The age of the eldest sister is 16 years.
An equation is used to show the relationship between two or more variables and numbers.
Let x represent the age of the older sister and y, z represent the other sisters ages.
Three sisters, whose average age is 10, all have different ages. Hence:
(x + y + z)/3 = 10 (1)
Also, When they get together in pairs, the average ages of two such pairs are 11 and 12, hence:
(x + y)/2 = 11 (2)
(x + z)/2 = 12 (3)
From equation 1, 2 and 3:
x = 16, y = 6, z = 8
The age of the eldest sister is 16 years.
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