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The difference between two natural numbers is 3 and the difference of their reciprocal is $\frac{3}{28}$ . The numbers are:

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4 and 7

14 and 2

4 and 6

7 and 5

answer is D.

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Detailed Solution

Given that the difference of the natural numbers

= 3

and difference of their reciprocal

= \frac{3}{28}

.
Let’s assume that the two natural numbers are m and m+1
According to the given condition,

⟹ \frac{1}{m} - \frac{1}{m + 3} = \frac{3}{28}

⟹ \frac{(m + 3) - m}{m (m + 3)} = \frac{3}{28}

⟹ \frac{3}{m^{2} + 3 m} = \frac{3}{28}

⟹ 28 \times 3 = 3 (m^{2} + 3 m)

⟹ 3 m^{2} + 9 m = 84

⟹ 3 m^{2} + 9 m - 84 = 0

⟹ m^{2} + 3 m - 28 = 0

⟹ m^{2} + 7 m - 4 m - 28 = 0

⟹ m (m + 7) - 4 (m + 7) = 0

⟹ (m - 4) (m + 7) = 0

⟹ m - 4 = 0 or m + 7 = 0

∴ m = 4 or m = - 7

Here, -7 is not a natural number
So, we will choose the value

m = 4

,
And

m + 3 = 4 + 3 = 7

.
Thus, the two natural numbers are 4 and 7.
Hence, the correct option is 4.

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