Bank Math

PrepBank · পাতা ১২৬ / ১৬১ · ১২,৫০১–১২,৬০০ / ১৬,১২৪

১২,৫০১.

In a box, there are 6 white, 4 black, and 2 yellow balls. If two balls are drawn one after the other without replacement, what is the probability that the first one is black and the second one is yellow?

ক
1/18
খ
1/22
গ
4/11
ঘ
3/8
ঙ
2/33

ব্যাখ্যা

Question: In a box, there are 6 white, 4 black, and 2 yellow balls. If two balls are drawn one after the other without replacement, what is the probability that the first one is black and the second one is yellow?

Solution:
মোট বলের সংখ্যা = 6 (সাদা) + 4 (কালো) + 2 (হলুদ) = 12টি

প্রথম বলটি কালো হওয়ার সম্ভাবনা = 4/12 = 1/3

প্রথম বলটি তোলার পর বাক্সে মোট বলের সংখ্যা = 12 - 1 = 11টি

দ্বিতীয় বলটি হলুদ হওয়ার সম্ভাবনা = 2/11

∴ প্রথমটি কালো এবং দ্বিতীয়টি হলুদ হওয়ার সম্ভাবনা:
= (প্রথমটি কালো হওয়ার সম্ভাবনা) × (দ্বিতীয়টি হলুদ হওয়ার সম্ভাবনা)
= (1/3) × (2/11)
= 2/33

১২,৫০২.

A man borrowed some money for 4 months. He asked the banker for the money and the banker charged Tk. 360 as interest at 6% per annum. What was the amount he borrowed?

ক
Tk. 12,000
খ
Tk. 15,000
গ
Tk. 16,000
ঘ
Tk. 18,000

ব্যাখ্যা

Question: A man borrowed some money for 4 months. He asked the banker for the money and the banker charged Tk. 360 as interest at 6% per annum. What was the amount he borrowed?

Solution:

এখানে

সময় n = 4 মাস

= 4/12 বছর

= 1/3 বছর

মুনাফা I = 360 টাকা

মুনাফার হার r = 6% = 6/100 = 3/50

আসল P = ?

আমরা জানি

I = Pnr

⇒ Pnr = I

⇒ P = I/nr

= 360/{(1/3) × (3/50)}

=360/(1/50)

= 360 × 50

= 18000 টাকা

১২,৫০৩.

A can do a piece of work in 42 days and B is thrice as efficient as A. If B joins A on 22nd day then in how many days will the work be completed?

ক
ক) 5.75
খ
খ) 5.25
গ
গ) 5.35
ঘ
ঘ) 5.45

ব্যাখ্যা

A alone can complete the work = 42 days

Formula used:
W = E × T

Where, W = The work, E = The efficiency, and T = The time

Let us assume the work will be completed in X days
⇒ The one day work of A = 1/42
⇒ The one day work of B = 3 × (1/42) = 1/14
⇒ The 21 days work of A = 21 × (1/42) = 1/2
⇒ The remaining work = 1 - 1/2 = 1/2
⇒ The efficiency of A and B together = (1/42 + 1/14) = 4/42 = 2/21
⇒ The remaining work will be completed = (1/2) × (21/2) = 21/4 = 5.25 days

∴ The required result will be 5.25 days.

১২,৫০৪.

A solid iron cube of 4m length is converted into a wire of 100m length. the circumference of the wire is-

ক
2.835m
খ
3.935m
গ
3.835m
ঘ
2.535m

ব্যাখ্যা

Question: A solid iron cube of 4m length is converted into a wire of 100m length. the circumference of the wire is-

Solution:
the volume of the cube is = 4³ m³
= 64 m³

the volume of the wire will be same as the cube.
let,
the radius of the wire is = r
∴ πr² × l = 64
⇒ r² = 64/(3.1416 × 100)
⇒ r² = 0.2037
⇒ r = 0.4513

∴ circumference = 2πr
= 2 × 3.1416 × 0.4513
= 2.835m

১২,৫০৫.

{(1 - tan²60°)/(1 + tan²60°)} + sin²60° = ?

ক
√3/2
খ
1/2
গ
√3/4
ঘ
1/4

ব্যাখ্যা

Question: {(1 - tan²60°)/(1 + tan²60°)} + sin²60° = ?

Solution:
(1-tan²60°)/(1+tan²60°) + sin²60°
= (1-(√3)²)/(1+(√3)²) + (√3/2)²
= (1 - 3)/(1+3) + 3/4
= -2/4 + 3/4
= 1/4

১২,৫০৬.

Find the average of numbers 87, 84, 86, 90, 82, 88, 78.

ক
86
খ
85
গ
84
ঘ
83
ঙ
82

ব্যাখ্যা

Question: Find the average of numbers 87, 84, 86, 90, 82, 88, 78.

Solution:

The sum of all the observations here is 87 + 84 + 86 + 90 + 82 + 88 + 78 = 595

Number of observations = 7

So, Average = 595/7 = 85

১২,৫০৭.

Which number will complete the series:
1, 3, 7, 15, 31, 63, 127, 97, 255, __?

ক
509
খ
511
গ
516
ঘ
519

ব্যাখ্যা

Question: Which number will complete the series:
1, 3, 7, 15, 31, 63, 127, 97, 255, __?

Solution:
3 - 1 = 2
7 - 3 = 4 = 2 × 2
15 - 7 = 8 = 4 × 2
31 - 15 = 16 = 8 × 2
63 - 31 = 32 = 16 × 2
127 - 63 = 64 = 32 × 2
225 - 97 = 128 = 64 × 2

∴ The next number of 127 will be = (255 + 128 × 2)
= 255 + 256
= 511

১২,৫০৮.

A boatman can row 96 km downstream in 8 hour. If the speed of the current is 4 km/hr, then find the time required to cover 8 km upstream?

ক
ক) 1 hr
খ
খ) 4 hrs
গ
গ) 2 hrs
ঘ
ঘ) 6 hrs
ঙ
ঙ) 3 hrs

ব্যাখ্যা

Speed downstream = 96/8 = 12 km/hr
Speed of current = 4 km/hr
Speed of the boatman in still water = 12 − 4 = 8 km/hr
Speed upstream = 8 − 4 = 4 km/hr
Time taken to cover 8 km upstream = 8/4 = 2 hrs

১২,৫০৯.

7q² - (5q - 2)(4q + 3) = ?

ক
- 13q² - 7q + 6
খ
- 13q² + 7q + 9
গ
- 8q² + 13q + 17
ঘ
- 8q² + 5q + 17

ব্যাখ্যা

Question: 7q² - (5q - 2)(4q + 3) = ?

Solution:
7q² - (5q - 2)(4q + 3)
= 7q² - {(5q × 4q) + (5q × 3) - (2 × 4q) - (2 × 3)}
= 7q² - (20q² + 15q - 8q - 6)
= 7q² - (20q² + 7q - 6)
= 7q² - 20q² - 7q + 6
= - 13q² - 7q + 6

১২,৫১০.

If 1³ + 2³ + 3³ + .... + 9³ = 2025, then the value of (0.11)³ + (0.22)³ + .... + (0.99)³ is close to :

ক
ক) 26.95
খ
খ) 36.95
গ
গ) 2.695
ঘ
ঘ) 3.695

ব্যাখ্যা

(0.11)³+(0.22)³+....+(0.99)³
=(0.11)³(1³+2³+....+9³)
=0.001331×2025
=2.695275
≈2.695

১২,৫১১.

What will be the compound interest of Tk. 3500 in 2 years at 20% per annum if the interest is compounded half - yearly?

ক
3125.34 Tk.
খ
1524.35 Tk.
গ
1624.35 Tk.
ঘ
1125.35 Tk.

ব্যাখ্যা

Question: What will be the compound interest of Tk. 3500 in 2 years at 20% per annum if the interest is compounded half - yearly?

Solution:
P =3500
r = 20% = 10% half - yearly
n = 2 years = 4 half - yearly

we know,
C = P(1 + r)ⁿ
= 3500 ( 1 + 10/100)⁴
= 3500 (11/10)⁴
= 5124.35
∴ compound interest = 5124.35 - 3500 = 1624.35 Tk.

১২,৫১২.

In how many ways can 3 guests from a group of 8 guests be seated around a circular table?

ক
36
খ
112
গ
3024
ঘ
280
ঙ
336

ব্যাখ্যা

Question: In how many ways can 3 guests from a group of 8 guests be seated around a circular table?

Solution:
8 জন থেকে 3 জন নির্বাচন করার উপায়:
⁸C₃ = 8!/(3! × 5!)
= (8 × 7 × 6)/(3 × 2 × 1)
= 336/6
= 56

3 জন ব্যক্তিকে একটি গোলাকার টেবিলে সাজানোর উপায় = (3 - 1)!
= 2!
= 2

∴ মোট উপায় = 56 × 2 = 112

১২,৫১৩.

Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R, 90 percent actually voted for R, and of those who did not say that they would vote for R, 5 percent actually voted for R. What percent of the group voted for R?

