বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Let A’s age 10 years ago be = x years
Then, B’s age 10 years ago = 2x years
ATQ, (x + 10) / (2x + 10) = 3/4
Or, 6x + 30 = 4x + 40
Or, x = 5
So, the total of their present ages = (x + 10 + 2x + 10)
= (5 + 10 + 2.5 + 10)
= 35 years.
Let daughter’s age be = A
and mother’s age be = B
ATQ, 2A + B = 70 ..... (i)
and, A + 2B = 95 ..... (ii)
(ii)×2 - (i)
⇒ 3B = 120
⇒ B = 40
Total age of the members = 16 × 22 = 352 years
Total age of 15 members at least = 15 × 19 = 285 years
∴ Possible maximum age = 352 - 285 = 67 years
ধরি,
C এর বয়স x বছর
তাহলে B এর বয়স = 2x বছর এবং A এর বয়স = (2x + 2) বছর
প্রশ্নমতে, x + 2x + 2x + 2 = 27
⇒ 5x = 27 - 2
⇒ x = 25/5
⇒ x = 5
∴ B এর বয়স (2×5) বছর = 10 বছর
A + B + C = 30×3 = 90 yrs ...... (1)
ATQ,
B - A = C - B
Or, A+C = 2B
From (1),
B + 2B = 90
Or, B = 30
∴ D = B + 40 = 30 + 40 = 70
So, B + D = 30+70 = 100 yrs
Let the age of Ali, Gazi and Masud be respectively 2x, 3x and 4x years
ATQ, 10 years ago, 2x + 3x + 4x = 93 - 30
9x = 63
x = 7
So, 10 years ago Masud's age was, 4x = 28 years
Now, Masud's age is = 38 years
Let,
Samir’s age is = x
So Babul’s age is = x - 2
ATQ,
x - 2 = 2(x - 2 - 2)
Or, x - 2 = 2x - 8
∴ x = 6
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:
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,
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:
Now (current ages):
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:
Total sum of their ages = 32 + 61 + 31 + 14 = 138
