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Q.

Form the pair of linear equations in the following problems.

Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son.

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a

x - 5 y + 8 = 0

and

x - 3 y - 12 = 0

b

x + 5 y + 8 = 0

and

x - 3 y - 12 = 0

c

x - 5 y - 8 = 0

and

x - 3 y - 12 = 0

d

x - 5 y + 8 = 0

and

x + 3 y - 12 = 0

answer is A.

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Detailed Solution

It is given that, two years ago, a father was five times as old as his son and two years later, his age will be 8 more than three times the age of the son.
Assume that the father is currently x years old and his son is currently y years old.
Create equations for the unknown variables x and y using the circumstances provided in the problem:
According to question,
Two years ago,
Age of father = (x – 2) year
Age of Son = (y – 2) year
Then, according to question,

x - 2 = 5 (y - 2)

\Rightarrow x - 2 = 5 y - 10

\Rightarrow x - 5 y + 8 = 0

After 2 years,
Age of father will be (x + 2) year
Age of Son will be (y + 2) year
Then, according to question,

x + 2 = 3 (y + 2) + 8

\Rightarrow x + 2 = 3 y + 6 + 8

\Rightarrow x - 3 y - 12 = 0

Therefore, pair of linear equations are,

x - 5 y + 8 = 0

and

x - 3 y - 12 = 0

.
Hence, option (1) is correct.

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