ক
56%
খ
59%
গ
62%
ঘ
65%

ব্যাখ্যা

Question: Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R, 90 percent actually voted for R, and of those who did not say that they would vote for R, 5 percent actually voted for R. What percent of the group voted for R?

Solution:
Let,
Group = 100 people
60% said they would vote R = 60 people

Of the 60 people only 90% actually voted R = 54

40% said they would NOT vote R = 40 people
Of the 40 people who would vote NOT R, 5% voted R instead = 2

So 54 + 2 = 56

১২,৫১৪.

If One-third of one-fourth of a number is 15, then three-tenth of that number is:

ক
54
খ
45
গ
36
ঘ
35

ব্যাখ্যা

Question: If One-third of one-fourth of a number is 15, then three-tenth of that number is:

Solution:
Let,
the number is 'x'
then ,
(1/3) × (1/4) × x = 15
⇒ x/12 = 15
⇒ x = 180

Now,
(3/10) × x = (3/10) × 180 = 18 × 3 = 54.
∴ three-tenths of that number is 54.

১২,৫১৫.

In a class of 60, 32 studied English, 28 studied Bengali and 6 did not study either. How many of the students studied both?

ক
6
খ
4
গ
12
ঘ
16

ব্যাখ্যা

Question: In a class of 60, 32 studied English, 28 studied Bengali and 6 did not study either. How many of the students studied both?

Solution:
মোট শিক্ষার্থীর সংখ্যা: 60
ইংরেজিতে পড়ে এমন শিক্ষার্থীর সংখ্যা n(E) = 32
বাংলায় পড়ে এমন শিক্ষার্থীর সংখ্যা n(B) = 28
কোনটিই পড়ে না এমন শিক্ষার্থীর সংখ্যা = 6

অন্তত একটি বিষয় পড়ে এমন শিক্ষার্থীর সংখ্যা = 60 - 6
= 54

উভয় বিষয়ে পড়ে = ইংরেজিতে পড়ে + বাংলায় পড়ে - অন্তত একটি বিষয় পড়ে
= 32 + 28 - 54
= 6

১২,৫১৬.

Which of the following is equivalent to the pair of inequalities 2x - 5 ≤ 7 and 3x + 4 > 10?

ক
2 < x ≤ 6
খ
3 ≤ x < 2
গ
x > 3
ঘ
x < 7

ব্যাখ্যা

Question: Which of the following is equivalent to the pair of inequalities 2x - 5 ≤ 7 and 3x + 4 > 10?

Solution:
Solve the first inequality,
2x - 5 ≤ 7
⇒ 2x ≤ 7 + 5
⇒ 2x ≤ 12
∴ x ≤ 6
And,
Solve the second inequality,
3x + 4 > 10
⇒ 3x > 10 - 4
⇒ 3x > 6
∴ x > 2

∴ We get 2 < x ≤ 6

১২,৫১৭.

How many 4 letter words with or without meaning can be formed out of the letters of the word 'TRIANGLE', where repetition of letters is not allowed?

ক
720
খ
1050
গ
1260
ঘ
1680
ঙ
None of the above

ব্যাখ্যা

Question: How many 4 letter words with or without meaning can be formed out of the letters of the word 'TRIANGLE', where repetition of letters is not allowed?

Solution:
Here,
'TRIANGLE' contains 8 different letters.

So the number of words = Number of arrangements of 8 letters, taking 4 at a time
= ⁸P₄
= (8 × 7 × 6 × 5)
= 1680

১২,৫১৮.

In a hostel, Food was available for 2000 students for 54 days, but after 15 days more students joined hostel and food lasts only for 20 more days. Determine how many students came in hostel?

ক
ক) 1650
খ
খ) 1700
গ
গ) 1900
ঘ
ঘ) 2100

ব্যাখ্যা

As it is given that food is there for 54 days for 2000 students,
But after 15 days, remaining food was sufficient for 2000 students for 39 days only ( as 54-15 = 39 )
Let x number of students came in hostel after 15 days,
=> Total number of students after 15 days = 2000 + x
=> Remaining food was enough for (2000 + x) students for 20 days
So here is indirect proportion, as more people and less food
=> 2000 : ( 2000 + x ) :: 20 : 39
=> 2000× 39 = (2000 + x )× 20
=> 3900 = 2000 + x
=> x = 3900 - 2000
=> x = 1900

১২,৫১৯.

How many positive integers less than 100 are neither multiples of 2 or 3?

ক
ক) 30
খ
খ) 31
গ
গ) 32
ঘ
ঘ) 33

ব্যাখ্যা

1) multiples of 2 till 100 = 100/2 = 50
2) Multiples of 3 till 100 = 100/3 = 33.33 = 33
add the two 50 + 33 = 83; subtract common terms that are multiple of both 2 and 3

LCM of 2 and 3 = 6
Multiples of 6 till 100 = 100/6 = 16.66 = 16
so total multiples of 2 and 3 = 83 - 16 = 67

∴ Number of positive integers less than 100 are neither multiples of 2 or 3 = 100 - 67 = 33

১২,৫২০.

ক
3
খ
1/2
গ
4
ঘ
5/8

ব্যাখ্যা

Question:

Solution:

১২,৫২১.

A boat has a crack in its hull which is leaking water into the boat and could sink the boat in 6 hours. The boat has a pump which can pump the water out in 8 hours. If the boat is 168 km away from the shore and the pump is running what is the minimum speed the boat should run at so that it can reach the shore before sinking?

ক
5 km/hour
খ
6 km/hour
গ
7 km/hour
ঘ
8 km/hour
ঙ
None of these

ব্যাখ্যা

Question: A boat has a crack in its hull which is leaking water into the boat and could sink the boat in 6 hours. The boat has a pump which can pump the water out in 8 hours. If the boat is 168 km away from the shore and the pump is running what is the minimum speed the boat should run at so that it can reach the shore before sinking?

Solution:
ছিদ্রপথে জাহজে ১ ঘণ্টায় পানি প্রবেশ করে = ১/৬ অংশ
পাম্প দ্বারা ১ ঘণ্টায় পানি বের হয় = ১/৮ অংশ
∴ ছিদ্রপথ ও পাম্প দ্বারা ১ মিনিটে পূর্ণ হয় = (১/৬) - (১/৮) অংশ
= (৪ - ৩)/২৪ অংশ
= ১/২৪ অংশ

∴ সম্পূর্ণ জাহাজ পূর্ণ হবে ২৪ ঘণ্টায়। তাই জাহাজটিকে ২৪ ঘণ্টায় ১৬৮ কিলোমিটার অতিক্রম করতে হবে।
অতএব, বেগ = ১৬৮/ ২৪ কি.মি./ঘণ্টা
= ৭ কি.মি./ঘণ্টা

১২,৫২২.

A circle and a rectangle have the same perimeter. The sides of the rectangle are 9 cm and 13 cm. what is the area of the circle?

ক
625 sq. cm
খ
308 sq. cm
গ
154 sq. cm
ঘ
77 sq. cm

ব্যাখ্যা

Question: A circle and a rectangle have the same perimeter. The sides of the rectangle are 9 cm and 13 cm. what is the area of the circle?

Solution:
Perimeter of the rectangle = 2(9 + 13)
= 44 cm

∴ Circumference of circle = 44 cm
⇒ 2πr = 44
⇒ r = 44/2π
⇒ r = (44 × 7)/(2 × 22)
∴ r = 7 cm

∴ Area of circle = πr²
= (22/7) × (7)²
= 154 sq. cm

১২,৫২৩.

How many different positive integers exist between 10⁶ and 10⁷, the sum of whose digits is equal to 2?

ক
6
খ
7
গ
14
ঘ
28
ঙ
None of these

ব্যাখ্যা

Question: How many different positive integers exist between 10⁶ and 10⁷, the sum of whose digits is equal to 2?

Solution:
10⁶ থেকে 10⁷ এর মধ্যে অর্থাৎ 10⁶ থেকে (10⁷ - 1) সংখ্যাগুলোর ডিজিট সংখ্যা হবে 7টি।
ডিজিট গুলির যোগফল 2 হবে, এমন দুটি সম্ভাবনা আছে।

১ম ক্ষেত্রে, দুটি ডিজিট 1 এবং অবশিষ্ট 5টি ডিজিট 0
এই ক্ষেত্রে সংখ্যাগুলো = 1100000, 1010000, 1001000, 1000100, 1000010, 1000001 = 6টি সংখ্যা

২য় ক্ষেত্রে, একটি ডিজিট 2 এবং অবশিষ্ট 6টি ডিজিট 0
এই ক্ষেত্রে সংখ্যাগুলো = 2000000 = 1টি সংখ্যা

সুতরাং, মোট সংখ্যা = 6 + 1 = 7টি।

১২,৫২৪.

Handsome : Beautiful : : Husband : ?

ক
ক) Women
খ
খ) Wife
গ
গ) Girl
ঘ
ঘ) She

ব্যাখ্যা

Handsome is related to Husband and Beautiful is related to Wife.

