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The ratio of the ages of Karthik and his son is 5:1. The present age of his son is 6 years. After how many years will the ratio of their ages be 7:3?
a)11
b)12
c)13
d)14
Correct answer is option 'B'. Can you explain this answer?
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The ratio of the ages of Karthik and his son is 5:1. The present age o...
Let present age of karthik = 5k and his son = 1k
Given 1k = 6 ==>5k = 30
Let x be the years after which their ages ratio becomes 7:3,
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The ratio of the ages of Karthik and his son is 5:1. The present age o...
Ratio of ages:
The ratio of Karthik's age to his son's age is given as 5:1. This means that for every 5 years Karthik ages, his son ages 1 year.
Given information:
The present age of Karthik's son is 6 years.
Finding the future ratio:
We need to find after how many years the ratio of their ages will be 7:3.
Let's assume that after x years, the ratio of their ages will be 7:3.
Calculating the ages after x years:
After x years, Karthik's age will be 5x and his son's age will be x.
Setting up an equation:
According to the given information, the present age of Karthik's son is 6 years. So, we can set up the following equation:
x = 6
Substituting x = 6 in the equation 5x = 7(6):
5(6) = 7(6)
30 = 42
This equation is not true, which means that after 6 years, the ratio of their ages will not be 7:3.
Finding the correct number of years:
We need to try different values of x until we find the correct one. Let's try x = 12.
After 12 years, Karthik's age will be 5(12) = 60 and his son's age will be 12.
Checking the ratio:
The ratio of their ages after 12 years is 60:12, which simplifies to 5:1. This is not the required ratio of 7:3.
After 12 years, the ratio of their ages is not 7:3.
Therefore, the correct answer is option B) 12.
The ratio of Karthik's age to his son's age is given as 5:1. This means that for every 5 years Karthik ages, his son ages 1 year.
Given information:
The present age of Karthik's son is 6 years.
Finding the future ratio:
We need to find after how many years the ratio of their ages will be 7:3.
Let's assume that after x years, the ratio of their ages will be 7:3.
Calculating the ages after x years:
After x years, Karthik's age will be 5x and his son's age will be x.
Setting up an equation:
According to the given information, the present age of Karthik's son is 6 years. So, we can set up the following equation:
x = 6
Substituting x = 6 in the equation 5x = 7(6):
5(6) = 7(6)
30 = 42
This equation is not true, which means that after 6 years, the ratio of their ages will not be 7:3.
Finding the correct number of years:
We need to try different values of x until we find the correct one. Let's try x = 12.
After 12 years, Karthik's age will be 5(12) = 60 and his son's age will be 12.
Checking the ratio:
The ratio of their ages after 12 years is 60:12, which simplifies to 5:1. This is not the required ratio of 7:3.
After 12 years, the ratio of their ages is not 7:3.
Therefore, the correct answer is option B) 12.
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