Question

The two number are in the ratio of 2: 3 and the product of their hcf and lcm is33750, then sum of the number is

Answer 1

see the solution in the picture

Answer 2

Answer:

$Sum \:of \: the \\numbers = 375$

Step-by-step explanation:

$Let\: a \:and\: b \: are \\two\: numbers \: and \: their \:LCM \\is \:l \:and \: HCF \:is \:h$

$Given \: a:b = 2:3\: and \\lh = 33750$

$Let \: a = 2x \: and \: b = 3x$

$We\: know \: that ,\\\boxed { a \times b= l \times h}$

$\implies 2x \times 3x = 33750$

$\implies 6x^{2}=33750$

$\implies x^{2}=\frac{33750}{6}\\=5675$

$\implies x = \sqrt{5675}\\=\sqrt{5^{4}\times 3^{2}}\\=5^{2}\times 3\\=75$

$\implies Sum \:of \: the \\numbers = a+b\\=2x+3x\\=5x\\=5\times 75\\=375$

Therefore,

$Sum \:of \: the \\numbers = 375$

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