Three years ago, the age of a person was six times the age of his younger brother. Eight years later, the age of the person will be three years less than twice the age of his younger brother. Find the present ages of the person and his younger brother.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 15 years and 5 years.
Let the person's present age be x years and the younger brother's present age be y years.
So, x - 3 = 6(y - 3)
⇒ x - 3 = 6y - 18
⇒ x - 6y = - 15 .....(1)
Also, x + 8 = 2(y + 8) - 3
⇒ x + 8 = 2y + 16 - 3
⇒ x - 2y = 5 .....(2)
Subtracting equation (1) from (2),
4y = 20
⇒ y = 20/4 = 5
Putting the value of y in equation (1),
x - 6(5) = -15
⇒ x - 30 = -15
⇒ x = -15 + 30 = 15
Therefore, the person's present age is 15 years, and the younger brother's present age is 5 years.