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:
i. a + c = e ii. b – d = d iii. e + a = b
Explanation:
a + c = e ... (i)
b – d = d
b = 2d ... (ii)
e + a = b ... (iii)
From (ii), we get,
Either b = 4 and d = 2 or b = 10 and d = 5
From (i) and (iii), we get,
2a + c = b ... (iv)
∴ b = 4 can easily be eliminated because there is no value of b that will satisfy equation (iv).
∴ b = 10 and d = 5
a = 4 or 6 and e = 6 or 4, but c = 2
Using equation (i), we have,
a = 4 and e = 6
Hence, option (b).
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