বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Let's father's age x and son's age is y
ATQ, x + y = 42 ....(i)
x - y = 22 .... (ii)
(i) - (ii) = 2y = 20
∴ y = 10
∴ son's age is 10 years
Solution:
Let the present age of Mira be x years.
So, her son's present age is x/30 years.
In 18 years:
- Mira's age will be: x + 18
- Her son's age will be: (x/30) + 18
According to the question:
x + 18 = 3 × ((x/30) + 18)
⇒ x + 18 = (3x/30) + 54
⇒ x + 18 = x/10 + 54
Multiplying both sides by 10 to eliminate the fraction:
⇒ 10x + 180 = x + 540
Now, solving for x:
⇒ 10x - x = 540 - 180
⇒ 9x = 360
⇒ x = 360/9
⇒ x = 40
Conclusion: The present age of Mira is 40 years.
Solution:
Let x and y be the ten's and unit's digits of the woman's age, respectively.
Then, Woman's age = 10x + y years
Husband's age = 10y + x years
According to the question:
(10y + x) − (10x + y) = (1/11) × (10y + x + 10x + y)
⇒ 9y − 9x = (1/11)(11y + 11x)
⇒ 9(y − x) = x + y
⇒ 9y − 9x = x + y
⇒ 10x = 8y
⇒ x = (4/5)y
Since y is a single-digit and must make x a whole number, the only valid value for y is 5.
⇒ x = 4
Therefore: Woman's age = 10×4 + 5 = 45 years
Let, 10 years ago there age was = x, 2x, 3x
∴ x + 2x + 3x = 90 - 30
⇒ 6x = 60
⇒x = 10
⇒ Present age of B is, 2x + 10 = 2×10 + 10 = 30 years
Solution:
Let the father's current age be x years,
and the son's current age be y years.
First condition: Eighteen years ago, the father was three times as old as the son.
⇒ x - 18 = 3(y - 18)
⇒ x - 18 = 3y - 54
⇒ x = 3y - 36 … (1)
But also, rearranging this gives:
3y = x + 36 ⇒ y = x/3 + 12 … (1a)
Second condition: Currently, the father is twice as old as the son.
⇒ x = 2y … (2)
Substituting (1a) into (2):
x = 2(x/3 + 12)
⇒ x = 2x/3 + 24
⇒ x - 2x/3 = 24
⇒ x/3 = 24
⇒ x = 72
Now from equation (2): y = x / 2 = 72 / 2 = 36
∴ Father's age = 72 years
Son's age = 36 years
Total of their present ages = 72 + 36 = 108 years
সমাধান:
ধরি,
- ববির বর্তমান বয়স = B বছর
- আরিফের বর্তমান বয়স = A বছর
- সামির বর্তমান বয়স = S বছর
প্রশ্নমতে:
A = 4B.............(১)
A + 4 = 36...........(২)
B + 6 = 2(S + 6)..........(৩)
(২) নং সমীকরণ থেকে পাই:
A = 36 − 4 = 32
(১) সমীকরণে প্রতিস্থাপন করলে:
32 = 4B ⇒ B = 8
(৩) নং সমীকরণ থেকে পাই:
8 + 6 = 2(S + 6)
14 = 2S + 12
⇒ 2S = 2
⇒ S = 1
∴ ৬ বছর পর সামির বয়স = S + 6 = 1 + 6 = 7 বছর
ধরি, জামিলের বয়স x বছর।
তাহলে জামিলের বাবার বয়স 3x বছর৷
প্রশ্নমতে, 2(x+16) = 3x+16
বা, 2x+32 = 3x+16
বা, x = 16
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
সুতরাং উত্তর উপরের কোনো অপশনে নেই।
Solution:
Suppose, 3 years ago Tina's age was x years.
Then:
- Kalam's age = 2x
- Meena's age = 2x - 30
Now (current ages):
- Tina = x + 3
- Kalam = 2x + 3
- Shaila = (2x + 3) - 47 = 2x - 44
According to the question:
x + 7 = 2 × (2x - 44 + 4)
⇒ x + 7 = 2 × (2x - 40)
⇒ x + 7 = 4x - 80
⇒ 3x = 87
⇒ x = 29
Current ages:
- Tina = 29 + 3 = 32
- Kalam = 2×29 + 3 = 61
- Meena = 61 - 30 = 31
- Shaila = 2×29 - 44 = 14
Total sum of their ages = 32 + 61 + 31 + 14 = 138
Given one star(S) equals four circles(C) and three circles equal four diamonds(D).
Then, S = 4C and 3C = 4D
Then, C = (4/3)D
∴ S = 4×(4/3)D
⇒ S = (16/3)D
Hence, S : D = 16 : 3
Let, these two numbers be 3x and 4x
then their LCM = 12x
Now, according to question,
12x = 60
Or, x = 5
Thus, the numbers are (3x = 3 × 5) = 15 and (4x = 4 × 5) = 20
Solution:
Let total number of students be T.
Section A and Section B each have T/2 students.
Given: Ratio of girls to boys in the total class is 3:5
So, total girls Gt = (3/8) × T
Total boys Bt = (5/8) × T
Also given: Ratio of girls to boys in Section A is 5:7
So, in Section A (T/2 students):
Girls Ga = (5/12) × T/2
Boys Ba = (7/12) × T/2
Now:
Gt = Ga + Gb
(3/8)T = (5/12)(T/2) + Gb
Gb = (3/8)T - (5/24)T = T/6
Bt = Ba + Bb
(5/8)T = (7/12)(T/2) + Bb
Bb = (5/8)T - (7/24)T = T/3
Therefore:
Gb / Bb = (T/6) / (T/3) = 1/2
Let,
A's profit = 42,360 = 5x
So, x = 42,360/5 = 8472
total profit = 5x + 7x + 8x = 20x = 20×8472
∴ The total profit is tk. 1,69,440
Let the numbers be 7x and 4x
ATQ,
(7x + 8) : (4x + 8) = 13 : 8
Or, 56x + 64 = 52x + 104
Or, 4x = 40
The smaller number is 40