প্রশ্নঃ Rakid lives 4km due west of Faisal's house. Asif lives 6km due north of Faisl's house and 4km due west of Hamed's house. What is the minimum distance from Rakib's house to Hamed's house?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Look at the picture below:
So, distance <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mn>8</mn><mn>2</mn></msup><mo>+</mo><msup><mn>6</mn><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>100</mn></msqrt><mo> </mo><mo>=</mo><mn>10</mn><mi>k</mi><mi>m</mi></math>
প্রশ্নঃ If a certain product that sells normally at 59 taka is on sale at two for 99 taka, then how much can Fahim save by purchasing 10 of that product?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
At two for 99 taka, two price of 10 product = 5 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mo> </mo></math> 99 = 495 tk
at original price ,, ,, ,, 10 ,, = 10 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mo> </mo></math> 59 = 590 tk
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math>he saves = 590 – 495 = 95 tk.
প্রশ্নঃ From the profits of a certain investment, Faisal got 1/3 of the total profit and three of his friends each got 1/3 of the rest. If Faisal and one of his friends got a total of 60000 taka, what was the total profit?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, total profit be taka x
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math>Faisal get taka <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mn>3</mn></mfrac></math>
So, each of the friends get <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mfenced><mrow><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mfrac><mi>x</mi><mn>3</mn></mfrac></mrow></mfenced></math> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mn>9</mn></mfrac></math>
So <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mn>3</mn></mfrac><mo> </mo><mo>+</mo><mfrac>
<mrow><mn>2</mn><mi>x</mi></mrow><mn>9</mn></mfrac></math> = 60,000
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mi>x</mi></mrow><mn>9</mn></mfrac></math> = 60,000
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math>x = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>60</mn><mo>,</mo><mn>000</mn><mo>×
</mo><mn>9</mn></mrow><mn>5</mn></mfrac></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> x = 1,08,000
প্রশ্নঃ A water tank with 64-gallon capacity is filled by pipe A and emptied by pipe B. If the rate of water flow through pipe A is 2 gallons per hour, how many gallons per hour should flow through pipe B so that when both pipes are open, the initially empty tank shold be full in exactly 96 hours?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, x gallons per hour should flow through pipe B
In 1 hour A flouss 2 gallons
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math>,, 96 hour A ,, (96 <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>×</mo></math> 2) ,, = 192 ,,
So 192 – 96x =64
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo>
<mfrac><mrow><mn>192</mn><mo> </mo><mo>-</mo><mo> </mo><mn>64</mn><mo> </mo></mrow><mn>96</mn></mfrac><mo> </mo>
<mo>=</mo><mo> </mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math>
প্রশ্নঃ If x is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Numbers that are divisible by 6 but not 4 are : 6, 18, 30 ..... all there numbers when divided by 12 cannot be an integer.
প্রশ্নঃ Three friends each contributed 8000 taka to buy a computer. If they bought the computer for 19500 taka plus 10% tax, how much money will each of them get back from the inital contribution?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
8000 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo></math> 3 = 24000 tk
19500 + 10% of 19500 = 21450 tk
21450 + 3 = 7150 tk
So, each of them get back Tk (8000 – 7150) = Tk 850
প্রশ্নঃ Rahat completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Total time taken = 10 hrs Let the time taken for first half of journey = x hours So, 21x = (10 – x) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo></math> 24 or, 21x = 240 – 24x or, 45x = 240 or, x = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn><mo> </mo><mo>×</mo> <mo> </mo><mfrac><mn>48</mn><mn>9</mn></mfrac><mo>+</mo><mn>24</mn><mo> </mo><mfenced><mrow><mn>10</mn><mo>-</mo><mo> </mo><mfrac><mn>48</mn><mn>9</mn></mfrac></mrow></mfenced></math> Hence, total journey = 21x + (10-x) 24 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>42</mn><mn>9</mn></mfrac></math> = 21x + (10 – x) 24 = 112 + 112 = 224 km |
প্রশ্নঃ In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is two-third of the number of students of 8 years of age which is 48. what is the total number of students in the school?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, the number be x then
Number of students above 8 years age = (100 - 201% of x) = 80% of x
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> 48 + <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math> of 48
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mn>80</mn><mn>100</mn></mfrac></math> x = 80
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> x= 100
প্রশ্নঃ The ratio of the age of a man and his wife is 4:3. At the time of their marriage the ratio was 5:3 and after 4 years this ratio will become 9:7. How many years ago were they married?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, gentleman's current age be g, women's w, and they were m years ago married.
Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>g</mi><mi>w</mi></mfrac><mo> </mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math>
and,<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>g</mi><mo>+</mo><mn>4</mn></mrow><mrow><mi>w
</mi><mo>+</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></math>
and, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>g</mi><mo>-</mo><mi>m</mi></mrow><mrow><mi>w</mi><mo>-</mo><mi>m</mi></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>5</mn><mn>3</mn></mfrac></math>
Solving, g = 32, m = 12, w = 24
প্রশ্নঃ The area of a rectangular plot is 460 square metres, if the lenght is 15% more than the breadth, what is the breadth of the plot?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, breadth = x metres
Then length = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>+</mo><mo> 
</mo><mfrac><mrow><mn>15</mn><mi>x</mi></mrow><mn>100</mn></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac>
<mrow><mn>15</mn><mi>x</mi></mrow><mn>100</mn></mfrac></math> metres
So, x <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mo> </mo><mfrac><mrow><mn>
115</mn><mi>x</mi></mrow><mn>100</mn></mfrac></math> = 460
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> 115<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup></math> = 46000
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup></math> = 400
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> x = 20
প্রশ্নঃ Hasib took a loan of 1400 tk with simple interest for as many years as the rate of interest. If he paid 126 th as interest at the end of the loan period , what was the rate of interest?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let rate=R% and time = R years
Then <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo> </mo><mfrac><mrow><mn>1
400</mn><mo> </mo><mo>×</mo><mo> </mo><mi>R</mi><mo>×</mo><mi>R</mi></mrow><mn>100</mn></mfrac></mrow>
</mfenced></math>= 126
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>14</mn><msup><mi>R</mi><mn>2</mn></msup></math> = 126
<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mn>2</mn></msup></math> = 9
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> R = 3
প্রশ্নঃ A batsman makes a score of 87 runs in the 17th ining and thus increases his average by 3. What is his average after 17th innings?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let the average after 17th match is x
then average before 17th match is x – 3
So, 16(x – 3) + 87 = 17x
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> x =87 – 48 = 39
প্রশ্নঃ Two student appeared at an examination. One of them secured 9 makes more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are :
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let their marks be (x + 9) and x
Then, x + 9 = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>56</mn><mn>100</mn></mfrac></math> (x + 9 + x)
25(x + 9) = 14 (2x +9)
3x = 99
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> x=33
so, their marks are 42 and 33
প্রশ্নঃ A die is rolled twice. What is the probability of getting a sum equal to 9?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Total number of out comes possible when a die is rolled = 6
Hence, total number of out comes possible when a die is rolled twice, n(s) = 6 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo></math> 6 =36
E = Geting a sum of 9 when the two dice fell = {(3,6), (4,5), (5,4), (6,3)}
Hence n (E) = 4
P(E) =<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mrow><mi>n</mi><mo>
(</mo><mi>S</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mo> </mo><mfrac><mn>4</mn><mn>36</mn></mfrac><mo> </mo><mo>=
</mo><mo> </mo><mfrac><mn>1</mn><mn>9</mn></mfrac></math>
প্রশ্নঃ Two tanks A and B are filled with petrol. Tank A holds 600 liters more than B. If 100 liters of petrol were taken out from each tank, tank A would then contain 3 times as much petrol as tank B. What is the total number of liters of fuel in the two full tanks?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, B has x litres, So A has (x + 600) litres
Accordly to the question,
(x + 500) = 3 (x - 100)
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> x + 500 = 3x – 300
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> 800 = 2x
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> x = 400
And total = 400 + 600 + 400 = 1400 litres.
প্রশ্নঃ Six bells starts ringing logether and ring at intervals of 4, 8, 10, 12, 15 and 20 seconds respectively. How many times will they ring together in 60 minutes?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
LCM of 4, 8, 10, 12, 15 and 20 = 120
120 seconds = 2 minutes
Hence all the bells will ring together in every 2 minutes
Hence, number of times they will ring together in 60 minutes = 1 + <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>60</mn><mn>2</mn></mfrac>
</math> = 31
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