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A father is 3 yrs more than thrice the age of his son. Three yrs later, the father will be 10 yrs more than twice the age of his son. The ratio of their ages is
  • a)
    3:1
  • b)
    33:10
  • c)
    4:1
  • d)
    5:2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A father is 3 yrs more than thrice the age of his son. Three yrs later...
Let father’s age be x & son’s age be y

By 1st condition:

3 + 3y = x (three plus three times age of son is father’s age)

By 2nd condition:

x + 3 = 2(y + 3) + 10 [here we are talking about 3 years hence. So 3 has to be added to their present ages, and then satisfy the condition]

So the final 2 equations are

x-3y = 3      (1)

x-2y = 13    (2)

Solving them we get

y = 10, x = 33

So the father’s present age is 33 and that of the son is 10.
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Most Upvoted Answer
A father is 3 yrs more than thrice the age of his son. Three yrs later...
Given:
Let the age of the son be x years.
The age of the father is 3 years more than thrice the age of the son, which can be represented as 3x + 3.

To find:
The ratio of their ages.

Solution:

Step 1: Set up the equation based on the given information.

According to the given information,
The age of the son = x years
The age of the father = 3x + 3 years

Step 2: Write the equation based on the information given three years later.

Three years later,
The age of the son = x + 3 years
The age of the father = (3x + 3) + 3 = 3x + 6 years

According to the given information, the father will be 10 years more than twice the age of his son.
So, we can write the equation as:
3x + 6 = 2(x + 3) + 10

Step 3: Solve the equation to find the value of x.

Let's solve the equation:
3x + 6 = 2x + 6 + 10
3x - 2x = 16
x = 16

Step 4: Calculate the ages of the son and the father.

The age of the son = x = 16 years
The age of the father = 3x + 3 = 3(16) + 3 = 51 years

Step 5: Find the ratio of their ages.

The ratio of their ages = Age of father : Age of son
= 51 : 16

Simplifying the ratio by dividing both numbers by their greatest common divisor, which is 1:
= 51 ÷ 1 : 16 ÷ 1
= 51 : 16

Therefore, the ratio of their ages is 51:16, which is equivalent to 33:10 in simplified form.

Therefore, the correct answer is option 'B' - 33:10.
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A father is 3 yrs more than thrice the age of his son. Three yrs later, the father will be 10 yrs more than twice the age of his son. The ratio of their ages isa)3:1b)33:10c)4:1d)5:2Correct answer is option 'B'. Can you explain this answer?
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