Question

what number should be aaded to each one 6,14,18,38 to make it equally proportionate

Answer 1

Let x be the number added,
Therefore,

(10+X) / (18+X) = (22+X) / (38+X)⇒380 + 48x + x² = 396 + 40x + x²⇒8x = 16⇒x = 2

Therefore, the number added, x = 2

Answer 2

$\huge{\underline{\underline {\mathtt{\purple{Hola\:}\pink{Mate}}}}}$

$\Large\bold\red{Question}$

What number should be added to each one of 6, 14, 18, 38 to make it equality proportionate?

$\Large\fbox\blue{Answer = 2}$

$\Large\bold\red{Solution}$

6, 14, 18, 38

If a, b, c, d are in proportion

⇒ a : b :: c : d

then ad = bc

Let x is added in the sequence numbers as to make it in proportion

(6 + x) : (14 + x) :: (18 + x) : (38 + x)

(6 + x) (38 + x) = (18 + x) (14 + x)

Now to save valuable time put value of x from options to make it proportion

(6+x) (38+x) = (14+x) (18+x)

⇒ x² + 44x + 228 = x² + 32x + 252

12x ⇒ 252 - 228

12x ⇒ 24

$\Large\fbox\blue{x ⇒ 2}$

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