A man 24

A man distributed 25300 EUR among his 3 sons A, B, C in such a way that the amounts of their parts at 10% simple interest in 2 years, 3 years, 4 years will be equal. A's share?

Correct answer:

A = 9100 Eur

Step-by-step explanation:

t = 25300 EUR r_{0} = 10 % = \frac{1 0}{1 0 0} = \frac{1}{1 0} = 0.1 S = A + 2 \cdot r_{0} \cdot A S = B + 3 \cdot r_{0} \cdot B S = C + 4 \cdot r_{0} \cdot C A + 2 \cdot r_{0} \cdot A = B + 3 \cdot r_{0} \cdot B B + 3 \cdot r_{0} \cdot B = C + 4 \cdot r_{0} \cdot C A + B + C = t A + 2 \cdot 0.1 \cdot A = B + 3 \cdot 0.1 \cdot B B + 3 \cdot 0.1 \cdot B = C + 4 \cdot 0.1 \cdot C A + B + C = 25300 1.2 A - 1.3 B = 0 1.3 B - 1.4 C = 0 A + B + C = 25300 R o w 3 - \frac{1}{1 . 2} \cdot R o w 1 \to R o w 3 1.2 A - 1.3 B = 0 1.3 B - 1.4 C = 0 2.083 B + C = 25300 P i v o t : R o w 2 \leftrightarrow R o w 3 1.2 A - 1.3 B = 0 2.083 B + C = 25300 1.3 B - 1.4 C = 0 R o w 3 - \frac{1 . 3}{2 . 0 8 3 3 3 3 3 3} \cdot R o w 2 \to R o w 3 1.2 A - 1.3 B = 0 2.083 B + C = 25300 - 2.024 C = - 15787.2 C = \frac{- 1 5 7 8 7 . 2}{- 2 . 0 2 4} = 7800 B = \frac{2 5 3 0 0 - C}{2 . 0 8 3 3 3 3 3 3} = \frac{2 5 3 0 0 - 7 8 0 0}{2 . 0 8 3 3 3 3 3 3} = 8400 A = \frac{0 + 1 . 3 B}{1 . 2} = \frac{0 + 1 . 3 \cdot 8 4 0 0}{1 . 2} = 9100 = 9100 Eur A = 9100 B = 8400 C = 7800

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