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Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum?
  • a)
    18.5%
  • b)
    14.4%
  • c)
    16.5%
  • d)
    19.5%
  • e)
    None of the Above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10%...
B. 14.4%
Explanation: x – (40/100)*x = 60x/100 40/100 at 15% p.a = 40/100 * 15/100 = 60x/1000 50/100*60x/100 = 30x/100 at 10% p.a = 30x/100 * 10/100 = 30x/1000 Balance amount = x – 40x/100 – 30x/100 = 30x/100 at 18% p.a = 18/100 * 30x/100 = 54x/1000 R = [(144x/1000)/x] * 100 = 14.4%
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Most Upvoted Answer
Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10%...
Given:
- Suresh lends 40% of his money at 15% per annum.
- Suresh lends 50% of the rest at 10% per annum.
- Suresh lends the rest at 18% per annum rate of interest.

To find: The annual rate of interest, if the interest is calculated on the whole sum.

Solution:
Let's assume Suresh has a total of Rs. 100.
Then, according to the question:
- He lends 40% of Rs. 100 at 15% per annum, which is Rs. 40 x 15% = Rs. 6.
- The remaining amount is Rs. 100 - Rs. 40 = Rs. 60.
- He lends 50% of Rs. 60 at 10% per annum, which is Rs. 30 x 10% = Rs. 3.
- The remaining amount is Rs. 60 - Rs. 30 = Rs. 30.
- He lends Rs. 30 at 18% per annum, which is Rs. 30 x 18% = Rs. 5.4.

Therefore, the total interest earned by Suresh is Rs. 6 + Rs. 3 + Rs. 5.4 = Rs. 14.4.

Now, we need to find the annual rate of interest if the interest is calculated on the whole sum.
Let the annual rate of interest be x%.

Then, using the concept of simple interest:
- Interest earned on the first part (40% of Rs. 100) = Rs. 40 * 15 * (1/100) = Rs. 6x/100
- Interest earned on the second part (50% of Rs. 60) = Rs. 30 * 10 * (1/100) = Rs. 3x/100
- Interest earned on the third part (remaining Rs. 30) = Rs. 30 * 18 * (1/100) = Rs. 54/100

Total interest earned = Rs. 6x/100 + Rs. 3x/100 + Rs. 54/100 = Rs. (9x + 54)/100

As per the question, the total interest earned is Rs. 14.4.

Therefore, (9x + 54)/100 = 14.4
=> 9x + 54 = 144
=> 9x = 90
=> x = 10

Hence, the annual rate of interest is 10%.

Therefore, option (b) 14.4% is incorrect, and the correct option is (e) None of the Above.
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Community Answer
Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10%...
B. 14.4%
Explanation: x – (40/100)*x = 60x/100 40/100 at 15% p.a = 40/100 * 15/100 = 60x/1000 50/100*60x/100 = 30x/100 at 10% p.a = 30x/100 * 10/100 = 30x/1000 Balance amount = x – 40x/100 – 30x/100 = 30x/100 at 18% p.a = 18/100 * 30x/100 = 54x/1000 R = [(144x/1000)/x] * 100 = 14.4%
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Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum?a)18.5%b)14.4%c)16.5%d)19.5%e)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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