What must be added to the numbers 10, 20, 30 and 50 so that

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What must be added to the numbers 10, 20, 30 and 50 so that the sums are proportional ?

1. 15
2. 12
3. 10
4. 8

Correct Option: C

Let x be added in each number to make them proportional.
∴ 10 + x : 20 + x :: 30 + x : 50 + x
⇒ (10 + x ) (50 + x )
= (20 + x ) (30 + x )
⇒ 500 + 50 x + 10x + x²
= 600 + 20x + 30x + x²
⇒ 500 + 60x + x²
= 600 + 50x + x²
⇒ 60x – 50x = 600 – 500 = 100
⇒ 10x = 100

⇒ x =	100	= 10
	10