Question

Kavitha is 9 years younger than Lizzy. 8 years ago, Lizzy was 2 times as old as Kavitha reduced by 1. How old are they now?

A) Lizzy is 23 years old, and Kavitha is 14 years old.
B) Lizzy is 31 years old, and Kavitha is 22 years old.
C) Lizzy is 27 years old, and Kavitha is 18 years old.
D) Lizzy is 19 years old, and Kavitha is 10 years old.

Answer 1

Lizzy is 27 years old, and Kavitha is 18 years old.

Step-by-step explanation:

Let's assume Lizzy's age is represented by L and Kavitha's age is represented by K.

1. From the given information, we know that K = L - 9 (Kavitha is 9 years younger than Lizzy).
2. 8 years ago, Lizzy's age was L - 8 and Kavitha's age was K - 8. According to the second equation, L - 8 = 2(K - 8) - 1 (Lizzy was 2 times as old as Kavitha reduced by 1).
3. Now we can substitute the first equation into the second equation: L - 8 = 2((L - 9) - 8) - 1.
4. Simplifying the equation, we get L - 8 = 2(L - 17) - 1.
5. Expanding and simplifying further, we get L - 8 = 2L - 34 - 1.
6. Combining like terms, we get L - 8 = 2L - 35.
7. Bringing all terms to one side, we get L - 2L = -35 + 8.
8. Simplifying further, we get -L = -27.
9. Dividing both sides by -1, we get L = 27 (Lizzy's age).
10. Substituting L = 27 into the first equation, we get K = 27 - 9 = 18 (Kavitha's age).

Therefore, Lizzy is 27 years old and Kavitha is 18 years old now.