৯ম - ১৩তম গ্রেড পরীক্ষার প্রস্তুতি

Clearly, 143 is divisible by 11. So, 143 is not prime.
289 is disible by 17. So, 289 is not prime.
117 is divisible by 3. So, 117 is not prime.
359 < (20)² and prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19.
and, 359 is not exactly divisible by any of them. Hence, 359 is a prime number.

Let x, x + 2, x + 4 and x + 6 represent numbers A, B, C and D respectively.
Then, (x+(x+2)+(x+4)+(x+6))/4 = 65
⇒ 4x+12 = 260
⇒ 4x = 248 ⇒ x = 62
So, A = 62, B = 64, C = 66, D = 68
∴ A × D = 62 × 68 = 4216.

Let the daughter's age be x years.
Then, mother age = 3x years
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ x = 12
Present age of daughter = 12 years

Let original number = 100.
New number = 120% of 120% of 100 = (120/100)×(120/100)×100 = 144
Decrease on 144 = 44. Decrease on 100 = ((44/144)×100)% = 30(5/9)%.

C.P. = Tk p. Gain = r%.
∴ S.P. = q = (100+r)% of Tk p = p(100+r)/100

Working hours of Anni = 6 hours.
Working hours of Jessy = 7 hours 30 minutes = 7(1/2) hours.
Required ratio = 6 : 7(1/2) = 6 : 15/2 = 12 : 15 = 4 : 5.

Let the required number of units of work be z

More men, More work (Direct proportion)
More working hours, More work (Direct proportion)
More days, More work (Direct proportion)

Men x:y, Hours per day x:y & Days x:y }::x:z
∴ x × x × x × z = y × y × y × x ⇔ z = y³/x²

let speed of boat in still water = x km/h
Speed of stream current = y km/h
According to question(ATQ),
24/(x−y)+36/(x+y) = 6 h ........... (i)
36/(x−y)+24/(x+y) = 13/2 h.............(ii)

In these type of questions, make factor of 24 and 36 and choose the common valueswhich satisfy the above equations.

24 = 2, 3, 4, 6, 8, 12
36=3, 4, 9, 12
Choose the common factor i.e.

Put this value in equation (i)
24/(x−y)+(36/12) = 6
⇒ 24/(x−y)+3 = 6
⇒ x−y = 8
∴ x+y = 12
∴ x = 10, y = 2
Speed of the current, y = 2 km/h

Radius of incircle = a/2√3.
Area of incircle = (π×a²)/12 cm²
∴ πa²/12 = 154
⇒ a² = (154×12×7)/22
⇒ a = 14√3
∴ Perimeter of the triangle = (3×14√3) cm
= (14×1.732) cm = 72.7 cm (approx.)

The pettern is followed by-
13×0.5+0.5 = 7 ≠ 6
7×1+1 = 8
8×1.5+1.5 = 13.5
13.5×2+2 = 29
29×2.5+2.5 = 75
75×3+3 = 228
Hence, 6 is wrong number and correct number is 7.