ব্যাংক প্রস্তুতি স্পেশালঃ UCBL Probationary officer 2017 - Math Solution

19 Apr 2021

1. Arif is now 5 times as old as Babu, but 7 years from now he will be 3 times as old as Babu. How is Arif now? 

Suppose,
 current age of Babu is = x years.
So, current age of Arif = 5x years.
here,
5x+7 = 3(x+7)
or, 2x = 14
or, x = 7
So, current age of Arif is = 5x = 5×7 = 35 yrs

2. Solution X is 10 percent alcohol by volume and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?

Here,
0.3  X y + 0.1  X 200 = 0.25(y+200)
Or, 0.05y = 50 – 20
Or, y = 30/0.05
Or, y = 600 ml

3. If c and d are two integers and   is defined in p and q as   (p,q) = (p+1)(q+2) and  (c,d) equals the product of 3 and 5, then what should be the value of c + d?

Given that,
(p,q) = (p+1)(q+2)
therefore,  (c,d) = 3*5 = (2+1) * (3+2)
Hence, c = 2, d = 3
Now, c+d = 2+3 = 5

4. The probability of rolling any number on a weighted 6-sided die, with face numbered 1 through 6, in directly proportional to the number rolled. What is the probability of getting 5, if the die is rolled only once?

Given ,
The probability of rolling any number with faces numbered 1 through 6 sided die, is directly proportional to
the number rolled
Total Number of rolling side = 1+2+3+4+5+6=21
Now,
P(1) = 1/21
P(2) = 2/21
P(3) = 3/21
P(4) = 4/21
P(5) = 5/21
P(6) = 6/21
The probability of getting a 5 if the die is rolled only once is 5/21 

 

5. If –2

Given,
-2 < a < 11 ————- (i)
3 < b < 12 ————– (ii)
(i)+(ii) =>
-2+3 < a+b < 11+12
or, 1 < a+b < 23. (Options ‘a’ and ‘d’ are true)
(i)-(ii) =>
-2-12 < a-b < 11-3
or, -14 < a-b < 8. (option ‘b’ is true)
(ii)-(i) =>
3-11 < b-a < 12-(-2)
or, -8 < b-a < 14.
Something greater than -8 is not necessarily greater than -7. so, option ‘c’ is not true.
(i)×(ii) =>
-2×3 < ab < 11×12
-6 < ab < 132.
Something greater than -6 is always greater than -24. so, option ‘e’ is true.

 

6. A car’s average speed is 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which is closest to the number of miles per gallon that the car’s average speed when it is driven 10 miles in the city and then 50 miles on the highway? 

To travel 10 miles in the city, the car requires = 10/25 = 2/5 gallons of gasoline
To travel 50 miles on the highway, the car requires = 50/40 = 5/4 gallons of gasoline.
So, to travel 60 miles, the car requires = 2/5 + 5/4 = 33/20 gallons of gasoline
Hence, miles per gallon = 60/(33/20) = 1200/33 = 36.36 ≈ 36 miles.

7. In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been?

 

Let the number be x.
Now given,
 x=5a+4
 a=9b+8
 b=13c+12

By putting  the value of b we get,
 a = 9(13c + 12) + 8  
or,a = (13  X 9)c + 116

Now, putting  the value of a we get ,

x = 5{(13   X  9)c + 116} + 4  
or, x = 585c + 584
So, we found that  when divided by 585 we get 584 as remainder

8. Two trains are moving in opposite direction at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is? 

Given ,
Length of slower train 1.10 KM or 1100 meter & Length of faster train 0.9 KM or 900 meter
And, 

Speed of Larger train = 60 km/h
 Speed of Smaller train = 90 km/h 
Here,
Time = (Length of Larger train + Length of Smaller train)/ (Speed of Larger train + Speed of Smaller train)   X 
5/18

= (1100 + 900) / (60+90)  X 5/18
= 2000/(150  X 5 /18)
= 2000/(25  X 5 /3)
= (2000  X 3) / 125
= 48 Seconds

 

9. Rahim gave half of his stamps to Karim. Karim gave half of his stamps to Fatima. Fatima gave 1/4 of the stamp given to her to Tonmoy and kept the remaining 12.how many stamps did Rahim start with?

 

Fatima had (1-1/4) = ¾ of the given stamps
That means, Fatema got = 12  X 4/3 = 16 from Karim
So, Karim had = 16  X 2 = 32 stamps
Therefore, Rahim had = 32  X 2 = 64 stamps

 

10. One baker can bake either 2 large cakes or 35 small cakes per hour. How many bakers are needed to bake 20 large cakes and 700 small cakes in 3 hours?

