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A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is:
- ARs 200
- BRs 600
- CRs 800
- DRs 1200
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Let x, y and z be his investments at 4%, 6%, and 8% respectively
Simple Interest on x at 4% for 1 year = Simple Interest on y at 6% for 1 year = Simple Interest on z at 8% for 1 year
We know that
SI = PRT/100
P = Principal, R = %Rate, T = Time
$(\Rightarrow \;\frac{{x\; \times \;4\; \times \;1}}{{100}}\; = \;\frac{{y\; \times \;6\; \times \;1}}{{100}}\; = \;\frac{{z\; \times \;8\; \times \;1}}{{100}})$
⇒ 4x = 6y = 8z
⇒ 2x = 3y = 4z
⇒ y = 2x/3 and z = x/2
We know that, x + y + z = 2600
⇒ x + 2x/3 + x/2 = 2600
⇒ 6x + 4x + 3x = 2600 × 6
⇒ 13x = 2600 × 6
⇒ x = (2600 × 6)/13 = 200 × 6 = 1200
∴ Money invested at 4% = Rs.1200
Simple Interest on x at 4% for 1 year = Simple Interest on y at 6% for 1 year = Simple Interest on z at 8% for 1 year
We know that
SI = PRT/100
P = Principal, R = %Rate, T = Time
$(\Rightarrow \;\frac{{x\; \times \;4\; \times \;1}}{{100}}\; = \;\frac{{y\; \times \;6\; \times \;1}}{{100}}\; = \;\frac{{z\; \times \;8\; \times \;1}}{{100}})$
⇒ 4x = 6y = 8z
⇒ 2x = 3y = 4z
⇒ y = 2x/3 and z = x/2
We know that, x + y + z = 2600
⇒ x + 2x/3 + x/2 = 2600
⇒ 6x + 4x + 3x = 2600 × 6
⇒ 13x = 2600 × 6
⇒ x = (2600 × 6)/13 = 200 × 6 = 1200
∴ Money invested at 4% = Rs.1200