Math Solution
Probashi Kollyan Bank
Executive Officer Cash
MCQ Exam of 01/11/2019
Solved by: Sultan Mahmud
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•• যথাসম্ভব শুদ্ধভাবে সমাধানের চেষ্টা করা হয়েছে। ভুল পেলে কমেন্টে জানানোর অনুরোধ রইল।
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33. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
Solution:
Relative speed = (46-36) km/hr = 10 km/hr
Time to pass = 36 sec = 36/3600 hr = 1/100 hr
Length = (10 × 1/100)/2 = 1/20 km = 1000/20 = 50 meters.
34. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together they can finish the work in 2 days. B can do the work alone in:
Solution:
A can do in 1 day = x part of the work
B can do in 1 day = 2x part of the work
C can do in 1 day = 3x part of the work
According to the question,
2(x+2x+3x) = 1
x = 1/12
So, B does 2×1/12 = 1/6 part of the work in 1 day
B alone can do the work in 6 days.
35. The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss incurred by selling the same article for Tk. 1280. At what price should the article be sold to make 25% profit?
Solution:
Suppose, the cost of the article is = Tk. x
according to the question,
(1920-x)/x - (x-1280)/x
2x = 3200
x = 1600
Required selling price = 1600 × 1.25 = 2000.
36. A person travels a certain distance at 3 km/hr and reaches 15 min late. If he travels at 4 km/hr, he reaches 15 min earlier. The distance he has to travel is:
Solution:
D/3 - D/4 = (15+15)/60
D/12 = 1/2
D = 6 km.
37. A boy traveled from the home to the college at the rate of 25 km/hr and walked back at the rate of 4 km/hr. If the whole journey took 5 hours 48 minutes, find the distance of the college from the home.
Solution:
D/25 + D/4 = 5 + 48/60
29D/100 = 29/5
D = 20 km.
38. (√1375 + √959) ÷ √292 × 19.003 = ?
Solution:
(√1375 + √959) ÷ √292 × 19.003
≈ (37 + 31) ÷ 17×19
≈ 68/17 × 19
≈ 76
close option 77.
39. Two men and three women can repair a bridge in 10 days while three men and two women can do same work in 8 days. If two men and one woman are used to finish this work, in how many days they will complete it?
Solution:
2m + 3w = 1/10 ----- (i)
3m + 2w = 1/8 ----- (ii)
-------------------------
5m + 5w = 1/10 + 1/8 = 9/40
1m + 1w = 9/200 ----- (iii)
(ii) - (iii) =>
2m + 1w = 1/8 - 9/200 = 16/200 = 1/12.5
So, they will complete it in 12.5 days.
40. A boatman takes twice as long to go to a distance upstream as to travel the same distance downstream. What is the ratio of the speed of the boatman (in still water) and the current?
Solution:
2 × D/(b+c) = D/(b-c)
2b - 2c = b + c
b = 3c
b : c = 3 : 1.
41. Speed of a boat in standing water is 9 km/hr and the speed of the stream is 1.5 km/hr. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Solution:
105/(9+1.5) + 105/(9-1.5) = 10+14 = 24 hr.
42. A, B and C invested capitals in the ratio of 4 : 6 : 9. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. Find the ratio of their time for which they contributed their capitals.
Solution:
4×a : 6×b : 9×c = 2 : 3 : 5
4a : 6b = 2 : 3
a : b = 6×2 : 3×4 = 12 : 12 = 1 : 1
6b : 9c = 3 : 5
b : c = 9×3 : 5×6 = 27 : 30 = 9 : 10
a : b : c = 1×9 : 9×1 : 1×10 = 9 : 9 : 10.
43. A trader marks his goods at 20% above the cost price. If he allows a discount of 5% for cash down payment, his profit percent for such transaction is:
Solution:
Profit percent = {(120 × 95/100) - 100}% = 14%.
44. If a = √3/2 then √(1+a) + √(1-a) = ?
Solution:
Suppose,
√(1+a) + √(1-a) = p
{√(1+a) + √(1-a)}² = p²
1+a + 2√(1+a)(√1-a) + 1-a = p²
2 + 2√(1-a²) = p²
2 + 2√{1 - (√3/2)²} = p²
2 + 2√(1 - 3/4) = p²
2 + 2 × 1/2 = p²
p² = 3
p = √3
So, √(1+a) + √(1-a) = √3.