১২,৫২৫.

A train 130 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

ক
42.8 km/hr
খ
48.8 km/hr
গ
51.8 km/hr
ঘ
55.8 km/hr

ব্যাখ্যা

Question: A train 130 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Solution:
Speed of the train relative to man = 130/10 m/sec
= 13 m/sec
= (13 × 3600)/1000 km/hr
= 46.8 km/hr

Let,
The speed of the train be x km/hr.
∴ Relative speed = (x - 5) km/hr.
⇒ x - 5 = 46.8
∴ x = 51.8 km/hr.

১২,৫২৬.

Find the volume of the cylinder whose radius 14 m and height 1.5 m.

ক
ক) 780 m³
খ
খ) 820 m³
গ
গ) 924 m³
ঘ
ঘ) 960 m³

ব্যাখ্যা

Question: Find the volume of the cylinder whose radius 14 m and height 1.5 m.

Solution:
We know that,
Volume of a cylinder = πr²h
= ((22/7) × 14 × 14 × 1.5) m³
= 924 m³

১২,৫২৭.

Of the three numbers, the first is twice the second is half of the third. If the average of the three numbers is 63, then difference of first and third numbers is-

ক
36
খ
42
গ
48
ঘ
54

ব্যাখ্যা

Question: Of the three numbers, the first is twice the second is half of the third. If the average of the three numbers is 63, then difference of first and third numbers is-

Solution:
Let,
the second number be = a
Then, first number is = 2a
And third number is = 4a

ATQ,
(2a + a + 4a)/3 = 63
⇒ 7a = (63 × 3)
⇒ 7a = 189
∴ a = 27

∴ Requried difference = 4a - 2a
= (4 × 27) - (2 × 27)
= 54

১২,৫২৮.

If 16^th March, 2005 is Wednesday, what was the day of the week on 16^th March, 2004?

ক
Tuesday
খ
Thursday
গ
Friday
ঘ
Saturday

ব্যাখ্যা

Question: If 16^th March, 2005 is Wednesday, what was the day of the week on 16^th March, 2004?

Solution:
Since ¹⁶th March is coming after February leap year will not count in 2004.
Odd day is 1.

∴ 16^th March, 2004 is Tuesday.

১২,৫২৯.

The ages of Rima and Bina are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

ক
10 years
খ
7 years
গ
3 years
ঘ
5 years

ব্যাখ্যা

Question: The ages of Rima and Bina are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

Solution:
Let Rima’s age be = 9x years.
Then Bina’s age = 8x years

According to the question,
(9x + 5)/(8x + 5) = 10/9
⇒ 9(9x + 5) = 10(8x + 5)
⇒ 81x + 45 = 80x + 40
⇒ 81x - 80x = 40 - 45
⇒ - x = - 5
∴ x = 5

∴ The difference in their ages = 9x - 8x = x = 5 years.

১২,৫৩০.

The area of a rectangle and square are equal. The side of the square is 12 cm and the smaller side of the rectangle is one-third that of the square. The length of the other side of the rectangle would be-

ক
54 cm
খ
48 cm
গ
36 cm
ঘ
72 cm

ব্যাখ্যা

Question: The area of a rectangle and square are equal. The side of the square is 12 cm and the smaller side of the rectangle is one-third that of the square. The length of the other side of the rectangle would be-

Solution:
given that,
Side of the square = 12 cm
Smaller side of the rectangle = one-third of the square’s side = 12/3 = 4 cm
And The area of a rectangle and a square are equal.

Now,
Area of the square = 12² = 144 cm²

∴ Area of rectangle = 144cm² [The area of a rectangle and a square are equal]

Let the other side of rectangle = L
Now,
4 × L = 144
⇒ L = 144/4
∴ L = 36 cm

So the other side of the rectangle is 36 cm.

১২,৫৩১.

Rina goes to school walking at 3 km/h and comes back home at 2 km/h. If she takes 5 hours in total for the round trip, how far is her school from her house?

ক
6 km
খ
7 km
গ
8 km
ঘ
9 km

ব্যাখ্যা

Question: Rina goes to school walking at 3 km/h and comes back home at 2 km/h. If she takes 5 hours in total for the round trip, how far is her school from her house?

Solution:
মনে করি,
স্কুল থেকে বাসার দূরত্ব = x কি. মি.

∴ স্কুলে যাওয়ার পথে প্রয়োজনীয় সময় = দূরত্ব/সময় = x/3 ঘণ্টা
এবং
বাসায় ফেরার পথে প্রয়োজনীয় সময় = দূরত্ব/সময় = x/2 ঘণ্টা

প্রশ্নমতে,
(x/3) + (x/2) = 5
⇒ (2x + 3x)/6 = 5
⇒ 5x/6 = 5
⇒ 5x = 6 × 5
⇒ 5x = 30
⇒ x = 30/5
⇒ x = 6

∴ স্কুল থেকে বাসার দূরত্ব = 6 কি. মি.

১২,৫৩২.

What number will replace the '?' mark?

ক
25
খ
30
গ
31
ঘ
33

ব্যাখ্যা

Question: What number will replace the '?' mark?

Solution:
নিচের ১ম সংখ্যা + নিচের দুই সংখ্যার পার্থক্য = উপরের সংখ্যা।

১ম চিত্রে, 30 + (30 - 15) = 45
তৃতীয় চিত্রে, 28 + (28 - 21) = 35

∴ দ্বিতীয় চিত্রে, 25 + (25 - 19) = 31

১২,৫৩৩.

If a ladder touches the roof of a wall and makes an angle of 45° with the 15 metre long wall, then the length of the ladder is-

ক
ক) 30m
খ
খ) 15m
গ
গ) 45m
ঘ
ঘ) 15√2m

ব্যাখ্যা

In right angled triangle ABC,
cos 45° = BC/AC
Or, 1/√2 = 15/AC [As, opposite angle of AB and BC is equal, length of both line is also equal]
∴ AC = 15√2

Therefore, the length of the ladder is 15√2 m.

১২,৫৩৪.

The average height of girls in a class is 5ft and that of boys is 5.7ft. If the average height of the students in class is 5.5 ft what could be the possible strength of boys and girls respectively in the class:

ক
ক) 50,20
খ
খ) 30,20
গ
গ) 20,30
ঘ
ঘ) 60,50

ব্যাখ্যা

ধরি,
ছাত্র সংখ্যা= x জন
ছাত্রী সংখ্যা = y জন

প্রশ্নমতে,
5.7x + 5y = 5.5 (x + y)
57x + 50y =55x + 55y
57x - 55x = 55y - 50y
2x = 5y
x/y = 5/2
x : y = 5 : 2
অনুপাতের যোগফল = 5 + 2 = 7
যা দ্বারা 50 + 20 = 70 বিভাজ্য
সম্ভাব্য ছাত্র ছাত্রী সংখ্যা হতে পারে = 50,20

১২,৫৩৫.

The average salary of 65 workers is Rs. 5680 out of which average salary of 31 workers is Rs. 2356 and that of 23 workers is Rs. 4589. What is the average salary of remaining workers?

ক
ক) Tk. 19832.25
খ
খ) Tk. 19732.50
গ
গ) Tk. 17328.81
ঘ
ঘ) Tk. 18734.47

ব্যাখ্যা

Total salary of 65 workers = 65 × 5680 = Tk. 369200
Total salary of 31 workers = 31 × 2356 = Tk. 73036
Total salary of 23 workers = 23 × 4589 = Tk. 105547
No. of remaining workers = 65 - 31 – 23 = 65 – 54 = 11
Total Salary of 11 workers = 369200 – 73036 – 105547
= 369200 – 178583
= Tk. 190617
Required average = 190617/11
= Tk. 17328.81
Hence, the required average is Tk. 17328.81

১২,৫৩৬.

There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Tk. 5,000 after 2 years at the same rate?

ক
ক) 1020
খ
খ) 1030
গ
গ) 1050
ঘ
ঘ) 1080

ব্যাখ্যা

ধরি
আসল P =100 টাকা
সরল মুনাফা I = 100 এর 80%
= 80 টাকা
সময় n = 8 বছর

মুনাফার হার = r
আমরা জানি
I = Pnr
r = I/Pn
={(100 × 80)/(100 × 8)}% = 10%
আবার
আসল P = 5000
সময় n = 4 বছর
চক্রবৃদ্ধি মুনাফা = P(1 + r)ⁿ - P
= 5000{(1 + 1/10)²} - 5000
= 5000 × 1.21 - 5000
= 6050 - 5000
= 1050

১২,৫৩৭.

How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?

ক
ক) 120
খ
খ) 360
গ
গ) 240
ঘ
ঘ) 424
ঙ
ঙ) None of these

ব্যাখ্যা

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.
Number of 7 digit numbers = 7!3! × 2! = 420
But out of these 420 numbers,
there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.
= 6!3! × 2! = 60
Hence the required number of 7 digits numbers = 420 - 60 = 360

১২,৫৩৮.

