‘B’ is 28 years older than ‘A’. After 12 years from now, the age of ‘B

‘B’ is 28 years older than ‘A’. After 12 years from now, the age of ‘B’ will be twice the age of ‘A’. The present age of ‘A’ is :

10 years
12 years
30 years
16 years
This question was previously asked in
UPSC CISF-AC-EXE – 2022
Let the present age of A be A years.
Let the present age of B be B years.
According to the first statement, ‘B’ is 28 years older than ‘A’:
B = A + 28 (Equation 1)

After 12 years from now:
Age of A will be A + 12 years.
Age of B will be B + 12 years.

According to the second statement, the age of ‘B’ will be twice the age of ‘A’ after 12 years:
B + 12 = 2 * (A + 12) (Equation 2)

Now, we substitute Equation 1 into Equation 2:
(A + 28) + 12 = 2 * (A + 12)
A + 40 = 2A + 24

Now, we solve for A:
40 – 24 = 2A – A
16 = A

So, the present age of A is 16 years.
Let’s verify:
If A = 16, then B = 16 + 28 = 44.
After 12 years, A’s age = 16 + 12 = 28.
After 12 years, B’s age = 44 + 12 = 56.
Is B’s age (56) twice A’s age (28)? Yes, 56 = 2 * 28. The condition is satisfied.

– Represent the unknown ages with variables.
– Translate the given information into algebraic equations.
– Solve the system of equations to find the unknown age.
This is a typical age-based problem that can be solved using simultaneous linear equations. Setting up the equations correctly based on the time references (present, after 12 years) is crucial.
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