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A person invested one-third of his money at \(3\frac{1}{2}\% \), one-fourth of his money at \(7\frac{1}{2}\% \), and the remaining at 8% per annum simple interest. If his yearly simple interest is Rs.1,479, then what is the sum invested (in Rs.)?
1. 22,300
2. 23,200
3. 21,500
4. 24,500

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Correct Answer - Option 2 : 23,200

Given:

A person invested one-third of his money at the rate of interest = \(3\frac{1}{2}\% \)

one-fourth of his money at the rate of interest =  \(7\frac{1}{2}\% \)

Remaining money at the rate of interest = 8%

Simple interest yearly = 1479

Formula used:

Simple interest = PTR/100

Calculations:

Let the sum of money be x

1/3rd  of amount = x/3

1/4 th of amount = x/4

Reamining amount = x - x/3 - x/4

⇒ (12x - 4x - 3x)/12 = 5x/12

Simple interst = [(x/3) × \(3\frac{1}{2}\) + (x/4)( \(7\frac{1}{2}\)) + (5x/2) × 8]/100

⇒ [(x/3) × (7/2) + (x/4)(15/2) + (5x/2) × 8]/100 = [(7x/6 + 15x/8 + 40x/2]/100

⇒ [(28x + 45x + 80x)/24]/100 = 153x/2400

Accordingly,

1479 = 153x/2400

⇒ x = 1479 × 2400/153

⇒ x = 23200

∴ The sum of amount is 23200

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