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In some code, letters, $a, b, c, d$ and $e$ represent numbers $2, 4, 5, 6$ and $10.$ However, we don't know which letter represent which number. Consider the following relationships:

1. $a + c = e$
2. $b – d = d$
3. $e + a = b$

1. $b = 4, d = 2$
2. $a = 4, e = 6$
3. $b = 6, e = 2$
4. $a = 4, c = 6$

Take a =4 , b=10 , c = 2 ,d =5 ,e =6

Put the following values into given relations

(1) a + c = e

=>4+2=6

(2) b - d = d

=>10 - 5 = 5

(3) e + a = b

=>6 + 4 = 10

These values satisfying all three relationships.

Hence, Option (2) a=4 ,e =6 is the correct choice.

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Note: each letters are assigned a unique value according to the question.

Option (A): $b=4,d=2$, it satisfies only condition (ii), same value $(4)$  for different letters (b,d). so it is wrong.

Option (B): $a=4,e=6$, put these values on (I) we get $c=2$,on (iii) we get $b=10$, using $b$ value we get $d=5$

Option (C): $b=6,e=2$, put this values on (iii) we get $a=4$,in (I) we get $c=2$. here we get the same value for the different letters (c,e) so it is wrong.

Option (D): $a=4,c=6$, put this values on (I) we get $e=10$,on (iii) we get $b=14$, from $(ii)$ we get $d=7$. since the value $7$ is not given in question so it is also wrong.
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