# Ram ji invested certain amount at the rate of 37% simple interest and some amount at the rate of 43% simple interest . He received yearly interest of

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Ram ji invested certain amount at the rate of 37% simple interest and some amount at the rate of 43% simple interest . He received yearly interest of Rs. 123. But  if he had interchanged the amount invested, he would have received Rs.6 less as interest. How much did he invest at 37% simple interest?
1. Rs. 400
2. Rs.300
3. Rs. 100
4. Rs.500

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Correct Answer - Option 3 : Rs. 100

Given

Some money was invested at the rate of 37% S.I. .

He received Rs. 123 as interest.

And some money was invested at the rate of 43% S.I.

When the amount was interchanged, The interest He received is Rs.(123 - 6) 117.

Formula Used

S.I =PRT/100

Basics of Linear Equations.

Calculation∶

Let the amount invested at 37% = Rs. x

And amount invested at 43% = Rs. y

According to Question,

123 = (x × 37 × 1)/100 + ( y × 43 × 1)/100

⇒ 37x + 43 y = 12300      (1)

Also, 117 = (43 × x × 1)/100 + (37 × y × 1)/100

⇒ 43x + 37 y = 11700      (2)

On adding eq.(1) and eq.(2) we get,

x + y = 300      (3)

On subtracting eq.(1) and eq.(2) we get,

y - x = 100      (4)

On adding eq.(3) and eq.(4) we get,

2y = 400

⇒ y = 200 and x = 100

∴ Amount received at 37% is Rs.100.