ব্যাংক প্রস্তুতি স্পেশালঃ BKB – (CASH ) -2017 Math Part

29 May 2021

33. The lengths of two sides of a triangle are 7 cm and 4 cm respectively. The length of the third side is –[BKB – (CASH ) -2017]

A. greater then 3cm 

B .less then 3cm 

C. equal to 3 cm 

D. all are true

•Solution: (A)

ত্রিভুজের যে কোন দুটি বাহুর সমষ্টি তার তৃতীয় বাহু অপেক্ষা বৃহত্তর হতে হবে। 

এখানে ৭ এবং ৪ এর ব্যবধান ৩ সুতরাং অপর বাহুটি অবশ্যই ৩ এর থেকে বড় হতে হবে। 

তাই উত্তর: third side should be greater than 3.

34. Consider that w + x = - 4, x + y = 25 and y + w = 15. Then the average of w, x, y is - [BKB – (CASH ) -2017]

A.3 

B.4 

C.5 

D.6

•Solution: (D)

W+x+x+y+y+w=-4+25+15

Or 2w+2x+2y=36

Or 2(w+x+y)=36

Or w+x+y=36/2=18

So average of w,x,y=18/3=6

35. How long will it take for an amount Tk. 450 to yield Tk. 81 as interest at 4.5% per annum of simple interest -[BKB – (CASH ) -2017]

A.4 years 

B. 4.5 years 

C.5 years 

D. 5.5 years

•Solution: (A)

১ বছরের সুদ = ৪৫০ এর ৪.৫% = ২০.২৫টাকা।

তাহলে ৮১ টাকা সুদ হতে সময় লাগবে ৮০/২০.২৫ = ৪ বছর।

36. Club A has 20 members and Club B has 27. If a total of 42 people belong to the two clubs, how many people belong to both clubs? [BKB – (CASH ) -2017]

A.3 

B. 4 

C.5 

D.6

•Solution: (C)

Here Total =42

But 20+27 = 47

So, Both is = 47-42 = 5

37. Today is Aziz's 12th birthday and his father's 40th birthday. How many years from today will Aziz's A father be twice as old as Aziz’s at that time? [BKB – (CASH ) -2017]

A.12 

B.24 

C.18 

D.16

•Solution: (D)

Let after x years Aziz’s fathers will be double

So,

2(12+x) = 40+x

Or, 24+2x = 40+x So, x = 16

 

38. If 61% of Bangladeshi people like cafe, and 74% like tea, how many like both? [BKB – (CASH ) -2017]

A 13% 

B. 16% 

C. 26% 

D.35%

•Solution: (D)

(61-74)%-100% = 35%

39. A grocer buys some eggs at Tk. 3 each. He finds that 12 of them are broken, but he sells the others at Tk. 4 each and makes profit of Tk. 96. How many eggs did he buy? [BKB – (CASH ) -2017]

A. 140 

B. 142 

C. 144 

D. 150

•Solution: (C)

Let, The grocer buys = x eggs

ATQ,

4(x-12)-3x = 96

Then, x = 144

 

40. What is the original price of a T-shirt, if the sale price after 16% discount Is 264? [BKB – (CASH ) -2017]

A. 300 

B. 214 

C. 320 

D. 314

•Solution: (D)

84% = 264 

So, 100% = 314.29 or 314

41. The present ages of John and Mary are In the ratio of 6 : 4 . Five years ago their ages were in the ratio of 5 : 3. How old is John now? [BKB – (CASH ) -2017]

A. 42 

B. 36 

C.30 

D. 24

•Solution: (C)

 

6x-5:4x-5 = 5:3

Or, 20x-25 = 18x-15 So, x = 5. John now is 65 = 30

 

42. A man buys doughnuts at the rate of Tk. 35 per 100 pieces and sells them at Tk. 7.20 per dozen. If the profit is Tk. 30, how many doughnuts did he buy? [BKB – (CASH ) -2017]

A.60 

B.120 

C.180 

D. 210

•Solution: (B)

Cost price of one doughnuts = 35/100 = 0.35

Selling price of one ‘’ = 7.20/12 = 0.6 tk

Profit in one doughnuts = 0.6-0.35 = 0.25tk

So. Total doughnuts = 30 / 0.25 = 120

43. If y% of x = 29, then x = ? [BKB – (CASH ) -2017]

A. 2900/y 

B. 29x/y 

C. 29y/x 

D.29xy

•Solution: (A)

y% of x=29

So x=29*100/y=2900/y

44. How many tangents (স্পর্শক ) to a circle can be drawn from an external point? [BKB – (CASH ) -2017]

A.1 

B.2 

C.3 

D.4

•Solution: (B)

