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Question

At present, Sharad is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of the ages of these three people 3 years ago was 63 years, then Sharad's present age (in years) is:

The correct answer is
45

Let S be Sharad's present age, Son be his son's present age, and D be his daughter's present age.

Establishing Present Age Relationships

  • According to the question, Sharad is three times as old as his son:

    $S = 3 \times Son$

  • The daughter is 3 years younger than the son:

    $D = Son - 3$

Calculating Ages 3 Years Ago

The ages of the three people 3 years ago would be:

  • Sharad's age: $S - 3$
  • Son's age: $Son - 3$
  • Daughter's age: $D - 3$

Using the Sum of Past Ages

The sum of their ages 3 years ago was 63 years:

$(S - 3) + (Son - 3) + (D - 3) = 63$

Simplify the equation:

$S + Son + D - 9 = 63$

Combine the ages to find the total present age sum:

$S + Son + D = 63 + 9$

$S + Son + D = 72$

Solving for Sharad's Present Age

Substitute the relationships from step 1 into the total present age sum equation:

$(3 \times Son) + Son + (Son - 3) = 72$

Combine the terms involving the son's age:

$5 \times Son - 3 = 72$

Add 3 to both sides to isolate the son's age term:

$5 \times Son = 72 + 3$

$5 \times Son = 75$

Divide by 5 to find the son's present age:

$Son = \frac{75}{5}$

$Son = 15$

Now, calculate Sharad's present age using the relationship $S = 3 \times Son$:

$S = 3 \times 15$

$S = 45$

Therefore, Sharad's present age is 45 years.

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Important Questions from Problem on Ages (Notes)

  1. A father said to his son, "I was as old as you are when I became your father." If the current age of father is 52 years, the age of son after 10 years will be___________.

  2. The sum of the age of A and 5 times the age of B is 55 years. When 3 times the age of A is added to 7 times the age of B, the result is 99 years. The sum of the ages (in years) of A and B is:
  3. The sum of the age of A and 3 times the age of B is 43 years. When 5 times the age of A is added to 2 times the age of B, the result is 98 years. The sum of the ages (in years) of A and B is:
  4. Eight years ago, the age of the mother was four times the age of her son. Eight years hence, the mother's age will be two times the age of her son. Find the ratio of the present age of the mother to the age of the son.
  5. The sum of the age of A and 5 times the age of B is 36 years. When 3 times the age of A is added to 7 times the age of B, the result is 62 years. The sum of the ages (in years) of A and B is:
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