বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Let, present ages of three persons 4x, 7x, 9x
Eight years ago, the sum of their ages was 56 years
At present, the sum of their ages i s
= 56 + 8 + 8 + 8 = 56 + 24 years = 80 years
4x + 7x + 9x = 80
⇒ 20x = 80
⇒ x = 4
The present age of the eldest person is = 4 × 9 = 36 years
Solution:
Let,
the capacity of 1 bucket = x the capacity of tank = 25x
Capacity of the new bucket = 2x/5
∴ Required number of buckets = 25x/(2x/5)
= (25x × 5)/2x = 125/2 = 62.5
Solution:
Let, the first and second numbers be x and y,
ATQ,
y - 30% of x = y (4/5)
⇒ y - (30x/100) = 4y/5
⇒ y - (3x/10) = 4y/5
⇒ (10y -3x)/10 = 4y/5
⇒ (10y - 3x)/2 = 4y
⇒ 10y - 3x = 8y
⇒ - 3x = 8y - 10y
⇒ 3x = 2y ⇒ x/y = 2/3
∴ x : y = 2 : 3
Solution:
Let the number of student and teacher be represented by S and T respectively.
S : T = 30 : 1
S/T = 30/1
S = 30T.............(1)
If number of students increases by 50 and number of teachers increases by 5
50 + S : T + 5 = 25 : 1
⇒ (50 + S)/(T + 5) = 25/1
⇒ S + 50 = 25(T + 5)
⇒ S + 50 = 25T + 125
⇒ 30T + 50 = 25T + 125 [From (1)]
⇒ 30T - 25T = 125 - 50
⇒ 5T = 75
⇒ T= 75/5 =15
∴ No of teachers=T=15
Solution:
Let the monthly income of one person be 4x and that of the other be 5x
Let the monthly expenses of one person be 7y and that of other be 9y
According to the question,
4x - 7y= 50...................(1)
5x - 9y= 50....................(2)
(1) × 9 - (2) × 7
36x - 63y - 35x + 63y = 450 - 350
x = 100
Monthly income of one person
= 4 ×100 = 400
Monthly income of the other person
= 5 × 100 = 500
Solution:
Let
2A = 3B = 4C = x
2A = x
A = x/2
3B =x
B = x/3
4C = x
C = x/4
A : B : C = x/2 : x/3 : x/4
= (x/2) × 12 : (x/3) × 12 : (x/4) × 12
= 6 : 4 : 3
Solution:
Let the total profit be Tk. 100.
After paying to charity, A's share = (95 × 3/5) = 57
If A's share is Tk. 57, total profit = 100.
If A's share is Tk. 855, total profit = (100/57) × 855 = 1500.
