বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক

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

Problem:
The ratio of present ages of P and Q is 3 : 4. Four years hence, this ratio would become 4 : 5. Find the present age of Q.

Step-by-Step Solution:

Let P's present age = 3x and Q's present age = 4x.

After 4 years, their ages will be:
P = 3x + 4
Q = 4x + 4

According to the problem, the new ratio is:
(3x + 4) / (4x + 4) = 4 / 5

Cross-multiplying gives:
5(3x + 4) = 4(4x + 4)
15x + 20 = 16x + 16

Simplifying:
15x - 16x = 16 - 20
-x = -4 → x = 4

Therefore, Q's present age = 4x = 4 × 4 = 16 years.

✅ Final Answer: Q is 16 years old.

Problem:
Jobin is one year older than three times Lina's age. If their ages currently add up to 33 years, then how old will Jobin be in 4 years?

Step-by-Step Solution:

Let Lina's current age be: x
Then, Jobin's current age = 3x + 1

According to the problem:
x + (3x + 1) = 33
⇒ 4x + 1 = 33
⇒ 4x = 32
⇒ x = 8

Lina's age = 8 years
Jobin's current age = 3×8 + 1 = 25 years

So, Jobin's age in 4 years = 25 + 4 = 29 years

✅ Final Answer: Jobin will be 29 years old in 4 years.