45. Some money is divided among three workers A, B and C such that 5 times A's share is equal to 12 times B's share which is equal to 6 times C's share. The ratio between the shares is ?
Solution:
5A = 12B
A : B = 12 : 5
12B = 6C
B : C = 6 : 12 = 1 : 2
So, A : B : C = 12×1 : 1×5 : 5×2 = 12 : 5 : 10.
46. At simple interest of 5%, 6% and 8% for three consecutive years, the interest earned is Tk. 760. Find the principal.
Solution:
P×5% + P×6% + P×8% = Tk. 760
P×19% = Tk. 760
P = Tk. 760÷19% = Tk. 760 ÷ 19/100 = Tk. 760 × 100/19 = Tk. 4000.
47. If the compound interest of a certain sum of money for two successive years be Tk. 225 and Tk. 238.50. What is the rate of interest per annum?
Solution:
If the principal for the earlier year is P, then the principal for the later year is (P+225)
If the rate of interest is x% then,
(P+225)×x% - P×x% = 238.50 - 225
225 × x% = 13.50
x% = 0.06 = 6%.
48. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
Solution:
Total number of balls = 4+5+6 = 15
3 balls can be drawn from 15 balls in 15C3 ways = 15!/3!12! = 455 ways
3 red balls can be drawn from 5 red balls in 5C3 ways = 5!/3!2! = 10 ways
Required probability = 10/455 = 2/91.
49. A word consists of 9 letters: 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability that more than one vowel will be selected?
Solution:
Probability of 3 vowels selected = (4C3)/(9C3) = 4/84
Probability of 2 vowels and 1 consonant selected = (4C2×5C1)/(9C3) = 6×5/84 = 30/84
Probability that more than one vowel will be selected = 4/84 + 30/84 = 34/84 = 17/42.
50. The ages of X and Y are in the proportion of 6 : 5 and total of their ages is 44 years. The proportion of their ages after 8 years will be:
Solution:
Age of X = 44 × 6/(6+5) = 24
Age of Y = 20
Proportion of their ages after 8 years = (24+8) : (20+8) = 32 : 28 = 8 : 7.
51. The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m³. Find the breadth of the wall.
Solution:
Breadth = x
Height = 5x
Length = 8×5x = 40x
According to the question,
x × 5x × 40x = 12.8 m³
200x³ = 12.8×100³ cm³
x³ = 12.8×1000000/200 cm³ = 64000 cm³
x = 40 cm.
52. A rectangular field is to be fenced on three sides leaving a side of 20m uncovered. If the area of the field is 680 m², how many meters of fencing will be required?
Solution:
Length of the other side of the field = 680m²/20m = 34 m
Length of fencing = 34×2 + 20 = 88 m.
53. A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What is the original number?
Solution:
N × 110/100 × 90/100 = N - 10
99N = 100N - 1000
N = 1000.
54. A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Solution:
Without leak, in 1 hr, the cistern is filled by 1/8 of its capacity
With the leak, in 1 hr, the cistern is filled by 1/10 of its capacity
So, in 1 hr, the leak empties = 1/8 - 1/10 = 1/40 of the cistern's capacity
So, it will take 40 hours to empty the full cistern.
55. A sum of Tk. 427 is to be divided among A, B and C such that 3 times A's share, 4 times B's share and 7 times C's share are all equal. The share of C is:
Solution:
3A = 4B = 7C = k
A = k/3
B = k/4
C = k/7
A : B : C = k/3 : k/4 : k/7 = 28 : 21 : 12 (multiplying them by their LCM 84)
C's share = Tk. 427 × 12/(28+21+12) = Tk. 84.
56. A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk. 855, the total profit is:
Solution:
Suppose, total profit = 100p
Charity = 100p × 5% = 5P
Profit share of A = (100p-5p) × 3/(3+2) = 57p
according to the question,
57p = 855
100p = 855×100/57 = 1500.
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