Question
Download Solution PDFA person invested in all ₹2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A person invested ₹2600 at 4%, 6%, and 8% per annum simple interest. The interest at the end of the year is the same for all investments.
Formula used:
Simple Interest (SI) = P × R × T / 100
Calculations:
Let the amount invested at 4% be ₹x.
Let the amount invested at 6% be ₹y.
Let the amount invested at 8% be ₹z.
Total amount invested: x + y + z = 2600
Since the interest earned is the same in all cases, we have:
(x × 4 × 1) / 100 = (y × 6 × 1) / 100 = (z × 8 × 1) / 100
⇒ 4x / 100 = 6y / 100 = 8z / 100
⇒ 4x = 6y = 8z
Let's assume 4x = 6y = 8z = k
⇒ x = k / 4
⇒ y = k / 6
⇒ z = k / 8
Given x + y + z = 2600:
⇒ k / 4 + k / 6 + k / 8 = 2600
⇒ (6k + 4k + 3k) / 24 = 2600
⇒ 13k / 24 = 2600
⇒ 13k = 2600 × 24
⇒ 13k = 62400
⇒ k = 4800
Now,
x = k / 4 = 4800 / 4 = 1200
∴ The correct answer is option (4).
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