SOLUTION: Amita invested some part of 35000 rupees at 4percent and rest at 5percent interest for one year. Altogether her gain was 1530. Find out amount she invested at two different rates w

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Question 1105653: Amita invested some part of 35000 rupees at 4percent and rest at 5percent interest for one year. Altogether her gain was 1530. Find out amount she invested at two different rates write answer in words
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.
interest + interest       = total interest.


0.04*x   + 0.05*(35000-x) = 1530

0.04x + 0.05*350000 - 0.05x = 1530

-0.01x = 1530 - 0.05*35000 = -220  ====>  x = %28-220%29%2F%28-0.01%29 = 22000.


Answer.  $22000 was invested at 4% and the rest $35000 - $22000 = $13000 was invested at 5%.


Check.   0.04*22000 + 0.05*13000 = 1530 dollars.   ! Correct !

On investment problems, see the lesson
    - Using systems of equations to solve problems on investment
in this site.



Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


I find the method of alligation is much easier and faster than the traditional algebraic method shown by the other tutor.

Find how much interest would be earned if the whole amount were invested at each of the two rates, and compare the actual amount of interest to those amounts, using the method of alligation.

.04%2835000%29+=+1400
.05%2835000%29+=+1750

Then the method of alligation does this with those numbers:

matrix%283%2C3%2C1400%2C%22%22%2C220%2C%22%22%2C1530%2C%22%22%2C1750%2C%22%22%2C130%29

The amounts in the first column are the amounts of interest if all the money were invested at each rate; the amount in the middle column is the actual amount of interest.
The numbers in the last column are the differences, calculated diagonally, between the numbers in the first and second columns.

When the numbers are used this way, the numbers in the last column show the ratio in which the two parts should be mixed.

So the ratio between the amounts invested at the lower and higher rates is 220:130, or 22:13. With a total of 35000 rupees, that means 22000 rupees at 4% and 13000 rupees at 5%.

With all the words of explanation, it looks like a lengthy process. But the actual calculations are quick and easy.