Question

Find the number which when added to 2,14,37 and 133 make them proportionate to each other.​

Answer 1

Answer:

3

Step-by-step explanation:

Given Find the number which when added to 2,14,37 and 133 make them proportionate to each other.

We need to add x to each of the four numbers. So it will be

(2 + x):(14 + x) : : (37 + x):(133 + x)

We know that product of means = product of extremes.

So (2 + x)(133 + 518 x) = (14 + x)(37 + x)

We get x^2 + 135 x + 266 = x^2 + 51 x + 518

    So 84 x – 252 = 0

       84 x = 252

        x = 252 / 84

         x = 3

So 5,17,40,136  

  5 x 136 = 17 x 40

    680 = 680

So we need to add 3 to make the numbers to be in proportion.

Answer 2

The "number 3 is added".

Step-by-step explanation:

Let x should be added.

(2 + x) : (14 + x) : (37 + x) : : (133 + x)

To find, the number should be added.

We know that,

a : b : c : : d

∴ a × d = b × c

⇒ (2 + x)(133 + x) = (14 + x)(37 + x)

⇒ 266 + 2x + 133x + $x^2$ = 518 + 14x + 37x + $x^2$

⇒ 266 + 135x  = 518 + 51x

⇒ 135x  - 51x = 518 - 266

⇒ 84x = 252

⇒ x = $\dfrac{252}{84}$

⇒ x = 3

Thus, the "number 3 is added".