If , then x = ?

ক
9
খ
4
গ
1
ঘ
6

ব্যাখ্যা

Question: If , then x = ?

Solution:

১২,৫৩৯.

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:

ক
ক) 4 cm
খ
খ) 6 cm
গ
গ) 8 cm
ঘ
ঘ) 12 cm

ব্যাখ্যা

Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:

Solution:
surface area of sphere = 4πr²
Curved Surface area of cylinder =2πr₁h
diameter = 12 cm
radius, r₁ = 6 cm

⇒ 4πr²=2πr₁h
⇒ r²= (6×12)/2
⇒ r²= 36
⇒ r = 6

radius of sphere 6 cm.

১২,৫৪০.

How many prime numbers are there between 56 and 100?

ক
8
খ
9
গ
10
ঘ
11

ব্যাখ্যা

Question: How many prime numbers are there between 56 and 100?

Solution:
56 থেকে 100 এর মধ্যবর্তী মৌলিক সংখ্যাগুলো হলো -
59, 61, 67, 71, 73, 79, 83, 89, 97

সুতরাং ৫৬ এবং ১০০ এর মধ্যবর্তী মৌলিক সংখ্যা হলো = 9 টি

১২,৫৪১.

What is the mean proportional of √5 and √125?

ক
ক) 5
খ
খ) 5√5
গ
গ) 25
ঘ
ঘ) 25√5

ব্যাখ্যা

Question: What is the mean proportional of √5 and √125?

Solution:
Mean proportional = √(√5 × √125)
= √(√625)
= √25
= 5

১২,৫৪২.

Nobody believes a man who lacks confidence in his ability. None should sit idle and shirk his duty on the plea that it is beyond his power to do without the help of others. Such a man always falls behind. He meets failures and suffers in the long run. So dependence on others is a great curse. The above passage suggests that everyone should possess the virtue of

ক
ক) punctuality
খ
খ) dignity
গ
গ) boldness
ঘ
ঘ) self-reliance

ব্যাখ্যা

প্রশ্নের মূলকথা হলো,
কেউ এমন মানুষকে বিশ্বাস করে না যার নিজের ক্ষমতার প্রতি আস্থা নেই। যে অন্যের সাহায্য ছাড়া তার দায়িত্ব পালন করতে পারবেনা ভাবে, তাকে সর্বদাই পিছিয়ে থাকতে হয়। তাকে সবসময় অসফলতা ও ভোগান্তি নিয়ে থাকতে হয়। সুতরাং, পরনির্ভরশীলতা হলো অভিশাপ স্বরূপ।
উল্লিখিত অনুচ্ছেদ থেকে এই পরামর্শ পাওয়া যায় যে, সকলের স্বনির্ভর থাকা জরুরি।

তাই সঠিক উত্তর হবে self-reliance (স্বনির্ভর)।

১২,৫৪৩.

A man sold two chairs at Tk. 1500 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is -

ক
ক) 3% loss
খ
খ) 4% loss
গ
গ) 4.5% gain
ঘ
ঘ) 5% gain

ব্যাখ্যা

question: A man sold two chairs at Tk. 1500 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is -

Solution:
in 20% profit,
selling price is 120 when buying price = 100
selling price is 1500 when buying price = (1500 × 100)/120
= 1250 Tk.

in 20% loss
selling price 80 if buying price = 100
selling price 1500 if buying price = (1500 × 100)/80
= 1875 Tk.

total selling price is = 1500 + 1500 = 3000 Tk.
total buying price is = (1250 + 1875) = 3125 Tk.

loss = 3125 - 3000 = 125

percentage of loss is = (125/3125) 100%
= (1/25) × 100%
= 4%

১২,৫৪৪.

A tank can be filled by pipe A in 4 hours and pipe B in 8 hours. At 2 pm pipe A was opened. At what time will the tank be filled if pipe B is opened at 3 pm?

ক
4 : 40 pm
খ
5 : 00 pm
গ
3 : 30 pm
ঘ
5: 30 pm

ব্যাখ্যা

Question: A tank can be filled by pipe A in 4 hours and pipe B in 8 hours. At 2 pm pipe A was opened. At what time will the tank be filled if pipe B is opened at 3 pm?

Solution:
পাইপ A এর কাজের হার = 1/4 অংশ/ঘন্টা
পাইপ B এর কাজের হার = 1/8 অংশ/ঘন্টা

বিকাল 2টা থেকে 3টা পর্যন্ত (1 ঘন্টায়), পাইপ A একা ট্যাঙ্কটির 1/4 অংশ পূর্ণ করে।

বাকি কাজ = 1 - 1/4 = 3/4 অংশ

বিকাল 3টার পর পাইপ A ও B একসাথে কাজ করবে।
একসাথে তাদের কাজের হার = (1/4 + 1/8) অংশ/ঘন্টা
= (2 + 1)/8 অংশ/ঘন্টা
= 3/8 অংশ/ঘন্টা

বাকি 3/4 অংশ পূর্ণ করতে সময় লাগবে = (বাকি কাজ)/(একসাথে কাজের হার)
= (3/4)/(3/8) ঘণ্টা
= 3/4 × 8/3 ঘণ্টা
= 2 ঘণ্টা

সুতরাং, বিকাল 3টার পর আরও 2 ঘন্টা সময় লাগবে।
অতএব, ট্যাঙ্কটি পূর্ণ হবে বিকাল 5 টায়।

১২,৫৪৫.

A box contains 56 in the form of coins of one tk, 50 paise and 25 paise. The number of 50 paise coins is double the number of 25 paise coins and four times the number of one tk coins. How many 50 paise coins are there in the box?

ক
46
খ
64
গ
72
ঘ
58

ব্যাখ্যা

Question: A box contains 56 in the form of coins of one tk, 50 paise and 25 paise. The number of 50 paise coins is double the number of 25 paise coins and four times the number of one tk coins. How many 50 paise coins are there in the box?

Solution:
Number of 1-tk coins = x
Number of 50 paise coins = 4x
Number of 25 paise coins = 2x

Ratio of their values = x : (4x/2) : (2x/4) = 2 : 4 : 1
Value of 50-paise coins = (4/7) × 56 = tk 32
Their number = 32 × 2 = 64

ATQ,
(x )(1) + (4x)(1/2) + 2x(1/4) = 56
⇒ x + 2x + (2/x) = 56
⇒ x = 56 × (2/7)
∴ x = 16

No. of 50p coins = 4 × 16 = 64.

১২,৫৪৬.

X, Y, Z subscribe Tk. 50,000 for a business. X subscribes Tk. 4000 more than Y and Y Tk. 5000 more than Z. Out of a total profit of Tk. 35,000, X receives-

ক
Tk. 14,700
খ
Tk. 12,700
গ
Tk. 14,500
ঘ
Tk. 11,700
ঙ
None of the above

ব্যাখ্যা

Question: X, Y, Z subscribe Tk. 50,000 for a business. X subscribes Tk. 4000 more than Y and Y Tk. 5000 more than Z. Out of a total profit of Tk. 35,000, X receives-

Solution:
Let, Z subscribes p taka
Y subscribes p + 5000 taka
X subscribes p + 5000 + 4000
= p + 9000 taka

p + p + 5000 + p + 9000 = 50000
⇒ 3p + 14000 = 50000
⇒ 3p = 36000
⇒ p = 12000 taka

X receives = {(p + 9000)/50000} × 35000
= (21000/50000) × 35000
= 14700 taka

১২,৫৪৭.

A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

ক
5 liters
খ
8 liters
গ
10 liters
ঘ
12 liters

ব্যাখ্যা

Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

Solution:
Amount of water = 150 × 20/100
= 30

Amount of wine = 120 liter

ATQ,
(30 + x)/(150 + x) = 25/100
⇒ (30 + x)/(150 + x) = 1/4
⇒ 120 + 4x = 150 + x
⇒ 4x - x = 150 - 120
⇒ 3x = 30
⇒ x = 30/3 = 10 liters

১২,৫৪৮.

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction?

ক
11/17
খ
11/15
গ
15/17
ঘ
13/15

ব্যাখ্যা

Let,
The original fraction be x/y
Let us assume that,
The value of x is 100 and the value of y is 100
Then the numerator of the resultant fraction is 250% of x,
That is {100 + (150/100) × 100}
Similarly the denominator of the resultant fraction is 450%
Given that,
(250% of x)/(450% of y)=25/51
⇒ (x/y) × (250/450) = 25/51
⇒ (x/y) = (25/51)/(250/450)
⇒ (x/y) = (25/51) × (450/250)
⇒ x/y = 15/17.

১২,৫৪৯.

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was-

ক
2500
খ
2700
গ
2900
ঘ
3100
ঙ
None of these

ব্যাখ্যা

Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was-

Solution:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
∴ Valid votes = 80%

Total valid votes = 7500 × (80/100)
1st candidate got 55% of the total valid votes.

