What number should be added to each of the numbers 7 8 10 and 12 so that the new numbers are in proportion?

Question 9 Linear Equations and Inequalities In one Variable Exercise 12.2

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Answer:

Let x be the required number

According to the given problem,

(12 + x), (22 + x), (42 + x) and (72 + x) are in proportion

So,

(12 + x) / (22 + x) = (42 + x) / (72 + x)

On cross multiplication, we get,

(12 + x) (72 + x) = (42 + x) (22 + x)

On simplification, we get,

12 (72 + x) + x (72 + x) = 42 (22 + x) + x (22 + x)

864 + 12x + 72x + x2 = 924 + 42x + 22x + x2

We get,

864 + 84x + x2 = 924 + 64x + x2

864 + 84x + x2 – 924 – 64x – x2 = 0

864 + 84x – 64x – 924 = 0

84x – 64x = 924 – 864

20x = 60

We get,

x = 60 / 20

x = 3

Therefore, the required number is 3

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