Here,

One baker can bake 2 large cakes per hour
So, it will take 20/2 = 10 hours for a single person to make to large cakes.
One baker can bake 35 small cakes per hour
So, it will take 700/35 = 20 hours for a single person to make small cakes.
This means that the task requires 10+20 = 30 hours of work time in total
If each baker contributes 3 hours each, that means it will take 30/3
= 10 bakers to finish the task

 

11. If n is even which of the following cannot be odd? 

Here, cannot be odd means must be even
Let, n =2, 4 etc
So if we check options.
we can get,

a) n+3 is always odd
b) 3n+1 is always odd
c) n^2 – 1 is always odd
d) 2(n+3) = 2  X odd = even  X odd = must be even 

 

12. The product of two numbers x and y is twice the sum of the numbers, What is the sum of the reciprocals of x and y?
Given ,
xy = 2(x+y)

Now,
1/x + 1/y
= (x+y)/xy
= (x+y)/2(x+y)
=1/2 

13. Two people start jogging at the same point and time but opposite direction. If the rate of one jogger is 2 mph faster than the other and after 3 hours they are 30 miles apart what is the rate of faster jogger.? 
Let,

 Speed of one jogger = x mph
Speed of faster jogger = x+2 mph

Here,
3x +3(x+2) = 30
Or, 6x = 24
Or, x = 4
Speed of faster jogger = 4+2 = 6 mph 

 

14. A worker is hired for 7 days. Each day he is paid 10 taka more than what he is paid for the previous day of work. The total amount he was paid in the first 4 days of work equated the total amount he was paid in the last 3 days. What was his starting pay?

Let,
 x be the starting pay
x, x+10, x+20, x+30, x+40, x+50, x+60
Here,
4x+60 = 3x+150
Or, x = 90

15. The length of 2 sides of a triangle is 7 and 11. If the length office the third side is an integer. What is the least possible perimeter of the triangle? 

We know,
The sum of two sides of a triangle is greater than the 3rd side and the difference of two sides is lower than the
3rd side
That means 3rd side will be lower than 11+7 = 18 & greater than 11-7 = 4 To ensure least possible perimeter
we can take the value of 3rd side as 5. Therefore, Perimeter = 7 + 11 + 5 = 23

 

16. A company generated revenue of tk 125000 in 2012 which was 12.5% of its gross revenue. In 2013 the gross revenue increases by tk 250000. What is the percentage increase in the revenue in 2013?

Here,
125000 = P  X 12.5%  X n ---- (a)
And
25000 = P  X r  X n ----- (b)
(b)/(a)
25000/125000 = r/12.5%
Or, r = 250  X 12.5%/125 = 0.25 = 25% (ans)

 

17. Annie invested a certain sum of money in a bank that paid simple interest. The amount grew to Tk. 240 at the end of 2 years. She wanted for another 3years and got a final amount Tk 300. What was the principal amount that she invested at the beginning?

Here,
I+P = 240
Or, Pnr + P = 240
Or, P(1+2r) = 240 ----- (a)
And, P(1+5r) = 300 ----- (b)
(a) / (b)
(1+2r) / (1+5r) = 4/5
Or, r = 1/10 = 0.1
Therefore, P = 240/1.2 = 200 Tk. (ans)

18. Moyna has n chocolates, where n is an integer such that 20 chocolates among 7 children?

n = (a multiple of 5) + 2 = (a multiple of 6) + 1
in the given range, the following numbers satisfy the condition [(a multiple of 5) + 2]
= 22, 27, 32, 37, 42, 47
in the given range, the following numbers satisfy the condition [(a multiple of 6) + 1]
= 25, 31, 37, 43, 49
If 37 is divided by 7, the remainder is 2.

19. The number 3 divides X with a result of Y and a remainder of 2. The number 3 divides Y with a result 2 and a remainder of 1. What is the value of X?

X = 3  X Y + 2
Y = 3  X 2 + 1
Or, Y = 7
And, X = 7  X 3 + 2 = 23

20. If (x+4) ^2 = 9, (y+3) ^2 = 25, then the minimum value of y/x is?

x = -1, -7 and y = 2, -8
y/x = - 2 (x = -1, y = 2)
y/x = -2/7 (x = -7, y=2)
y/x = 8 (x =-1, y = -8)
y/x = 8/7 (x = -7, y = -8)