Question

A number 385 divided into two parts in such a way that the lcm and hcf of the two parts are 660 and 55 respectively. find the two parts

Answer 1

Let one part of the number be x. Therefore the second part is 385-x.
Now we know that the LCM of these is 660 and HCF of these is 55.
We also know that
$x(385 - x) = 660 \times 55 \\ 385x - {x}^{2} = 11 \times 110 \times 11 \times 5 \\ 385x - {x}^{2} = 36300 \\ {x}^{2} - 385x + 36300 = 0$
Solve this quadratic equation to get the answer as
$x = \frac{385 + - (55)}{2} \\ x = 165 \: \: \: \: \: \: \: \: \: \: x = 220$
Which gives
$385 - x = 220 \: \: \: \: \: \: \: \: \: \: \: \: = 165$

Answer 2

Answer:

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