Hence the 2nd candidate should have got 45% of the total valid votes
Valid votes that 2nd candidate got = total valid votes × (45/100) = 7500 × (80/100) × (45/100) = 2700

১২,৫৫০.

A jar contains white, red and green marbles in the ratios 2 : 3 : 5. Six more green marbles are added to the jars and the ratio becomes 2 : 3 : 7. How many white marbles are there in the jar?

ক
ক) 6
খ
খ) 7
গ
গ) 8
ঘ
ঘ) 9

ব্যাখ্যা

সাদা , লাল এবং সবুজ মার্বেলের অনুপাত 2 : 3 : 5
সাদা মার্বেল আছে = 2x
সবুজ মার্বেল আছে = 5x

এখানে
2x : (5x + 6) = 2 : 7
2x/(5x + 6) = 2/7
x/(5x + 6) = 1/7
7x = 5x + 6
7x - 5x = 6
2x = 6
x = 3
সাদা মার্বেল আছে = 2 × 3 = 6

১২,৫৫১.

A five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. What is the probability that the number is divisible by 4?

ক
ক) 1/5
খ
খ) 5/6
গ
গ) 3/4
ঘ
ঘ) None of these

ব্যাখ্যা

A number divisible by 4 formed using the digits 1, 2, 3, 4 and 5 has to have the last two digits 12 or 24 or 32 or 52.
In each of these cases, the five digits number can be formed using the remaining 3 digits in 3! = 6 ways.
A number divisible by 4 can be formed in 6 × 4 = 24 ways.
Total number that can be formed using the digits 1, 2, 3, 4 and 5 without repetition
= 5! = 120
Required probability,
= 24/120
= 1/5

১২,৫৫২.

A sum of money is to be divided among P, Q, R, S in the ratio 7 : 3 : 5 : 2. If R gets Tk. 2000 more than S, what is Q's share?

ক
Tk. 3100
খ
Tk. 2000
গ
Tk. 2200
ঘ
Tk. 2300

ব্যাখ্যা

Question: A sum of money is to be divided among P, Q, R, S in the ratio 7 : 3 : 5 : 2. If R gets Tk. 2000 more than S, what is Q's share?

Solution:
Let their shares be 7x, 3x, 5x, and 2x respectively.

ATC,
5x - 2x = 2000
⇒ 3x = 2000
⇒ x = 2000/3

Therefore,
Q's share = 3x
= 3 × (2000/3)
= 2000 taka.

১২,৫৫৩.

A train running at the speed of 120 km/h crosses a pole in 12 seconds. What is the length of the train?

ক
350 meter
খ
380 meter
গ
400 meter
ঘ
450 meter

ব্যাখ্যা

Question: A train running at the speed of 120 km/h crosses a pole in 12 seconds. What is the length of the train?

Solution:
Speed = 120 km/h
= (120 × 5/18) m/sec
= 100/3 m/sec

∴ Length of the train = (100/3 × 12) m
= 400 m

১২,৫৫৪.

P can complete a work in 10 days, Q in 15 days, and R in 30 days. P stops working 2 days before the completion of the work, and Q stops 3 days before completion. R continues working alone till the end. What was the total number of days taken to complete the entire work?

ক
4 days
খ
7 days
গ
10 days
ঘ
15 days

ব্যাখ্যা

Question: P can complete a work in 10 days, Q in 15 days, and R in 30 days. P stops working 2 days before the completion of the work, and Q stops 3 days before completion. R continues working alone till the end. What was the total number of days taken to complete the entire work?

Solution:
ধরি, সম্পূর্ণ কাজটি শেষ হতে মোট সময় লাগে y দিন।

∴ P কাজ করেছে (y - 2) দিন
P-এর কাজের অংশ = (y - 2)/10

Q কাজ করেছে (y - 3) দিন
Q-এর কাজের অংশ = (y - 3)/15

R পুরো y দিন কাজ করেছে, তাই তার কাজের অংশ = y/30

শর্তমতে,
(y - 2)/10 + (y - 3)/15 + y/30 = 1
⇒ {3(y - 2) + 2(y - 3) + y} / 30 = 1
⇒ 3y - 6 + 2y - 6 + y = 30
⇒ 6y - 12 = 30
⇒ 6y = 42
∴ y = 7

∴ সম্পূর্ণ কাজ সম্পন্ন করতে 7 দিন সময় লেগেছে।

১২,৫৫৫.

Which of the following numbers is not divisible by 3?

ক
729
খ
567
গ
1458
ঘ
1376

ব্যাখ্যা

Question: Which of the following numbers is not divisible by 3?

Solution:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Checking each number:
729: 7 + 2 + 9 = 18, and 18/3 = 6 → divisible
567: 5 + 6 + 7 = 18, and 18/3 = 6 → divisible
1458: 1 + 4 + 5 + 8 = 18, and 18/3 = 6→ divisible
1376: 1 + 3 + 7 + 6 = 17, and 17/3 = 5.66 → not fully divisible

∴ 1376 can not be divided by 3

১২,৫৫৬.

A rectangular sheet of paper, 10cm long and 8cm wide has squares of side 2cm cut from each of its corner. The sheet is then folded to form a tray of depth 2cm. What is the volume of this tray?

ক
48 cm³
খ
56 cm³
গ
24 cm³
ঘ
36 cm³

ব্যাখ্যা

Question: A rectangular sheet of paper, 10cm long and 8cm wide has squares of side 2cm cut from each of its corner. The sheet is then folded to form a tray of depth 2cm. What is the volume of this tray?

Solution:
Length of tray = 10 - (2 × 2) = 10 - 4 = 6 cm.
Breadth of tray = 8 - (2 × 2) = 4 cm.
Depth of tray = 2 cm.

∴ Volume of tray = 6 × 4 × 2 = 48 cm³

১২,৫৫৭.

In what ratio should milk costing Tk 40 per litre be mixed with milk costing Tk 60 per litre to get a mixture worth Tk 50 per litre?

ক
1 : 1
খ
2 : 3
গ
1 : 2
ঘ
1 : 3

ব্যাখ্যা

Question: In what ratio should milk costing Tk 40 per litre be mixed with milk costing Tk 60 per litre to get a mixture worth Tk 50 per litre?

Solution:
Use the allegation method:
Cheaper = 40, Costlier = 60, Mean = 50
=> Ratio = (60 – 50):(50 – 40) = 10:10 = 1:1

Alternative:
Let Tk 40 per liter is consists of x liters,
Tk 60 per liter is conists of y liters.
total milk = (x+y) liters
and price of mixture is 50 tk per liter

Now,
→ 40x + 60y = 50(x + y)
→ 40x + 60y = 50x + 50y
→ 10y = 10x
→ x : y = 1 : 1

১২,৫৫৮.

The universal set of U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}, B = {3, 5, 6} then determine (A′ ∩ B′)

ক
ক) {1, 4}
খ
খ) {2, 4, 6}
গ
গ) {1, 2, 4, 6}
ঘ
ঘ) {2, 4}

ব্যাখ্যা

Question: The universal set of U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}, B = {3, 5, 6} then determine (A′ ∩ B′)

Solution:
দেওয়া আছে,
U = {1, 2, 3, 4, 5, 6}
A = {1, 3, 5}
B = {3, 5, 6}

A‘ = U - A
= {1, 2, 3, 4, 5, 6} - {1, 3, 5}
= {2, 4, 6}

B‘ = U - B
= {1, 2, 3, 4, 5, 6} - {3, 5, 6}
= {1, 2, 4}

এখন,
(A‘ ∩ B‘) = {2, 4, 6} ∩ {1, 2, 4}
= {2, 4}

১২,৫৫৯.

Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?

ক
ক) 23 ft
খ
খ) 42 ft
গ
গ) 54 ft
ঘ
ঘ) 68 ft

১২,৫৬০.

A tank that was 10% full was emptied into a 50-liter bucket. If the oil now fills 40% of the bucket's volume. Then what is half of the capacity of the tank in liters?

ক
100 liters
খ
150 liters
গ
200 liters
ঘ
50 liters

ব্যাখ্যা

Question: A tank that was 10% full was emptied into a 50-liter bucket. If the oil now fills 40% of the bucket's volume. Then what is half of the capacity of the tank in liters?

Solution:
দেওয়া আছে,
বালতির আয়তন = 50 লিটার
∴ বালতির 40% = 50 × (40/100) = 20 লিটার
তার মানে বালতিতে ট্যাংক থেকে 20 লিটার তেল ঢালা হয়।
তাহলে, ট্যাংকের 10% ধারন ক্ষমতা = 20 লিটার

∴ অর্ধেক বা 50% ধারন ক্ষমতা = 50 × (20/10) = 100 লিটার

১২,৫৬১.

At what rate percent of simple interest will a sum of money double itself in 15 years ?

ক
ক) (13/3)%
খ
খ) (15/3)%
গ
গ) (10/3)%
ঘ
ঘ) (20/3)%

ব্যাখ্যা

Let the principal be x.
Then, the amount after 15 years be 2x.
Let the rate of interest be R.
S.I. = 2x - x = x

Then,
S.I. = P × R × T/100
⇒ x = x × R × 15/100
⇒ R = 100/15
= 20/3
∴ The rate of interest is 20/3%.

