What number must be added to each of the numbers 15 17 34 and 38 to make them in proportion?

Given:

The numbers 104, 34, 110 and 36

Concept used:

If a, b, c and d are four numbers and they are in continued proportion

Then a ∶ b ∶∶ c ∶ d 

⇒ ad = cb 

⇒ a/b = c/d

Calculation

Let the number x added

Now, according to question,

(104 + x) ∶ (34 + x) ∶∶ (110 + x) ∶ (36 + x)

⇒ (104 + x) × (36 + x) = (110 + x) × (34 + x) 

⇒ 3744 + 36x + 104x + x2 = 3740 + 34x + 110x + x2

⇒ 3744 + 140x = 3740 + 144x

⇒ 4x = 4

Then x = 1

∴ The required number is 1.

Alternate Method

Calculations:

Let the number x added

Now, according to question,

(104 + x) ∶ (34 + x) ∶∶ (110 + x) ∶ (36 + x)

⇒ (104 + x)/(34 + x) = (110 + x)/(36 + x)

Let’s check options one by one,

For 1 option,

After adding 9 to each number, numbers will be 113, 43, 119 and 45

For them to be in continued proportion this ratio must be equal

⇒ 113/43 ≠ 119/45

Hence option 1 is not correct

For 2 option,

After adding 3 to each number, numbers will be 107, 37, 113 and 39

For them to be in continued proportion this ratio must be equal

⇒ 107/37 ≠ 113/39

Hence option 2 is not correct

For 3 option,

After adding 1 to each number, numbers will be 105, 35, 111 and 37

For them to be in continued proportion this ratio must be equal

⇒ 105/35 = 111/37 = 3

Hence option 3 is correct

For 4 option,

After adding 4 to each number, numbers will be 108, 38, 114 and 40

For them to be in continued proportion this ratio must be equal

⇒ 108/38 ≠ 114/40

Hence option 4 is not correct

∴ The correct answer is option 3.

What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?

Let x be added to each number, then numbers will be15 + x, 17 + x, 34 + x, and 38 + x.Now according to the condition`(15 + x)/(17 + x) = (34 + x)/(38 + x)`⇒ (15 – x)(38 + x) = (34 + x)(17 + x)

⇒ 570 + 53x + x2 = 578 + 51x + x2

∴ 4 is to be added.

Concept: Concept of Proportion

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