The average age of a woman and her daughter is 46 years. The ratio of their ages is 15:8 respectively. What will be the respective ratio of their ages after 8 years?Options :8 : 510 : 1717 : 105 : 8

Let's solve this step by step:

Step 1: The average age of a woman and her daughter is 46 years. This means the sum of their ages is 46*2 = 92 years.

Step 2: The ratio of their ages is given as 15:8. So, the sum of the ratio numbers is 15+8 = 23.

Step 3: Now, let's find the value of 1 ratio. It will be 92/23 = 4 years.

Step 4: Therefore, the woman's age is 154 = 60 years and the daughter's age is 84 = 32 years.

Step 5: After 8 years, the woman will be 60+8 = 68 years old and the daughter will be 32+8 = 40 years old.

Step 6: The new ratio of their ages will be 68:40. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 4. So, the simplified ratio is 17:10.

So, the respective ratio of their ages after 8 years will be 17:10.

Let's solve this step by step:

Step 1: The average age of a woman and her daughter is 46 years. This means the sum of their ages is 46*2 = 92 years.

Step 2: The ratio of their ages is given as 15:8. So, we can divide the total age (92 years) in this ratio to find their individual ages.

Step 3: The sum of the ratio 15:8 is 15+8 = 23.

Step 4: The woman's age is (15/23)*92 = 60 years and the daughter's age is (8/23)*92 = 32 years.

Step 5: After 8 years, the woman will be 60+8 = 68 years old and the daughter will be 32+8 = 40 years old.

Step 6: The new ratio of their ages will be 68:40.

Step 7: Simplify this ratio by dividing both numbers by their greatest common divisor, which is 4. So, the simplified ratio is 17:10.

So, the respective ratio of their ages after 8 years will be 17:10.

The problem states that the average age of a woman and her daughter is 46 years. This means that the sum of their ages is 46 * 2 = 92 years.

The ratio of their ages is given as 15:8. This means that the sum of their ages (92 years) is divided in the ratio 15:8.

Let's denote the woman's age as 15x and the daughter's age as 8x. Therefore, 15x + 8x = 92. Solving this equation gives x = 4.

So, the woman's current age is 15 * 4 = 60 years and the daughter's current age is 8 * 4 = 32 years.

After 8 years, the woman will be 60 + 8 = 68 years old and the daughter will be 32 + 8 = 40 years old.

Therefore, the ratio of their ages after 8 years will be 68:40. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 4.

So, the simplified ratio is 17:10.

Therefore, the answer is 17 : 10.