১২,৫৬২.

Age of a mother 10 years ago was 3 times the age of her son. After 10 years, the mother's age will be twice that of his son. Find the ratio of their present ages?

ক
ক) 11 : 7
খ
খ) 9 : 5
গ
গ) 7 : 4
ঘ
ঘ) 7 : 3

ব্যাখ্যা

We are given that,
age of mother 10 years ago was 3 times the age of her son
So,
let the age of the son be x and as the mother's age is 3 times the age of her son, let it be 3x, three years ago.
At present,
Mother's age will be (3x + 10) and son's age will be (x + 10)
After 10 years,
Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10

Mother's age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30
(3x + 10) : (x + 10) = 7 : 3.

১২,৫৬৩.

On a certain sum of money, the simple interest for 2 years is Tk. 300 at the rate of 6% per annum. If the same sum is invested at compound interest at the same rate for the same period, how much more interest would be earned?

ক
Tk. 9
খ
Tk. 12
গ
Tk. 29
ঘ
Tk. 19
ঙ
Tk. 20

ব্যাখ্যা

Question: On a certain sum of money, the simple interest for 2 years is Tk. 300 at the rate of 6% per annum. If the same sum is invested at compound interest at the same rate for the same period, how much more interest would be earned?

Solution:
We know,
SI = (P × r × n)/100
⇒ 300 = (P × 6 × 2)/100
⇒ 300 = 12P/100
⇒ P = (300 × 100)/12
∴ P = Tk. 2500

Compound Interest = P(1 + r/100)ⁿ - P
= 2500(1 + 6/100)² - 2500
= 2500 × (1.06)² - 2500
= 2500 × 1.1236 - 2500
= 2809 - 2500
= Tk. 309

∴ Extra interest earned = 309 - 300 = Tk. 9

১২,৫৬৪.

Find the sum of two numbers, which are greater than 29 and have H.C.F. and L.C.M. of 29 and 4147 respectively.

ক
858
খ
696
গ
1050
ঘ
4147

ব্যাখ্যা

Question: Find the sum of two numbers, which are greater than 29 and have H.C.F. and L.C.M. of 29 and 4147 respectively.

Solution:
Product of two numbers = Product of their H.C.F. and L.C.M.
Product of two numbers = 29 × 4147 = 120263

Two numbers are greater than 29.
Therefore, let the two numbers be 29x and 29y.
So, 29x × 29y = 120263
xy = 143

Factors of 143 are: 1, 11, 13, and 143
Case: 1) If we consider factors of 143 as 1 and 143 (co-primes), then we get the value of two numbers x and y = (29 and 4147) ------ (Which is wrong: As it is given that, the numbers are greater than 29)

Case: 2) If we consider factors of 143 as 11 and 13 (co-primes), then we get the value of two numbers x and y = (319, 377) ------ (These two values are greater than 29. So, it is the correct answer)
Therefore, the two numbers are 319 and 377.

Sum of two numbers = 319 + 377 = 696

১২,৫৬৫.

Three dice are rolled together. What is the probability as getting at least one 4?

ক
1/216
খ
91/216
গ
1/4
ঘ
1/3
ঙ
None of these

ব্যাখ্যা

Question: Three dice are rolled together. What is the probability as getting at least one 4?

Solution:
Total number of ways = 6 × 6 × 6 = 216
Probability of getting number 4 at least one time
= 1 - (Probability of getting no number 4)
= 1 - (5/6) × (5/6) × (5/6)
= 1 - 125/216
= (216 - 125)/216
= 91/216

১২,৫৬৬.

A child swims in still water at 4.5 km/hr. The river is flowing at a rate of 1.5 km/hr. Find the average speed of the child if he swims the same distance upstream and downstream.

ক
ক) 3 km/hr
খ
খ) 3.5 km/hr
গ
গ) 4 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

∴ X+Y = 4.5+1.5 = 6 km/hr and X-Y = 4.5-1.5 = 3 km/hr
Let distance be D km

Downstream time = Distance/Speed = D/6
Upstream time = D/3

Average speed = Total distance/Time taken = (D + D)/(D/6 + D/3)
= (6 × 2D)/3D
= 4 km/hr.

১২,৫৬৭.

At every stop after the first, half of the passengers leave the bus, and no new passengers board after the first stop. If only 4 people get off at the fourth stop, how many passengers boarded the bus at the first stop?

ক
12
খ
32
গ
38
ঘ
42

ব্যাখ্যা

Question: At every stop after the first, half of the passengers leave the bus, and no new passengers board after the first stop. If only 4 people get off at the fourth stop, how many passengers boarded the bus at the first stop?

Solution:
After stop 4: The number of people on the bus = 4
After stop 3: The number of people on the bus = 8
After stop 2: The number of people on the bus = 16
After stop 1: The number of people on the bus = 32

Hence, the number of passengers boarded the bus at the first stop = 32

১২,৫৬৮.

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

ক
16 cm
খ
18 cm
গ
15 cm
ঘ
24 cm

ব্যাখ্যা

Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

Solution:

2(l + b)/b = 5/1

⇒ 2l + 2b = 5b

⇒ 3b = 2l

∴ b = (2/3)l

Then,
Area = 216 cm²
⇒ l × b = 216
⇒ l × (2/3)l = 216
⇒ l² = 324
∴ l = 18 cm

১২,৫৬৯.

A, B and C started a business with the investment of Tk.4000, Tk.3000 and Tk.2000 respectively. At the end of the year, the profit received by B and C together is Tk.1500 more than the profit received by A. What is the total profit of the business?

ক
Tk.13500
খ
Tk.12480
গ
Tk.11350
ঘ
Tk.15550

ব্যাখ্যা

Question: A, B and C started a business with the investment of Tk.4000, Tk.3000 and Tk.2000 respectively. At the end of the year, the profit received by B and C together is Tk.1500 more than the profit received by A. What is the total profit of the business?

Solution:
বিনিয়োগের অনুপাত, A : B : C = 4000 : 3000 : 2000 = 4 : 3 : 2

ধরি, মোট লাভ = x টাকা
সুতরাং,
A এর লাভ = 4x/9
B এবং C এর একত্রে লাভ = (3x/9) + (2x/9) = 5x/9

প্রশ্নমতে,
⇒ 5x/9 = (4x/9) + 1500
⇒ (5x/9) - (4x/9) = 1500
⇒ (5x - 4x)/9 = 1500
⇒ x/9 = 1500
⇒ x = 1500 × 9
⇒ x = 13500

∴ মোট লাভ 13500

১২,৫৭০.

A two-digit number is 7 times the sum of its digits. The number that is formed by reversing its digits is 36 less than original number. What is number?

ক
48
খ
84
গ
75
ঘ
57

ব্যাখ্যা

Question: A two-digit number is 7 times the sum of its digits. The number that is formed by reversing its digits is 36 less than original number. What is number?

Solution:
Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y
∴ 10x + y = 7(x + y)
⇔ 3x = 6y
⇔ x = 2y

Number formed by reversing the digits = 10y + x
∴ (10x + y) - (10y + x) = 36
⇒ 9x - 9y = 36
⇒ x - y = 4
⇒ 2y - y = 4
∴ y = 4

So, x = 2y = 2 × 4 = 8
Hence, the number is = 10 × 8 + 4 = 84.

১২,৫৭১.

In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

ক
90
খ
96
গ
102
ঘ
128

ব্যাখ্যা

Question: In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

Solution:
The answer key for true-false questions can be = 2³ = 8
but, the correct answers to all true-false questions cannot be the same

So, The answer key for true-false questions must be = 8 - 2(TTT,FFF)
= 6

The answer key for multiple-choice questions = 4 × 4
= 16

Total possible answer key = 6 × 16
= 96

১২,৫৭২.

The average of two numbers is 6.5 and the square root of their product is 6. What are the numbers?

ক
ক) 11 and 2
খ
খ) 8 and 5
গ
গ) 10 and 3
ঘ
ঘ) 9 and 4
ঙ
ঙ) 9 and 5

ব্যাখ্যা

According to the question,
(x + y)/2 = 6.5,
or, x + y = 13 and
xy = 36,
Now substitute the value of x and y from the option and find the answer.

১২,৫৭৩.

A man invests in a 16% stock at 128. The interest obtained by him is?

ক
ক) 10%
খ
খ) 12.5%
গ
গ) 6 %
ঘ
ঘ) 15%

ব্যাখ্যা

Question: A man invests in a 16% stock at 128. The interest obtained by him is?

Solution:
By investing Tk. 128, income derived = Tk. 16
By investing Tk. 100, income derived
= Tk. (16/128) × 100
= Tk. 12.5

∴ Interest obtained = 12.5%

১২,৫৭৪.

Labib started a business with Tk. 2100 and is joined afterward by Shishir with Tk. 3600. After how many months did Shishir join if the profits at the end of the year are divided equally?

