‘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 :
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.
– Translate the given information into algebraic equations.
– Solve the system of equations to find the unknown age.