs. 6000
Second part (8000 - x) = 8000 - 6000 = Rs. 2000