ক
4 months
খ
5 months
গ
6 months
ঘ
7 months

ব্যাখ্যা

Question: Labib started a business with Tk. 2100 and is joined afterward by Shishir with Tk. 3600. After how many months did Shishir join if the profits at the end of the year are divided equally?

Solution:
Suppose,
Shishir joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ Shishir joined after 5 months

১২,৫৭৫.

How many times are the hands of a clock at right angle in a day?

ক
22 times
খ
44 times
গ
48 times
ঘ
24 times
ঙ
None of these

ব্যাখ্যা

Question: How many times are the hands of a clock at right angle in a day?

Solution:
In 12 hours, they are at right angles 22 times.
∴ In 24 hours, they are at right angles = 2 × 22 = 44 times.

So the hands of a clock are at a right angle 44 times in a day.

১২,৫৭৬.

Two workers can complete a job in 24 days while working together. First one of the two workers works alone for 16 days then the other worker works for 24 days alone. If it is known that only 20% of assigned work is left after 40 days, then find out the time (in days) taken by the slower worker to complete the remaining work.

ক
12 days
খ
16 days
গ
20 days
ঘ
24 days

ব্যাখ্যা

Question: Two workers can complete a job in 24 days while working together. First one of the two workers works alone for 16 days then the other worker works for 24 days alone. If it is known that only 20% of assigned work is left after 40 days, then find out the time (in days) taken by the slower worker to complete the remaining work.

Solution:
Let,
the rate of the first worker be 'a' and of the second worker be 'b'.
in 24 days of working together they can complete the total work.
∴ 24a + 24b = 1...........(i)

first worker worked for 16 days alone and second worker worked for 24 days alone to complete 80% of the work.
∴ 16a + 24b = 8/10 = 4/5..............(ii)

subtracting (ii) from (i) we get,
24a + 24b - 16a - 24b = 1 - 4/5
8a = 1/5
a = 1/40

putting a = 1/40 om equation(1) we get,
6/10 + 24b = 1
24b = 1 - 6/10
b = 1/60

so, b is the slower worker.
b can complete the work in 60 days.
as 20% of the work is remaining,
total time to complete the remaining work by b is = 20% of 60 = 12 days

১২,৫৭৭.

What is the H.C.F. of 30, 50, 70?

ক
10
খ
120
গ
150
ঘ
1050

ব্যাখ্যা

30 = 3 × 10
50 = 5 × 10
70 = 7 × 10
H.C.F. of 30, 50, 70 = 10

১২,৫৭৮.

Calculate the area of the triangle with a perimeter of 180cm and sides in the ratio 2 : 3 : 4.

ক
300 cm²
খ
900√15 cm²
গ
3000√15 cm²
ঘ
300√15 cm²

ব্যাখ্যা

Question: Calculate the area of the triangle with a perimeter of 180cm and sides in the ratio 2 : 3 : 4.

Solution:
Let,
The lengths of the triangle's sides be 2x, 3x, and 4x.
Triangle's perimeter = 180cm

Now,
2x + 3x + 4x = 180
⇒ 9x = 180
⇒ x = 20 cm

Then the sides of the triangle are 40 cm, 60 cm, and 80 cm.
Let a = 40 cm, b = 60 cm, c = 80 cm and s = 180/2 = 90 cm

∴ Area of triangle = √[s(s - a)(s - b)(s - c)]
= √[90 × 50 × 30 × 10]
= √1350000
= √(90000 × 15)
= 300√15 cm²

১২,৫৭৯.

One-third of Ratul's marks in Mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English?

ক
ক) 180
খ
খ) 160
গ
গ) 60
ঘ
ঘ) 40

ব্যাখ্যা

Question: One-third of Ratul's marks in Mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English?

Solution:
Let Ratul's marks in Mathematics and English be x and y respectively.
Then,
(1/3)x - (1/2)y = 30
Or, (2x - 3y)/6 = 30
Or, 2x - 3y = 180 ---------- (1)
and x + y = 240 ----------- (2)
Equation (2) is multiplied by 3 then we get,
3x + 3y = 720 ------------ (3)

Adding (1) & (3) we get,
5x = 900
∴ x = 180

From equation (2)
180 + y = 240
∴ y = 60

∴ Ratul's marks in English = 60

১২,৫৮০.

The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq m. The length of the rectangle is -

ক
ক) 30 m
খ
খ) 40 m
গ
গ) 50 m
ঘ
ঘ) 60 m

ব্যাখ্যা

The perimeter of the square = 160 m.
Side of square = (160/4) m
= 40 m.
Area of square = (40 × 40) m² = 1600 m²
Area of rectangle = (1600 - 100) m² = 1500 m²
Let the length and breadth of the rectangle be 'l' and 'b' respectively.
Then, 2(l + b) = 160
⇒ (l + b) = 80
⇒ b = 80 - l.

∴ lb = 1500
⇒ l(80 - l) = 1500
⇒ 80l - l² = 1500
⇒ l² - 80 l + 1500 = 0
⇒ (l - 50)(l - 30) = 0
⇒ l = 50. or l = 30

Hence, length = 50 m, breadth = 30 m.

১২,৫৮১.

A geometric series has its first term as 1 divided by square root of 3, and its common ratio is √3. Which term in the sequence is 81√3?

ক
8^th
খ
11^th
গ
9^th
ঘ
10^th

ব্যাখ্যা

Question: A geometric series has its first term as 1 divided by square root of 3, and its common ratio is √3. Which term in the sequence is 81√3?

Solution:
First term, a = 1/√3
Common ratio, r = √3
Let, the n-th term = ar^{n - 1}
⇒ (1/√3) . (√3)^{n - 1} = 81√3
⇒ (√3)^{n - 1} = 81√3 × √3
⇒ (√3)^{n - 1} = 243
⇒ (√3)^{n - 1} = (√3)¹⁰⇒ n - 1 = 10
∴ n = 11

So, the 11th term is 81√3.

১২,৫৮২.

If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

ক
60
খ
70
গ
75
ঘ
80

ব্যাখ্যা

Question: If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

Solution:
According to the question,
60 × (A/100) = 75 × (B/100)
60A = 75B
4A = 5B
B = 4A/5

Again
B = A × (x/100)
4A/5 = A × (x/100)
4/5 = x/100
5x = 400
x = 400/5
x = 80

১২,৫৮৩.

If m men can do a work in r days, then the number of days taken by (m + n) men to do it is:

ক
ক) (m + n)/mr
খ
খ) (m + n)/mn
গ
গ) m/r(m + n)
ঘ
ঘ) mr/(m + n)

ব্যাখ্যা

Question: If m men can do a work in r days, then the number of days taken by (m + n) men to do it is:

Solution:
m men can do a work in r days.
1 men can do a work in mr days.
∴ (m + n) men can do a work in mr/(m + n) days.

১২,৫৮৪.

The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

ক
98%
খ
91%
গ
93%
ঘ
95%

ব্যাখ্যা

Question: The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

Solution:
Let each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= length × breadth × height = 10 × 10 × 10 = 1000 cubic unit.
After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.
Now, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
% increase in volume = (980/1000) × 100 = 98%

১২,৫৮৫.

Which of the following can be arranged into a 5 -letter English word?
A. HRGST B. RILSA C. TOOMT D. WQRGS

ক
ক) a & d
খ
খ) c & d
গ
গ) b & c
ঘ
ঘ) a & c

ব্যাখ্যা

b & c - এর বর্ণগুলোকে সাজালে গঠিত শব্দ দুটি যথআক্রমে LIRAS (তুরস্কের মুদ্রা) ও MOTTO।
b- এর থেকে LIARS (মিথ্যেবাদী) শব্দটিও পাওয়া যায়।

১২,৫৮৬.

A person 1.5 meters tall sees the top of a building in a small mirror placed on the ground. The mirror is 2 meters away from the person's feet and 80 meters away from the base of the building. What is the height of the building?

ক
45 meters
খ
54.5 meters
গ
60 meters
ঘ
80 meters

ব্যাখ্যা

Question: A person 1.5 meters tall sees the top of a building in a small mirror placed on the ground. The mirror is 2 meters away from the person's feet and 80 meters away from the base of the building. What is the height of the building?

Solution:

ধরি, মানুষের উচ্চতা, AB = 1.5 m
মানুষ এবং আয়নার দূরত্ব, BC = 2 m
ভবনের উচ্চতা, ED = h
ভবন এবং আয়নার দূরত্ব, CD = 80 m

আলোর প্রতিফলনের সূত্র অনুসারে, ∠ACB = ∠ECD (আপতন কোণ = প্রতিফলন কোণ)।
∴ ΔABC এবং ΔEDC সদৃশ।

সদৃশ ত্রিভুজের ধর্ম অনুসারে:
AB/ED = BC/CD
⇒ 1.5/h = 2/80
⇒ h × 2 = 1.5 × 80
⇒ 2h = 120
∴ h = 60 m

অতএব, ভবনটির উচ্চতা = 60 meters

১২,৫৮৭.

