Question

If the same number be added to the numbers 5,11,15 and 31 then the resultant numbers are in proportion. Find the number.

Class 8 ICSE board. ​

Answer 1

Step-by-step explanation:

Given :

The same number added to the numbers 5, 11, 15 and 31.

The resultant number in proportion.

Find :

The required number.

Solution :

Let the number be x.

Then,

5 + x, 11 + x, 15 + x and 31 + x are in proportion.

That is,

$\frac{5 + x}{11 + x} = \frac{15 + x}{31 + x}$

$= > (5 + x)(31 + x) = (11 + x)(15 + x)$

$= > 155 + 36x + {x}^{2} = 165 + 26x + {x}^{2}$

$= > 36x - 26x = 165 - 155$

$= > 10x = 10$

$= > x = \frac{10}{10}$

$= > x = 1.$

Hence :

The required number is 1.

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Answer 2

Step-by-step explanation:

$\frac{5 + x}{11 + x} = \frac{15 + x}{31 + x}$

$= > (5 + x)(31 + x) = (11 + x)(15 + x)$

$= > 155 + 36x + {x}^{2} = 165 + 26x + {x}^{2}$

$= > 36x - 26x = 165 - 155$

$= > 10x = 10$

$= > x = \frac{10}{10}$

$= > x = 1.$