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Q.

The three rational numbers between 5 7  and  6 7  are:


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a

21 25 , 22 25 , 23 25  

b

21 28 , 22 28 , 23 28 .  

c

21 30 , 22 30 , 23 30  

d

21 32 , 22 32 , 23 32   

answer is B.

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Detailed Solution

It is given that the two numbers are 5 7  and  6 7  .
We know that the rational numbers between x and y are x + d, x + 2d and x + 3d, where
d= yx n+1  .
Let x= 5 7  and y= 6 7  .
Here, x<y   and we must find three rational numbers, so n=3  . d= 6 7 5 7 4   = 1 7 4    = 1 28  
Since the three rational number between x   and y   are x+d   , x+2d   and x+3d  , x+d= 5 7 + 1 28           = 20+1 28           = 21 28  
  x+2d= 5 7 + 2 28             = 20+2 28             = 22 28  
  x+3d= 5 7 + 3 28             = 20+3 28             = 23 28  
Hence, the three rational numbers between 5 7  and  6 7  are  21 28 , 22 28 , 23 28 .  
Therefore, the correct option is (2).
 
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