Question

divide 2000 into two such parts that one third of a part equals to the half of another part . Also find the difference between the two parts.​

Answer 1

Answer:

$let \: one \: number \: be \: x \: \\ so \: another \: will \: be \: (2000 - x) \\ one \: third \: of \: first \: part = \frac{x}{3} \\ half \: of \: second \: part = \frac{1}{2} \times (2000 - x) \\ = 1000 - \frac{x}{2}$

Now one third of first part = half of second part

so

$\frac{x}{3} = 1000 - \frac{x}{2} \\ \frac{x}{3} + \frac{x}{2} = 1000 \\ \frac{2x + 3x}{6} = 1000 \\ \frac{5x}{6} = 1000 \\ x = \frac{1000 \times 6}{5} \\ x = 1200$

$so \: first \: part = 1200 \\ second \: part = (2000 - 1200) = 800 \\ difference \: between \: two \\ parts \: = 1200 - 800 = 400$