946 . A motorist must complete 180-mile trip is 4 hours. If he averages 50 miles an hour for the first three hours of the trip , how fast must ( in terms of mile per hour ) he travel in the last hour ?

A. 30
B. 32
C. 40
D. None of these

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Answer: Option A

Explanation:

= 180 - (50*3) hrs

= 180 - 150 hrs

= 30 hrs.

Bangladesh Bank - Officer - 2001

A. 35
B. 37
C. 37.5
D. 40

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Answer: Option C

Explanation:

Total time spent in the whole journy = 150/50 + 150/30 = 3 + 5 = 8 hours

The average speed of the whole journy = total distance/total time = (150 + 150)/8 = 37.5 km/hr

948 . A natural number when increased by 12, equals 160 times reciprocal. The number is-

A. 16
B. 8
C. 6
D. 18

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Answer: Option B

Explanation:

Step 1: Construct the equation based on given condition.
let the required natural number be x.
According to the question,
x+12=160x
On multiplying by x on both sides, we get
x^2+12x−160=0,

Step 2: Find roots using factorization.
By splitting the middle term, we get :
⇒x^2+(20x−8x)−160=0
⇒x^2+20x−8x−160=0
⇒x(x+20)−8(x+20)=0
⇒(x+20)(x−8)=0
⇒x=8
[x≠−20 because it is not a natural number]
hence, the required natural number is 8.

বাংলাদেশ পল্লী বিদ্যুতায়ন বোর্ড || সহকারী প্রকৌশলী (28-07-2023)

A. 145
B. 253
C. 370
D. 352
E. None of these

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Answer: Option B

Explanation:

The sum of the three digits is 10: A + B + C = 10

The middle digit (B) is equal to the sum of the other two digits (A and C): B = A + C

The number will be increased by 99 if its digits are reversed. This means that if we reverse the order of the digits, we get a new number that is 99 greater than the original number.

Now, let's use this information to solve for the values of A, B, and C.

From equation 1, we know that A + B + C = 10.

From equation 2, we know that B = A + C.

Now, we can substitute the value of B from equation 2 into equation 1:

A + (A + C) + C = 10

Simplify the equation:

2A + 2C = 10

Divide both sides by 2:

A + C = 5

Now, we have two equations:

A + C = 5
B = A + C
Since B = A + C and A + C = 5, we can conclude that B = 5.

Now that we know B is 5, we can use the fact that the number will be increased by 99 if its digits are reversed. This means that the original number is 99 less than the reversed number.

Let's represent the original number as ABC and the reversed number as CBA. The difference between the reversed and original numbers is 99:

CBA - ABC = 99

Now, substitute the values of B (5) and A + C (5) into the equations:

(100C + 10B + A) - (100A + 10B + C) = 99

Now, simplify:

100C + 10B + A - 100A - 10B - C = 99

Combine like terms:

99C - 99A = 99

Now, divide both sides by 99:

C - A = 1

Now, we have two equations:

A + C = 5
C - A = 1
Solve this system of equations:

From equation 2, we can express C in terms of A: C = A + 1.

Now, substitute this into equation 1:

A + (A + 1) = 5

Combine like terms:

2A + 1 = 5

Subtract 1 from both sides:

2A = 4

Divide by 2:

A = 2

Now that we know A is 2, we can find C:

C = A + 1 = 2 + 1 = 3

So, A = 2, B = 5, and C = 3. Therefore, the number is ABC = 253.

দুর্নীতি দমন কমিশনের সহকারী পরিচালক-১২.০৪.২০১৩

A. 73
B. 82
C. 91
D. 95

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Answer: Option C

Explanation:

Let's use algebra to solve this problem. Let the two-digit number be represented as 10a + b, where 'a' is the tens digit and 'b' is the units digit.

We are given two conditions:

The sum of the digits is 10, so we can write the equation: a + b = 10

When 72 is subtracted from the number, the digits are interchanged. This means that 10a + b - 72 becomes 10b + a. We can write this as another equation: 10a + b - 72 = 10b + a

Now, let's solve this system of equations:

From equation 1, we can express 'b' in terms of 'a': b = 10 - a

Substitute this expression for 'b' into equation 2: 10a + (10 - a) - 72 = 10(10 - a) + a

Now, simplify and solve for 'a': 10a + 10 - a - 72 = 100 - 10a + a

Combine like terms: 9a + 10 - 72 = 100 - 9a

Subtract 10 from both sides: 9a - 62 = 100 - 9a

Add 9a to both sides: 18a - 62 = 100

Add 62 to both sides: 18a = 162

Divide by 18: a = 9

Now that we have found 'a' to be 9, we can find 'b' using the first equation: a + b = 10 9 + b = 10

Subtract 9 from both sides: b = 10 - 9 b = 1

So, the tens digit 'a' is 9, and the units digit 'b' is 1. Therefore, the two-digit number is 91.

951 . A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by which of the following?

