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Some part of Rs 9500 was lent at the rate of 15% per annum simple interest and the remaining part at the rate of 20% per annum simple interest. The total interest received after 3/2 years is Rs 2565. What is the ratio of money lent at the rate of 15% and 20%?
  • a)
    11 : 8
  • b)
    12 : 7
  • c)
    2 : 3
  • d)
    5 : 4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Some part of Rs 9500 was lent at the rate of 15% per annum simple inte...
Let the two parts be Rs. ‘x’ and Rs. (9500 - x)
∵ Simple interest = (Principal × Rate × Time)/100
⇒ Simple interest at 15% p.a. on Rs. x = (x × 15 × 3/2)/100 = 0.225x
⇒ Simple interest at 20% p.a. on Rs. (9500 - x) = [(9500 - x) × 20 × 3/2]/100 = 2850 - 0.3x
Now, total interest = Rs. 2565
⇒ 0.225x + 2850 - 0.3x = 2565
⇒ 0.3x - 0.225x = 2850 - 2565
⇒ 0.075x = 285
⇒ x = 285/0.075 = Rs. 3800
⇒ 9500 - x = 9500 - 3800 = Rs. 5700
∴ Required ratio = 3800 ∶ 5700 = 2 ∶ 3
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Most Upvoted Answer
Some part of Rs 9500 was lent at the rate of 15% per annum simple inte...
Given information:
- Part of Rs 9500 was lent at 15% per annum simple interest.
- Remaining part was lent at 20% per annum simple interest.
- Total interest received after 3/2 years is Rs 2565.

To find:
- Ratio of money lent at 15% and 20%.

Let's solve this problem step by step.

Step 1: Find the interest for the amount lent at 15% per annum.
Let the amount lent at 15% be x.
Interest for this amount = x * 15% * 3/2 = 0.15x * 3/2 = 0.225x

Step 2: Find the interest for the amount lent at 20% per annum.
Let the amount lent at 20% be Rs (9500 - x).
Interest for this amount = (9500 - x) * 20% * 3/2 = 0.2(9500 - x) * 3/2 = 0.3(9500 - x)

Step 3: Total interest received is given as Rs 2565.
So, 0.225x + 0.3(9500 - x) = 2565
0.225x + 2850 - 0.3x = 2565
-0.075x = -285
x = -285 / -0.075
x = 3800

Step 4: Ratio of money lent at 15% and 20%.
Money lent at 15% = Rs 3800
Money lent at 20% = Rs (9500 - 3800) = Rs 5700

Ratio = 3800 : 5700 = 2 : 3

Therefore, the ratio of money lent at the rate of 15% and 20% is 2 : 3. Answer choice (C) is correct.
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Some part of Rs 9500 was lent at the rate of 15% per annum simple interest and the remaining part at the rate of 20% per annum simple interest. The total interest received after 3/2 years is Rs 2565. What is the ratio of money lent at the rate of 15% and 20%?a)11 : 8b)12 : 7c)2 : 3d)5 : 4Correct answer is option 'C'. Can you explain this answer?
Question Description
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