Question

A man invested an amount at 10% per annum and another amount at 8% per annum simple interest .Thus,he received Rs.1350 as annual interest .Had he interchanged the amounts invested ,he would have received Rs.45 less as interest .What amounts did he invest at different rates?
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Answer 1

Answer:

Step-by-step explanation:

Given A man invested an amount at 10% per annum and another amount at 8% per annum simple interest .Thus,he received Rs.1350 as annual interest .Had he interchanged the amounts invested ,he would have received Rs.45 less as interest .What amounts did he invest at different rates?

Let the amount invested at 10% and 8% be x and y

Now x x 10 x 1 / 100 = y x 8 x 1 / 100 = 1350

10 x + 8 y = 135000 -------------(1)  

Since rate is same we get

 x x 8 x 1 / 100 = y x 10 x 1 / 100 = 1350 – 45

 8 x + 10 y = 130500------------(2)

From 1 and 2 we get by solving simultaneous equation,

 10 x + 8 y = 135000 x 8

   8 x + 10 y = 130500 x 10

 80 x + 64 y = 1080000

 80 x + 100 y = 1305000

- 36 y = - 225000

-   y = 6250

10 x + 8 y = 135000

10 x + 50,000 = 135000

10 x = 85000

x = 8500

So the amount invested are Rs 8,500 at 10% and Rs 6,250 at 8%

Answer 2

amount invested at 10% be rs X

amount invested at 8% be rs Y

now ,

x×1×10/100 + y×8×1/100=1350

10x+8y=135000........(1)

again the amounts are interchanged

x×8×1/100 + y×10×1/100 = 1350-45

8x/100+10y/100=1305

8x+10y=130500.........(2)

multiplying eqn 1 by 10 and eqn 2 by 8 and subtracting the results

100x+80y=1350000

64x+80y=1044000

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36x = 306000

x=8500

putting value of x in (1)

85000+8y=135000

8y=135000-85000

8y= 50000

y=6250