৯ম - ১৩তম গ্রেড পরীক্ষার প্রস্তুতি

437 > 22
All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19
161 is divisible by 7, and 221 is divisible by 13
373 is not divisible by any of the above prime numbers.
Therefore 373 is prime

Let the number be x
According to question, (4/5)x − (45x/100) = 56
⇒ (16x/20) − (9x/20) = 56
⇒ 7x/20 = 56
⇒ x = (56×20)/7
⇒ x = 8×20 = 160
∴ 65% of x = (65/100)×160 = 104

The given three numbers are 2a, 5a and 7a
LCM of 2a, 5a and 7a = 2 × 5 × 7 × a = 70a

Cost of one pen = X
Cost of pencil = X/3
6X + 3(X/3) = 84
6X+X = 84
7X = 84
X = 12
4 pens = 4X = 48
5 pencils = 5(X/3) = 20
Total cost = 68

(1/12)×x = 3/8
x = (3/8)÷(1/12)
x = (3/8)×12
x = 9/2
3/8 is 9/2 th part of 1/12

Let the numbers be 3x, 4x and 6x
Then, 3x × 4x × 6x = 1944
⇔ 72x³ = 1944 ⇔ x³ = 27
⇔ x = 3
∴ Largest number = 6x = 18

Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years. Then, daughter age = (68 - x) years
∴ (x+4)/(68−x+4) = 14/5 ⇒ 5(x+4) = 14(72−x)
⇒ 5x+20 = 1008−14x
⇒ 19x = 988
⇒ x = 52
∴ Daughter's present age = (68-52) years = 16 years.

C.P. of 1 kg = Tk (420/70) = Tk 6.
S.P. of 1 kg = Tk 6.50.
∴ Gain % = ((0.50/6)×100)% = (25/3)% = 8(1/3)%

Let the numbers be 3x and 5x.
Then, (3x-9)/(5x - 9) = 12/23
⇒ 23(3x-9) = 12(5x-9)
⇒ 69x-207 = 60x-108
⇒ 9x = 99
⇒ x = 11.
∴ Larger number = (5×11) = 55.

Let the required number of days be x
7 men ≡ 10 women
⇒ 14 men ≡ 20 women
(14 men and 20 women) ≡ (20+20) women = 40 women
More length, More days (Direct proportion)
More women, Less days (Indirect proportion)
Length 100:600 & Women 40:10 }::10:x
∴ 100 × 40 × x = 600 × 10 ×10
⇔ x = (600×10×10)/(100×40) = 15.

Let the total distance be x km. Then,
((1/2)x)/21 + ((1/2)x)/24 = 10 ⇒ (x/21)+(x/24) = 20
⇒ 15x = 168×20 ⇒ x = (168×20)/15 = 224 km.

Let cost of 1 litre milk be Tk 1
Milk in 1 litre mixture in A = 8/13 litre
C.P. of 1 litre mixture in A = Tk 8/13
Milk in 1 litre mixture in B = 5/7 litre
C.P. of 1 litre mixture in B = Tk 5/7
Milk in 1 litre of final mixture = (900/13)×(1/100)×1 = 9/13 litre
Mean price = Tk 9/13
By the rule of alligation, we have:

∴ Required ratio = 2/91 : 1/13 = 2 : 7

Let sum = Tk x. Then, S.I. = Tk x.
∴ Rate = (100×S.I.)/P×T = (100×x)/(x×12)% = 25/3 % = 8(1/3)%

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103
Solving the two equations, we get: l = 63 and b = 40
∴ Area = (l x b) = (63 x 40) m² = 2520 m²