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The three rational numbers between $57 and 67$ are:

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2125, 2225, 2325

2128, 2228, 2328 .

2130, 2230, 2330

2132, 2232, 2332

answer is B.

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Detailed Solution

It is given that the two numbers are

57 and 67

.
We know that the rational numbers between x and y are x + d, x + 2d and x + 3d, where

d = y − x n + 1

.
Let

x = 57 and y = 67

.
Here,

x < y

and we must find three rational numbers, so

n = 3

d = 67 − 57 4 = 174 = 128

Since the three rational number between

x

and

y

are

x + d

x + 2 d

and

x + 3 d

∴ x + d = 57 + 128 = 20 + 1 28 = 2128

∴ x + 2 d = 57 + 228 = 20 + 2 28 = 2228

∴ x + 3 d = 57 + 328 = 20 + 3 28 = 2328

Hence, the three rational numbers between

57 and 67 are 2128, 2228, 2328 .

Therefore, the correct option is (2).

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