Question

The two numbers are in the ratio 3 ratio 4 and the product of their LCM and HCF is 10800. The sum of the numbers is
(a)180
(b)210
(c)225
(d)240

Answer 1

Two numbers are in the ratio 3 : 4

Let the common multiple be x

So, let the first number be 3x and second number be 4x

We will use the fomrula of :-

1st number × 2nd number = Product of HCF and LCM

☛ 3x × 4x = 10800

☛ 12x² = 10800

☛ x² = $\dfrac{10800}{12}$

☛ x² = 900

∴ x = 30

∴ 1st number ☛ 3x

☛ 3 × 30

☛ 90

∴ 2nd number ☛ 4x

☛ 4 × 30

☛ 120

∴ The sum of the numbers ☛ 90 + 120

☛ $\pink{\underline{\pink{\underline{\tt{\red{210\:i.e.\:Option\:b}}}}}}$

Answer 2

The answer is (B) 210

Let the ratio constant be x

No's = 3x,4x

LCM*HCF=10800

LCM*HCF= product of No's ( formula)

10800=3x*4x

10800=12 x^2

900=x^2

√900=x

30=x

No 1=90

No 2=120

Thus,Sum = 90+120

=210