A. 3
B. 5
C. 5
D. 11
E. None of these

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Answer: Option D

Explanation:

ধরি, দুটি সংখ্যা ১৫ ও ১২।

তাহলে ১৫ কে interchange করে পাই ৫১। অর্থাৎ,১৫+৫১=৬৬

আবার ১২ কে interchange করে পাই ২১। অর্থাৎ,১২+২১=৩৩

৬৬ এবং ৩৩ উভয়েই ১১ দ্বারা বিভাজ্য।

উত্তর: ১১

952 . A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number its digits are interchanged. Find the number .

A. 81
B. 72
C. 27
D. 54

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Answer: Option A

Explanation:

Let X and Y be the digits of decimal and unit places respectively. So, the number is 10X + Y. If 63 is subtracted from the number, it becomes 10Y + X.

Now, X + Y = 9 - - - - - - - (i)

Again, 10X + Y - 63 = 10Y + X

or, 10X - X + Y - 10Y = 63

or, 9X - 9Y = 63

or, X - Y = 63/9

or, X - Y = 7 - - - - - - (ii)

[(i) + (ii)]>> X + Y + X - Y = 9 + 7

or, 2X = 16

or, X = 8

So, 8 + Y = 9

or, Y = 9 - 8 = 1

So, the number is 81.

953 . A number is 250 percent of another number . If the sum of the numbers is 98 . Find the value of the larger number?

A. 58
B. 60
C. 66
D. 70

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Answer: Option D

Explanation:

প্রধান প্রশাসনিক কর্মকর্তার কার্যালয় ( প্রতিরক্ষা মন্ত্রণালয়) সহকারী পরিচালক ০৫.০৪.২০১৯

A. 51
B. 61
C. 71
D. 81

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Answer: Option B

Explanation:

Let the number be x

x - 36 = 86 - x

2x = 122

x = 122 ÷ 2 = 61

955 . A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is the number?

A. 3.5
B. 6
C. 8
D. None of these

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Answer: Option C

Explanation:

Hints: ধরি সংখ্যটি, x

তাহলে, 3{2x + 9} = 75

2x + 9 = 25

2x = 25 - 9

x = 8

956 . A number is doubled and 9 is added. If the resultant is trebled, it beomes 75. What is that number?

A. None of these
B. 6
C. 8
D. 3.5

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Answer: Option C

Explanation:

ধরি, সংখ্যাটি x

( 2x + 9) × 3 = 75

2x + 9 = 25

2x = 16

x = 8

957 . A number is greater than 3 but less than 8. Also, it is greater than 6 but less than 10. The number is -

A. 8
B. 5
C. 6
D. 7

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Answer: Option D

Explanation:

10>x>6

Here, x must be one from 7,8,9

8>x>3

Here, x must be one from 4,5,6,7

So, the only ans is 7 as per both of the conditions

(ans)

958 . A number is selected at random from 40 to 50 inclusive. What is the probability that the number is prime number?

A. 3/11
B. 3/10
C. 2/11
D. 1/5
E. None of these

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Answer: Option E

Explanation:

Total number of numbers = 59 - 40 + 1 = 20

Prime numbers : 41, 43, 47, 53, 59 = 5 in total

So, the probability = 5/20 = 1/4

959 . A number when divided by 3 leaves a remainder 1 . When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?

A. 2
B. 3
C. 4
D. 5

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Answer: Option C

Explanation:

960 . A number when divided by 627 leaves a remainder 43. By dividing the same number by 19, the remainder will be-

A. 32
B. 43
C. 13
D. 5

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Answer: Option D

Explanation:

Let number be the x.

We know that, dividend = divisor X quotient + remainder When x is divided by 627, the remainder is 43.

x = 627k+ 43, where k is quotient.

Here x is multiple of 627.

Let us consider the factor s of 627, 6273 × 19 × 11

We have to find the remainder when dividing by 19 so expressing the equation in term of 19 is helpful.

As 4319x2+5

Therefore x = 3 × 19 × 11 × k+ (19×2+5)=19(33k+2) +5 x = 19(33k+2) +5

So, on dividing x by 19 the remainder will be 5.

Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018

946 . A motorist must complete 180-mile trip is 4 hours. If he averages 50 miles an hour for the first three hours of the trip , how fast must ( in terms of mile per hour ) he travel in the last hour ?

947 . A motorist travels to a place 150 km away at an average speed of 50 km and returns at 30 km per hour. What is his average speed for the whole journey in km per hour?

948 . A natural number when increased by 12, equals 160 times reciprocal. The number is-

949 . A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. what is the number?

950 . A number consists of two digits, the sum of the digit is 10. If 72 is subtracted from the number, the digits are interchanged. Find the number.

951 . A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by which of the following?

952 . A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number its digits are interchanged. Find the number .

953 . A number is 250 percent of another number . If the sum of the numbers is 98 . Find the value of the larger number?

954 . A number is as much greater than 36 as the less than 86. Find the number.

955 . A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is the number?

956 . A number is doubled and 9 is added. If the resultant is trebled, it beomes 75. What is that number?

957 . A number is greater than 3 but less than 8. Also, it is greater than 6 but less than 10. The number is -

958 . A number is selected at random from 40 to 50 inclusive. What is the probability that the number is prime number?

959 . A number when divided by 3 leaves a remainder 1 . When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?

960 . A number when divided by 627 leaves a remainder 43. By dividing the same number by 19, the remainder will be-

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