The ratio of the ages of two friends is 3:4. If the sum of their ages is 56 year

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Question: The ratio of the ages of two friends is 3:4. If the sum of their ages is 56 years, what is the age of the older friend? (2019)

Options:

Correct Answer: 32

Exam Year: 2019

Solution:

Let the ages be 3x and 4x. Then, 3x + 4x = 56 => 7x = 56 => x = 8. Older friend\'s age = 4x = 32.

The ratio of the ages of two friends is 3:4. If the sum of their ages is 56 years, what is the age of the older friend? (2019)

The ratio of the ages of two friends is 3:4. If the sum of their ages is 56 years, what is the age of the older friend? (2019)

Step 1: Understand the ratio of the ages. The ratio of the ages of the two friends is given as 3:4.
Step 2: Assign variables based on the ratio. Let the age of the first friend be 3x and the age of the second friend be 4x, where x is a common multiplier.
Step 3: Write an equation for the sum of their ages. According to the problem, the sum of their ages is 56 years. So, we can write the equation: 3x + 4x = 56.
Step 4: Combine like terms in the equation. This gives us 7x = 56.
Step 5: Solve for x. To find x, divide both sides of the equation by 7: x = 56 / 7, which simplifies to x = 8.
Step 6: Find the age of the older friend. Since the older friend's age is represented by 4x, we calculate it as 4 * 8 = 32.
Step 7: Conclude that the age of the older friend is 32 years.

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