৯ম - ১৩তম গ্রেড পরীক্ষার প্রস্তুতি

We know,
LCM × HCF = 1st number × 2nd number
Let 1st number = K
2nd number = 4K
K × 4K = 21 × 84
K = 21
Then number = 21, 84
So, larger number = 84

Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y
∴ 10x+y = 7(x+y)
⇔ 3x = 6y
⇔ x = 2y

Number formed by reversing the digits = 10y + x
∴(10x+y)−(10y+x) = 18
⇔ 9x−9y = 18
⇔ x−y = 2
⇔ 2y−y = 2
⇔ y = 2
So, x = 2y = 4
Hence, the number is 42.

Failed candidates in English = (100 - 70) = 30%
Failed candidates in Mathematics = (100 - 80) = 20%
Candidates who fail in both subject = 10% Candidates who only fail in English = 30 - 10 = 20%
Candidates who only fail in Mathematics = 20 - 10 = 10%
Percentage of passed students in both subject
= 100 - (Candidates who only fail in English + Candidates who only fail in Mathematics + Candidates who fail in both subject)
= 100 - (20 + 10 + 10)
= 60%
According to the question,
60% of students = 144
Total students :
= 144/60 × 100
= 240

According to the question,
Cost price of 70 litres of milk = Rs. 630
Added 5 litres of water
Now, the solution becomes = 75 litres
Cost price of water = Rs. 0
∴ Selling price of 1 litre milk = Rs. 9
Selling price of 75 litres milk = 9 × 75 = Rs. 675
Profit = Selling price - Cost price
= 675 - 630
= 45
Profit = Profit/Cost price × 100
= 45/630 × 100
= 50/7
= 7(1/7)%

Reduction in price 20% amount of sugar will increase 25%
It means,
25% = 6 Kg.
So,
Initially, total Sugar = 6 × 4 = 24Kg.
Thus,
Original price of the sugar was, 240/24
= 10 Taka per kg.

Let the second number be x
Then, first number = 2x, 3rd number = 4x
∴ 2x + x + 4x = 56 × 3
⇒ 7x = 168
⇒ x = 24
∴ Required difference
= 4x - 2x
= 2x
= 2 × 24
= 48

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) = 145
⇒ 5(x+4) = 14(72−x)
⇒ 5x+20 = 1008−14x
⇒ 19x = 988
⇒ x = 52

∴ Daughter's present age
= (68 - 52) years
= 16 years

Second : Third = 9:16
Third : First
= 4:1
= 16:4
∴ Second : Third : First = 9:16:4
Second number = (116 × 9/29) = 36

Speed of man,
= 4 kmph
= (4×5) / 18 m/sec
In 3 min (180 sec) man will go = (20×180) / 8 = 200 m.
That means the diagonal of the square field = 200 m.
Diagonal of square,
= Side of Square × √2 = 200 m.
→ Side of Square = 200/√2
Area of Square = Side²
Area = (200×200)/2
= 20000 sqm.

Speed,
= (60×5/18) m/sec
= 50/3 m/sec
Total distance covered = (100 + 140) m = 240 m
∴ Required time = (240×350)sec = 725sec = 14.4 sec

Let the Arrangement be,
B G B G B G B
4 boys can be seated in 4! Ways
Girl can be seated in 3! Ways
Required number of ways,
= 4! × 3!
= 144

Let principal = 5 units
Hence interest = 5×2/5 = 2 units
Time = 10 years
By using formula, Rate% = 2/5 × 100/10 = 4%

বাইনারি - ২ ভিত্তিক সংখ্যা পদ্ধতি
অক্টাল - ৮ভিত্তিক সংখ্যা পদ্ধতি
ডেসিমেল - ১০ ভিত্তিক সংখ্যা পদ্ধতি
হেক্সাডেসিমেল - ১৬ ভিত্তিক সংখ্যা পদ্ধতি

ধানের উন্নত জাতঃ ইরাটম , হীরা , মুক্তা, আশা , মালা , হরি , নারিকা-১
গমের উন্নত জাতঃ বলাকা, দোয়েল , সোনালিকা, আকবর , আনন্দ, কাঞ্চন, শতাব্দী
তুলার উন্নত জাতঃ রুপালী ও ডেলফোজ
ভুট্টার উন্নত জাতঃ বর্ণালি ও শুভ্রা ,উত্তরণ
তামাকের উন্নত জাতঃ সুমাত্রা , ম্যানিলা
আলুর উন্নত জাতঃ ডায়মন্ড , কার্ডিনাল, সিন্দুরী
টমেটো উন্নত জাতঃ বাহার, মানিক, রতন, মিন্টো, ঝুমকা , শ্রাবণী
বেগুনের উন্নত জাতঃ শুকতারা , তারাপুরী ,ইওরা
কলার উন্নত জাতঃ মোহনবাশী, কানাইভোগ, অগ্নিশ্বর , বীজটবা ইত্যাদি

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