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Problems on Ages

মোট প্রশ্ন৬০৭এই পাতা৫প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Problems on Ages

PrepBank · পাতা ৭ / ৭ · ৬০১–৬০৫ / ৬০৭

৬০১.
The average age of 15 colleague of a office is 23. If the minimum age requirement for being a member of the office is 19 years, what is the possible maximum range of the ages?
  1. ক
    51 years
  2. খ
    67 years
  3. গ
    57 years
  4. ঘ
    79 years
ব্যাখ্যা
প্রশ্ন: The average age of 15 colleague of a office is 23. If the minimum age requirement for being a member of the office is 19 years, what is the possible maximum range of the ages?

সমাধান:
15 জনের গড় বয়স 23 বছর
∴ 15 জনের মোট বয়স = 15 × 23 = 345 বছর

1 জনের সর্বনিম্ন বয়স 19 বছর
∴ 14 জনের সর্বনিম্ন মোট বয়স = 19 × 15 = 266 বছর

অতএব, একজনের সর্বোচ্চ বয়স হতে পারে = 345 - 266 = 79 বছর
৬০২.
Age of the father is equal to the sum of ages of his three sons. If in 19 years, one third of father's age will be equal to one fifth the sum of the ages of the sons. What is the age of the father?
  1. ক
    58
  2. খ
    48
  3. গ
    38
  4. ঘ
    28
ব্যাখ্যা
Question: Age of the father is equal to the sum of ages of his three sons. If in 19 years, one third of father's age will be equal to one fifth the sum of the ages of the sons. What is the age of the father?

Solution:
Let,
The age of the father now  = a
Sum of the ages of three sons = b
Now, a = b

After 19 years, Father's age = a + 19
Age's of three son's = b + (3 × 19) = b + 57

ATQ, (1/3)(a + 19) = (1/5)(b + 57)
⇒ 5a + 95 = 3b + 171
⇒ 5a - 3a = 171 - 95 [∵ b = a]
⇒ 2a = 76
∴ a = 38
৬০৩.
A father said to his son, ''I was as old as you are at the present at the time of your birth''. If the father's age is 38 years now, what was the son's age five years back?
  1. ক
    12
  2. খ
    18
  3. গ
    17
  4. ঘ
    16
  5. ঙ
    14
ব্যাখ্যা

Fathers age when his son was born= son's present age
Fathers age when his son was born + son's present age = father's present age
Therefore, 2 (Son's present age) = 38
=> Son's present age = 19
=> Son's age five years back = 19 − 5 = 14

৬০৪.
Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.
  1. ক
    32.5 years
  2. খ
    27.5 years
  3. গ
    25 years
  4. ঘ
    24.9 years
  5. ঙ
    None of these
ব্যাখ্যা
Question: Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.

Question:
Let age of Romi be y
Nisha is 15 years elder than Romi = (y + 15). So Nisha's age 5 years ago = (y + 15 - 5).
Romi's age before 5 years = (y - 5)
5 years ago, Nisha is 3 times as old as Romi
(y + 15 - 5) = 3 (y - 5)
⇒ (y + 10) = (3y - 15)
⇒ 2y = 25
⇒ y = 12.5
Romi's age = 12.5 years
Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.
৬০৫.
The captain of Bangladesh Cricket Team is 26 years old and the wicket keeper is 4 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
  1. ক
    ক) 21
  2. খ
    খ) 22
  3. গ
    গ) 23
  4. ঘ
    ঘ) 24
  5. ঙ
    ঙ) None
ব্যাখ্যা
ধরি, দলের গড় বয়স x
তাহলে দলের মোট বয়স 11x (যেহেতু টিমে খেলোয়াড় থাকে এগারোজন)
দেওয়া আছে, ক্যাপ্টেনের বয়স 26 বছর
এবং উইকেট কিপারের বয়স 26+4 = 30 বছর
তাহলে তাদেরকে ছাড়া দলের গড় বয়স {11x - (26+30)}/9
প্রশ্নমতে, (11x - 56)/9 = x - 1
বা, 11x - 56= 9x - 9
বা, 2x = 47
বা, x = 47/2=23.5
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