বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Let, Sabina's age 8 years ago be x years.
Then, her present age = (x + 8) years.
according to the question,
x + 8 = (9/7) . x
⇒ 7x + 56 = 9x
⇒ 2x = 56
⇒ x = 28
∴ Sabina’s age now = (x + 8) years = (28 + 8) = 36 years.
Her daughter’s age now = (1/6) × 36 years = 6 years.
Her daughter’s age 3 years ago = (6 – 3) = 3 years.
Solution:
Let, Nishi’s age be 6x years.
Then, Rimi’s age = 5x years.
Now
∴ (6x + 9)/(5x + 9) = 9/8
⇒ 8(6x + 9) = 9(5x + 9)
⇒ 48x - 45x = 81 - 72
⇒ 3x = 9
⇒ x = 3
∴ Difference in their ages = (6x - 5x) years
= x years
= 3 years.
Solution:
Let, son's current age = x
Then, man’s age = 3x
After 5 years, Son’s age = x + 5 and Man’s age = 3x + 5
ATQ,
⇒ x + 5 + 3x + 5 = 70
⇒ 4x + 10 = 70
⇒ 4x = 60
∴ x = 15
So , son’s current age is 15 years.
Solution:
Let the present ages of Amir and his mother be 2x and 5x respectively.
ATQ,
(2x + 4) : (5x + 4) = 5 : 11
(2x + 4)/(5x + 4) = 5/11
⇒ 22x + 44 = 25x + 20
⇒ 25x - 22x = 44 - 20
⇒ 3x = 24
∴ x = 8
Amir's present age = (2 × 8) = 16 years
Solution:
Let,
Tuhin's present age = x years
∴ Rina's present age = 3x years
ATQ,
3x - 4 = 5(x - 4)
⇒ 5x - 20 = 3x - 4
⇒ 5x - 3x = 20 - 4
⇒ 2x = 16
∴ x = 8
So Rina's present age = (3 × 8) = 24 years
Solution:
Let,
The age of Tania = x
The age of Rina = x + 20
ATQ,
x + 20 = 2(x + 5)
⇒ x + 20 = 2x + 10
⇒ x = 10
Solution:
Let the ages of children be x, (x + 4), (x + 8), (x + 12) and (x + 16) years.
Then,
x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 70 5x + 40 = 70
5x = 70 - 40
⇒ 5x = 30
⇒ x = 6
∴ Age of the eldest child = x + 16 = 6 + 16 = 22 years.
Solution:
Let, the daughter's age be x years
Then, mother's age = 3x years
According to the question,
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ 3x - 2x = 24 - 12
∴ x = 12
Solution:
ধরি, বর্তমানে আয়েশার বয়স x এবং তার ভাইয়ের বয়স y
১০ বছর আগে, আয়েশা তার ভাইয়ের বয়সের তিন গুণ ছিল। অর্থাৎ
⇒ x - 10 = 3(y - 10).......... (১)
আবার, বর্তমানে আয়েশা তার ভাইয়ের চেয়ে ১০ বছর বড়।
x = y + 10
এখন, x এর মান (১) এ বসিয়ে পাই,
⇒ (y + 10) - 10 = 3(y - 10)
⇒ y = 3y - 30
⇒ y - 3y = - 30
⇒ - 2y = - 30
∴ y = 15
তার ভাইয়ের বর্তমান বয়স 15 বছর।
Solution:
Let, The age of 4 children = x years, x + 3 years, x + 6 years, x + 9 years
ATQ,
x + (x + 3) + (x + 6) + (x + 9) = 54
⇒ 4x + 18 = 54
⇒ 4x = 54 - 18
⇒ 4x = 36
⇒ x = 36 ÷ 4
∴ x = 9
So the age of the elder children is = 9 + 9 = 18 years
Solution:
Let A’s present age be ‘x’ years.
According to the question,
x + 15 = 5 (x - 5)
⇒ x + 15 = 5 x - 25
⇒ 4x = 40
⇒ x = 10
⇒ A’s present age = 10 years
Therefore, A’s age 3 years hence = 10 + 3 = 13 years.
Solution:
The given condition is,
⇒ A + B = (B + C) + 15
⇒ A + B = B + C + 15
⇒ A + B - B - C = 15
⇒ A - C = 15
⇒ C = A − 15
∴ C is 15 years younger than A.
Solution:
Let the mother's present age be x years.
Then, the person’s present age = (2/5)x years.
According to the question:
After 8 years:
(2x/5) + 8 = (1/2)(x + 8)
Multiply both sides to eliminate fractions:
(2x + 40) / 5 = (x + 8) / 2
⇒ 2(2x + 40) = 5(x + 8)
⇒ 4x + 80 = 5x + 40
⇒ 80 - 40 = 5x - 4x
⇒ x = 40
✅ Mother’s present age = 40 years
Problem: Seven years ago, Arun's age was 6x years and Ashok's age was 8x years. Their current age difference is 12 years. Find Ashok's present age.
Solution:
Let,
7 years ago:
Arun's age = 6x
Ashok's age = 8x
At present:
Arun = 6x + 7
Ashok = 8x + 7
Given that the current age difference is 12 years:
(8x + 7) − (6x + 7) = 12 ⇒ 8x + 7 − 6x − 7 = 12 ⇒ 2x = 12 ⇒ x = 12 ÷ 2 ⇒ x = 6
Therefore,
Ashok's present age = 8x + 7 = 8 × 6 + 7 = 55 years
Problem:
The ratio of present ages of Moni and Roni is 6 : 5. After 10 years, the ratio becomes 8 : 7. Find the difference in their present ages.
Step-by-Step Solution:
Step 1: Let the present ages be:
Moni = 6x
Roni = 5x
Step 2: After 10 years:
Moni = 6x + 10
Roni = 5x + 10
Given ratio:
(6x + 10) / (5x + 10) = 8 / 7
Step 3: Cross multiplying:
7(6x + 10) = 8(5x + 10)
42x + 70 = 40x + 80
42x - 40x = 80 - 70
2x = 10 → x = 5
Step 4: Their current ages:
Moni = 6 × 5 = 30 years
Roni = 5 × 5 = 25 years
✅ Final Answer: Difference = 30 − 25 = 5 years