Ram invested some amount at the rate of 15% simple interest and a certain amount at the rate of 20% simple interest. He received yearly int… — Answer & Discussion

Ram invested some amount at the rate of 15% simple interest and a certain amount at the rate of 20% simple interest. He received yearly interest of Rs. 1900. But if he had interchanged the amounts invested, he would have received Rs. 550 more as interest. How much did he invest at 20% simple interest?

ARs. 710.63
BRs. 714.28
CRs. 711.62
DRs. 765.41

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Discussion 1

CCommunity28 Jun 2019

Let us take the two cases before and after interchanging the amounts, to know the principal for the latter case.

Let the amount invested at 15% be x and the amount invested at 20% be y

For case 1(before interchanging the amounts),

We know, Simple interest = (P × R × T)/100

1900 = (15x + 20y)/100

38000 = 3x + 4y

Multiplying whole equation with 4, we get

152000 = 12x + 16y ----(1)

For case 2(after interchanging the amounts),

1900 + 550 = (15y + 20x)/100

49000 = 3y + 4x

Multiplying whole equation with 3, we get

147000 = 12x + 9y ----(2)

Subtracting equation 2 from 1, we get,

152000 - 147000 = 16y - 9y

y = Rs. 714.28

∴ The amount invested at 20% was Rs. 714.2