Alice and Tara's present age is in the ratio of 13:5 respectively. After 4 years, the ratio of their ages will become 7:3 respectively. What is Alice's present age?4 years old20 years old52 years old55 years old
Question
Alice and Tara's present age is in the ratio of 13:5 respectively. After 4 years, the ratio of their ages will become 7:3 respectively. What is Alice's present age?4 years old20 years old52 years old55 years old
Solution
Let's solve the problem step by step:
Step 1: Let's assume Alice's present age as 13x and Tara's present age as 5x, where x is a common factor.
Step 2: After 4 years, Alice's age will be 13x + 4 and Tara's age will be 5x + 4.
Step 3: According to the given information, the ratio of their ages after 4 years will be 7:3. So, we can write the equation as (13x + 4)/(5x + 4) = 7/3.
Step 4: Cross-multiplying the equation, we get (13x + 4) * 3 = (5x + 4) * 7.
Step 5: Expanding the equation, we get 39x + 12 = 35x + 28.
Step 6: Simplifying the equation, we get 4x = 16.
Step 7: Dividing both sides of the equation by 4, we get x = 4.
Step 8: Now, we can find Alice's present age by substituting the value of x into the equation. Alice's present age = 13x = 13 * 4 = 52.
Therefore, Alice's present age is 52 years old.
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