Standard Bank Ltd - Trainee Asst. Officer - 22.01.2016/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ If a number is divisible by 102 then it is also divisible by which of the following number?

বর্ণনাঃ

As 102 is divisible by 2, 3 and 17 then the number which is divisible by 102 is also divisible by all of three numbers.

প্রশ্নঃ All 120 students in a class play cricket or football or both, 75 play cricket and 60 play football. How many students play both?

বর্ণনাঃ

<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mi>A</mi><mo>&#x222A;</mo><mi>B</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>n</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>+</mo><mi>n</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>-</mo><mi>n</mi><mo>(</mo><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>)</mo></math>
⇒ 120 = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo>+</mo><mn>60</mn><mo>-</mo><mi>n</mi><mo>(</mo><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>)</mo></math>
⸫ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mi>A</mi><mo>&#x2229;</mo><mi>B</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mn>15</mn></math>

প্রশ্নঃ In a group of 4 people, the height of the group members are 5 feet 4 inches, 5 feet, 5 feet 6 inches, and 4 feet 10 inches. The average height of the group members is :

বর্ণনাঃ

First we convert all the length to inches (the smaller unit), then we average and finally conver to feet and inchs. At 12 inches make 1 foot, so
Average = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mo>(</mo><mn>5</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>4</mn><mo>)</mo><mo>+</mo><mn>4</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>6</mn><mo>+</mo><mn>10</mn></mrow><mn>4</mn></mfrac></math>
= <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mo>&#xD7;</mo><mn>19</mn><mo>+</mo><mn>4</mn><mo>+</mo><mn>6</mn><mo>+</mo><mn>10</mn></mrow><mn>4</mn></mfrac></math>
= <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>228</mn><mo>+</mo><mn>5</mn><mo>+</mo><mn>6</mn><mo>+</mo><mn>10</mn></mrow><mn>4</mn></mfrac></math>
= 62 inches
= <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>62</mn><mn>12</mn></mfrac></math> feet
= 5.1666 feet

প্রশ্নঃ If x+y=4 and y+z=8 and z+x=6, then 2x-y-z=?

বর্ণনাঃ

x+y=4
y+z=8
z+x=6
⸫ 2x+2y+2z=4+8+6
Now 2x+2y+2z-3(y+z)=4+8+6-3(y+z)
2x-y-z=4+8+6-3×8 [y+z=8]
=-6

প্রশ্নঃ Son's age is now one third of father's age. In 12 years from now son's age will be one half of father's age. What is the son's age

বর্ণনাঃ

Let, the son's age be x, so father's age is 3x
Now, x+12 = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>12</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math>
⇒ 2x+24 = 3x+12
⇒ x = 12

প্রশ্নঃ A typist can type 125 pages, 36 lines cach, 11 words in each line in 5 days. How many pages of 30 lines each and 12 words to each line can he type in 6 days?

বর্ণনাঃ

In 5 days writes 36 lines with 11 words and produces 125 pages
⸫  "  1   "   "   36  "   "   11  "   "    "   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>125</mn><mn>5</mn></mfrac></math>  pages 
⸫ "   1   "   "   1    "   "    1  "   "   "    <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>125</mn><mo>&#xD7;</mo><mn>36</mn><mo>&#xD7;</mo><mn>11</mn></mrow><mn>5</mn></mfrac></math>  "
⸫ "   1  "   "  30  "    "   12   "   "   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>125</mn><mo>&#xD7;</mo><mn>36</mn><mo>&#xD7;</mo><mn>11</mn><mo>&#xD7;</mo><mn>6</mn></mrow><mrow><mn>5</mn><mo>&#xD7;</mo><mn>30</mn><mo>&#xD7;</mo><mn>12</mn></mrow></mfrac></math>  "
= 165  pages

প্রশ্নঃ what is the total interest on Tk. 800 at 12.5% per annum for 9 months?

বর্ণনাঃ

1 = pnr
= <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn><mo>&#xD7;</mo><mfrac><mrow><mn>12</mn><mo>.</mo><mn>5</mn></mrow><mn>100</mn></mfrac><mo>&#xD7;</mo><mfrac><mn>9</mn><mn>12</mn></mfrac></math>
= 75

প্রশ্নঃ A radio costs a shopkeeper Tk. 64. At what price must he sell it if he is to make a profit of 20% on the selling price?

বর্ণনাঃ

for 20% profit, 
If cost price is 100 then selling price is 120
⸫ "  "   "    "   1    "    "      "     "   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>120</mn><mn>100</mn></mfrac></math> 
⸫ "   "   "    "   64  "   "     "     "   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>120</mn><mo>&#xD7;</mo><mn>64</mn></mrow><mn>100</mn></mfrac></math>
= 76.80

প্রশ্নঃ 5% merchandise of a trader was stolen and another 5% was damaged during transportation. At what profit (in %) should he sell the rest of the merchandise so that he can make an overall profit of 20%?

বর্ণনাঃ

The remaining is (100-5-5)% = 90% of the merchendise unit.
The difference between merchandise and profit = (120-90) = 30 unit
90% merchandise (unit) has to make 30 unit profit 
⸫ 1%  "     "    "   "   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>30</mn><mn>90</mn></mfrac></math>  "   "
⸫ 100% "     "  "  "  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>30</mn><mo>&#xD7;</mo><mn>100</mn></mrow><mn>90</mn></mfrac></math>  "   "
= 33.33%

প্রশ্নঃ If the area of a square increase by 69%, then side of the square increases by ---

বর্ণনাঃ

It is best to back calculation from the answer.
For 13% increse in side, area increases = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>+</mo><mn>13</mn><mo>+</mo><mfrac><mrow><mn>13</mn><mo>&#xD7;</mo><mn>13</mn></mrow><mn>100</mn></mfrac><mo>=</mo><mn>27</mn><mo>.</mo><mn>69</mn><mo>%</mo></math>
For 29%  "  "  "   "   "   "  = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>+</mo><mn>29</mn><mo>+</mo><mfrac><mrow><mn>29</mn><mo>&#xD7;</mo><mn>29</mn></mrow><mn>100</mn></mfrac><mo>=</mo><mn>66</mn><mo>.</mo><mn>41</mn><mo>%</mo></math>
For 30%  "  "   "  "   "   "  = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>+</mo><mn>30</mn><mo>+</mo><mfrac><mrow><mn>30</mn><mo>&#xD7;</mo><mn>30</mn></mrow><mn>100</mn></mfrac><mo>=</mo><mn>69</mn><mo>%</mo></math>

প্রশ্নঃ Marathon is to race as hibernation is to

বর্ণনাঃ

Marathon is a type of race which is long in duration. Hibernation is a type of sleep that is also long long in duration.

প্রশ্নঃ Find the missing number of the following series. 212, 179, 146, 113?

বর্ণনাঃ

212-179=33, 179-146=33, 146-133= 33 so the desired blank number can be find.

প্রশ্নঃ If APPLE converts to ELPPA then 256478 would be?

বর্ণনাঃ

The letters are just written reversibly.

প্রশ্নঃ Which number replaces the question mark?

বর্ণনাঃ

Every digit is the sum of immediate two diagonal digit.

Like, 6=4+2, 3=2+1, Folkway this pattern, 7=1+6, so? = 7-1=6