If the sum of the ages of A and B is 50 and A is 10 years older than B, how old is B?

Let B's age be x. Then A's age is x + 10. The equation is x + (x + 10) = 50. Simplifying gives 2x + 10 = 50, so 2x = 40, and x = 20. Thus, B is 20 years old.

A mother is four times as old as her son. After 20 years, the mother will be twice as old as her son. What are their current ages?

Let the son's age be x. Then the mother's age is 4x. After 20 years, the equation is (4x + 20) = 2(x + 20). Simplifying gives 4x + 20 = 2x + 40, so 2x = 20, and x = 10. The son is currently 10 years old, and the mother is 40 years old.

If the age of a grandfather is 5 times that of his grandson and the sum of their ages is 60, how old is the grandson?

Let the grandson's age be x. Then the grandfather's age is 5x. The equation is x + 5x = 60. Simplifying gives 6x = 60, so x = 10. Thus, the grandson is 10 years old.

Ten years ago, the ages of two friends were in the ratio 3:5. If the older friend is currently 4 years older than the younger friend, how old is the younger friend now?

Let the younger friend's age ten years ago be 3x and the older friend's age be 5x. The equation is 5x + 10 = 3x + 4. Simplifying gives 2x = -6, which is not possible. Re-evaluate the problem statement.

If A is twice as old as B now, and in 4 years, A will be 10 years older than B, what are their current ages?

Let B's age be x. Then A's age is 2x. In 4 years, the equation is (2x + 4) = (x + 4) + 10. Simplifying gives 2x + 4 = x + 14, so x = 10. B is currently 10 years old, and A is 20 years old.

If the age of a woman is 3 years less than twice the age of her daughter and the sum of their ages is 45, how old is the daughter?

Let the daughter's age be x. Then the woman's age is 2x - 3. The equation is x + (2x - 3) = 45. Simplifying gives 3x - 3 = 45, so 3x = 48, and x = 16. Thus, the daughter is 16 years old.

Three years ago, Tom was three times as old as his sister. If Tom is currently 21 years old, how old is his sister now?

Three years ago, Tom was 21 - 3 = 18 years old. Let his sister's age three years ago be y. The equation is 18 = 3y, giving y = 6. Therefore, his sister is now 6 + 3 = 9 years old.

If the present ages of A and B are in the ratio 5:3 and the sum of their ages is 48, what is the age of A?

Let A's age be 5x and B's age be 3x. The equation is 5x + 3x = 48. Simplifying gives 8x = 48, so x = 6. Thus, A is 5 * 6 = 30 years old.

In 6 years, the age of a man will be 4 times his son's age. If the son is 3 years old now, how old will the man be in 6 years?

Let the man's current age be x. In 6 years, the equation is (x + 6) = 4(3 + 6). Simplifying gives x + 6 = 4 * 9, so x + 6 = 36, and x = 30. The man will be 30 + 6 = 36 years old in 6 years.

If Maria is 3 years older than Tom, and the sum of their ages is 27, what is Tom's age?

Let Tom's age be x. Then Maria's age is x + 3. The equation is x + (x + 3) = 27. Simplifying gives 2x + 3 = 27, so 2x = 24, and x = 12. Therefore, Tom is 12 years old.

In 6 years, Jake will be 4 times as old as he was 2 years ago. How old is Jake now?

Let Jake's current age be x. In 6 years, he will be x + 6. Two years ago, he was x - 2. The equation is x + 6 = 4(x - 2). Simplifying gives x + 6 = 4x - 8, so 3x = 14, and x = 14/3. Thus, Jake is currently approximately 4.67 years old.