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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. एक व्यक्ति की वर्तमान आयु उसकी माँ की आयु का $2/9$ वाँ भाग है । 10 वर्ष बाद, वह अपनी माँ की आयु का $4/11$ वाँ भाग हो जाएगा । 15 वर्ष बाद माँ की आयु कितनी होगी?
  2. एक आदमी अपने बेटे से 24 साल बड़ा है । दो साल बाद, उसकी उम्र उसके बेटे की उम्र से दोगुनी हो जाएगी । उसके बेटे की वर्तमान आयु है
  3. एक पिता ने अपने बेटे से कहा, "मैं तुम्हारे जन्म के समय तुम्हारी वर्तमान उम्र के बराबर था।" यदि पिता की उम्र अब 38 वर्ष है, तो पाँच वर्ष पहले बेटे की उम्र थी
  4. समीर और आनंद की वर्तमान आयु क्रमशः $5:4$ के अनुपात में है । तीन साल बाद, उनकी आयु का अनुपात क्रमशः $11:9$ हो जाएगा । आनंद की वर्तमान आयु वर्षों में क्या है ?
  5. कमला अपने छोटे भाई से दो गुना बड़ी है। यदि उनके बीच के आयु में अंतर 15 वर्ष है, तो उसके छोटे भाई की आयु क्या होगी ?
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