The sum of the ages of Yash and his father is 90 years. When Yash is as old as his father’s present age, he will be five times as old as his son Suraj’s present age. Suraj will be 12 years older than Yash’s present age, when Yash is as old as his father at present. How old is Suraj at present?
12 years
Let Y be Yash's current age and F be his father's current age.
We are given that \(Y + F = 90\).
When Yash is as old as his father's present age (F), the time elapsed will be \(F - Y\).
At that time, Suraj's age will be \(S + (F - Y)\), where S is Suraj's current age.
According to the problem, Yash's age then will be five times Suraj's age at present:
\(F = 5S\)
Also, when Yash is as old as his father's present age (F), Suraj will be 12 years older than Yash's present age:
\(S + (F - Y) = Y + 12\)
We have three equations:
- \(Y + F = 90\)
- \(F = 5S\)
- \(S + F - Y = Y + 12\)
From equation (1), \(F = 90 - Y\).
Substitute this into equation (2): \(90 - Y = 5S\).
From equation (3), \(S + F - 2Y = 12\).
Substitute \(F = 90 - Y\) into this equation: \(S + 90 - Y - 2Y = 12\), which simplifies to \(S - 3Y = -78\).
Now we have two equations with two variables:
- \(90 - Y = 5S\)
- \(S - 3Y = -78\)
From equation (4), \(Y = 90 - 5S\).
Substitute this into equation (5): \(S - 3(90 - 5S) = -78\)
\(S - 270 + 15S = -78\)
\(16S = 192\)
\(S = 12\)
Therefore, Suraj's present age is 12 years.
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