বৃত্তের বহি:স্থ কোন বিন্দু থেকে ঐ বৃত্তে দুটি মাত্র স্পর্শক অংকন করা সম্ভব।

45. The one-third of the complementary (Supplementary) angle to 30° is -[BKB – (CASH ) -2017]

A.1500 

B.1000 

C.500 

D.100

•Solution: (C)

Supplementary angle to 30 is 180-30 = 150 whose one third is 50

46. If the area of a rhombus is 54 sq. cm and the length of one of the diagonals is 6 cm then the length of the other diagonal is -[BKB – (CASH ) -2017]

A. 18 

B. 12 

C. 9 

D. 6

•Solution: (A)

Area of rhombus is ½(x*6) = 54 or 3x = 54 So, x = 18

47. If one number exceeds another number by 14 and the larger number is times the smaller number, then the smaller number is -[BKB – (CASH ) -2017]

A. 13 

B. 26 

C. 28 

D. 31

•Solution: (C)

3/2 = 1.5

Let small number is x, so large number is 1.5x 

ATQ, 

1.5x-x = 14 or. 0.5x = 14 so, x = 28

Alternative solution: 

let large 3x and small 2x

So 3x-2x=14

Or x=14

So smaller=2*14=28

 

 

48. The ratio between two numbers is 3:4 and their sum is 420. The greater one of the two numbers is -[BKB – (CASH ) -2017]

A. 360 

B.240 

C 180 

D 120

•Solution: (B)

If the number is 3x and 4x then 3x+4x =420 or 7x =420 so x = 60 so the greater number is 460 = 240

49. If 4^x+1=32, then x =? [BKB – (CASH ) -2017]

A. 2 

B.3 

C.2/3 

D.3/2

•Solution: (d)

4^x+1=32

Or, 22(x+1) =25 = or, 2x+2 = 5 or 2x = 3 So, x =

50.log root 3^81 [BKB – (CASH ) -2017]

A. 9 

B.7 

C.6 

D. 8

•Solution: (D)

51. What will be the difference between simple and compound interest at 10% on a sum of Tk. 1000 after 4 years? [BKB – (CASH ) -2017]

A.Tk.31.90 

B. Tk. 32.10 

C. 44.90 

D. Tk. 64.10

•Solution: (D)

Formal Solution:

simple interest=1000*10*4/100=400 tk

10%=1/10

So compound=1000*(1+1/10)^4-1000

=1000*(11/10)^4 -1000
=1000*11*11*11*11/10*10*10*10 -1000

=1464.1-1000 =464.1

So difference=464.1-400=64.1

এ ধরণের চক্রবৃদ্ধি সুদকষার অংকে যাদের সমস্যা আছে তারা আজকে রাত ১০ টায় আমার নেয়া লাইভ ক্লাসে জয়েন করতে পারেন, খাতা কলম ক্যালকুলেটর ছাড়াই কয়েক সেকেন্ডে উত্তর বের করার নিয়ম শেখানো হবে। । 

52. If A's income is 25% less than that of B, then what percent is B’s income more than that of A? [BKB – (CASH ) -2017]

 

A. 33.33 

B. 66.67 

C.11.67 

D. 31.50

•Solution: (A)

let B income 100 

So A’s income=75

So B’s income more than A in %= 25*100/75=100/3=33.33%

53. After a 20% price decrease, a computer monitor is on sale for Tk. 7200. What is its original price? [BKB – (CASH ) -2017]

A.Tk. 9000 

B. Tk. 10000 

C. Tk. 11000 

D. Tk 12000

•Solution: (A)

80% = 7200 S, 100% = 9000

54. The numbers 2, 3, 5 and x have an average equal to 4. What is the value of x? [BKB – (CASH ) -2017]

A.4 

B. 6 

C 8 

D.10

•Solution: (B)

Total = 4*4 = 16

Other number is 16- (2+3+5) = 6

Alternative solution: 

2+3+5+x=44

Or 10+x=16

Or x=16-10

Or x=6

55. If 15 is the 6th number in a series of 6 consecutive odd numbers what is 4th number in the series? [BKB – (CASH ) -2017]

A. 7 

B. 9 

C. 11 

D. 13

•Solution: (C)

The series is 5, 7, 9,11,13 and 15

So 4th number is 11

56. How many permutations of seven different letters may be made? [BKB – (CASH ) -2017]

A. l 

B. 7 

C 7! 

D.6!

•Solution: (C)
 

number of permutations=7 factorial or 7!