What number should be added to 2 5 10 19 so that the resulting numbers are in proportion?

What number must be added to each of the numbers 10,18,22,38 to make them in proportion?

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Solution

The correct option is C [2]

Given numbers: 10,18,22,38
Let the number be x.
⇒10+x:18+x=22+x:38+x
⇒[10+x][38+x]=[18+x][22+x]
380+10x+38x+x2=396+18x+22x+x2
48x−40x=396−380
8x=16
∴x=2

Solution

Determine the number that must be added:

Let a be the number added to each of these given numbers.

According to the question:

12+a:22+a::42+a:72+a⇒12+a22+a=42+a72+a

Now, solve the above equation using the cross multiplication method.

12+a72+a=42+a22+a⇒12×72+12a +72a+a2=42×22+42a+22a+a2⇒864+84a+a2=924+64a+ a2⇒84a-64a=924-864⇒ 20a=60⇒ a=6020∴ a=3

Hence, if we add 3 to each of the given numbers then they become proportional.

How do you make a number proportional?

What should be added so that the numbers are in proportion?

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