A boat goes 8 km upstream in 24 minutes. The speed of the stream is 4 km/hr. The speed of boat in still water is -

ক
ক) 24 km/hr
খ
খ) 25 km/hr
গ
গ) 26 km/hr
ঘ
ঘ) 22 km/hr

ব্যাখ্যা

Speed upstream = 8/(24/60)
= 20 km/hr.
Speed of the stream = 4 km/hr.
Speed of boat in still water = (20 + 4)
= 24 km/hr.

১২,৫৮৮.

Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1 : 4. What is the ratio of gold and silver in the newly formed alloy?

ক
ক) 11 : 9
খ
খ) 20 : 30
গ
গ) 9 : 11
ঘ
ঘ) 25 : 35
ঙ
ঙ) 80 : 20

ব্যাখ্যা

A:: - G : S = 40 : 60
B:: - G : S : C = 35 : 40 : 25
New, G : S = {(1×40) + (4×35)} : {(40×4) + (1×60)}
= 180 : 220
= 18 : 22
= 9 : 11 [Answer. ]

১২,৫৮৯.

How much would I have to pay for a book which cost Tk. 80 to produce, if the printing company sold it to a book seller at 25% profit and the book seller sold it to me at a profit of 20%?

ক
Tk. 105
খ
Tk. 110
গ
Tk. 112
ঘ
Tk. 120

ব্যাখ্যা

Question: How much would I have to pay for a book which cost Tk. 80 to produce, if the printing company sold it to a book seller at 25% profit and the book seller sold it to me at a profit of 20%?

Solution:
উৎপাদন খরচ = 80 টাকা

25% লাভে
উৎপাদন খরচ 100 টাকা হলে বিক্রয়মূল্য = 100 + 25 বা 125 টাকা
উৎপাদন খরচ 1 টাকা হলে বিক্রয়মূল্য = 125/100 টাকা
উৎপাদন খরচ 80 টাকা হলে বিক্রয়মূল্য = (125 × 80)/100 টাকা
= 100 টাকা

কোম্পানির বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য

খুচরা বিক্রেতার 20% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 100 + 20 বা 120 টাকা

∴ বইয়ের জন্য আমাকে 120 টাকা দিতে হবে।

১২,৫৯০.

A clock slows down by one minute every 24 hours. How long will it take to slow down by one hour?

ক
ক) 60 days
খ
খ) 45 days
গ
গ) 30 days
ঘ
ঘ) 75 days

ব্যাখ্যা

Since the clock takes 24 hours or 1 day to slow down by 1 minute.
So, it will take 60 days to slow down 60 minutes or 1 hour.

১২,৫৯১.

8 years ago, the ratio of A’s age to B’s age was 4:5. At present the ratio of B’s age to C’s age is 4:5. At present, the difference between A’s age and C’s age is 30 years, then what is the sum of the ages of A, B and c?

ক
ক) 138 years
খ
খ) 160 years
গ
গ) 148 years
ঘ
ঘ) 152 years
ঙ
ঙ) 164 years

ব্যাখ্যা

Let, 8 years ago,
the age of A and B was 4x and 5x respectively. Age of C = y
so, the present age of A and B is 4x + 8 and 5x + 8 respectively

A/Q,
5x + 8 : y = 4 : 5 ------------ (1)
y - (4x + 8) = 20 ----------- (2)
Solving this equation we will get x = 8 and y = 60

So, present age of Age of A = 4×8 + 8
= 40
and present age of B = 5×8 + 8
= 48
From equation (1),
C = {(5x + 8) × 5} ÷ 4 = 60

So, the total age of A, B & C= 40 + 48 + 60
= 148

১২,৫৯২.

A man can swim in still water at 8 km/hr. If the river is flowing at 2km/hr he takes 80 minutes to reach a place and return back, how far is the place?

ক
4 km
খ
3 km
গ
4.5 km
ঘ
5 km

ব্যাখ্যা

Question: A man can swim in still water at 8 km/hr. If the river is flowing at 2km/hr he takes 80 minutes to reach a place and return back, how far is the place?

Solution:
Let the place is x km far.

Speed downstream = 8 + 2 = 10 km/hr
Speed upstream = 8 - 2 = 6 km/hr

Time = Distance/Speed

So, as per question;
x/6 + x/10 = 80/60
⇒ (5x + 3x)/30 = 4/3
⇒ 8x/30 = 4/3
⇒ 24x = 120
∴ x = 120/24 = 5 km

১২,৫৯৩.

What is the parameter of a rectangle that is 24 meter wide and has the same area as another rectangle that is 64 meter long and 48 meter wide?

ক
ক) 112 meter
খ
খ) 152 meter
গ
গ) 224 meter
ঘ
ঘ) 256 meter
ঙ
ঙ) 304 meter

ব্যাখ্যা

Question: What is the parameter of a rectangle that is 24 meter wide and has the same area as another rectangle that is 64 meter long and 48 meter wide?

Solution:
ধরি
আয়তক্ষেত্রের দৈর্ঘ্য = x

প্রশ্নমতে
x × 24 = 64 × 48
x = (64 × 48)/24
x = 128

অতএব
পরিসমা = 2(128 + 24) মিটার = 304 মিটার

১২,৫৯৪.

A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3?

ক
1
খ
3
গ
5
ঘ
6

ব্যাখ্যা

Question: A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3?

Solution:
Total number of button = 14 + 6 + 12 + 8 = 40

If 25 buttons are removed, there are (40 - 25) = 15 buttons remaining in the bag.

If the chance of drawing a red button is now 1/3, then 5 of the 15 buttons remaining must be red.
The original total of red buttons was 6.
So, (6 - 5) = 1 red button was removed.

১২,৫৯৫.

Two pipes P and Q, when opened alone can fill the tank in 20 and 30 hours respectively. If both pipes are opened together, then in how many hours will the tank be filled?

ক
ক) 8 hours
খ
খ) 10 hours
গ
গ) 12 hours
ঘ
ঘ) 14 hours

ব্যাখ্যা

Question: Two pipes P and Q, when opened alone can fill the tank in 20 and 30 hours respectively. If both pipes are opened together, then in how many hours will the tank be filled?

Solution:
Part of tank filled by pipe P in 1 hour = 1/20
Part of tank filled by pipe Q in 1 hour = 1/30

Tank filled by both pipes in 1 hour = (1/20) + (1/30)
= (5/60)
= 1/12

∴ Complete tank will be filled by both in 1/(1/12) hours
= 12 hours

১২,৫৯৬.

What sum of money will amount to Tk. 520 in 5 years and to Tk. 568 in 7 years at simple interest?

ক
ক) Tk 400
খ
খ) Tk 420
গ
গ) Tk 360
ঘ
ঘ) Tk 380

ব্যাখ্যা

Question: What sum of money will amount to Tk. 520 in 5 years and to Tk. 568 in 7 years at simple interest?

Solution:
(Principal + Interest) in 5 years → 520
(Principal + Interest) in 7 years → 568

∴ Interest in 2 years = 48 Tk
∴ Interest in 1 year = 48/2 Tk
∴ Interest in 5 years = (48 × 5)/2 Tk
= Tk. 120

Principal = 520 - 120 = 400 Tk

১২,৫৯৭.

A train crosses a bridge and a bike standing on the bridge in 40 seconds, 25 seconds respectively. What is the length of the bridge if the speed of the train is 50.4km/hr?

ক
180
খ
210
গ
183
ঘ
255

ব্যাখ্যা

Given that,
The speed of the train = 50.4km/hr
= 50.4 x 5/18 m/sec
= 14 m/sec
The train crosses a bike(standing object) in 25 seconds.
Then,
Length of the train = (14 x 25)m
= 350 m.
Now,
let, the length of the bridge is X m.
the train crosses the bridge in 40 seconds.
Then, (X + 350)/40 = 14
⇒ X + 350 = 14 x 40
⇒ X = 560 - 350
⇒ X = 210
Hence the bridge is 210m long.

১২,৫৯৮.

A grocer has a sale of Tk. 6430, Tk. 6932, Tk. 6850, Tk. 7235 and Tk. 6560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?

ক
5469
খ
4993
গ
5989
ঘ
6455

ব্যাখ্যা

Question: A grocer has a sale of Tk. 6430, Tk. 6932, Tk. 6850, Tk. 7235 and Tk. 6560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?

Solution:
Total sale for 5 months = Tk. (6430 + 6932 + 6850 + 7235 + 6560) = Tk. 34007.

Required sale = Tk. [(6500 × 6) - 34009]
= Tk. (39000 - 34007)
= Tk. 4993

১২,৫৯৯.

The probability that a card drawn from a pack of 52 cards will be a diamond or a king is -

ক
2/13
খ
4/13
গ
1/13
ঘ
1/52

ব্যাখ্যা

Question: The probability that a card drawn from a pack of 52 cards will be a diamond or a king is -

Solution:
Here, n(S) = 52
There are 13 cards of diamond (including one king) and there are three more kings.
Let E = event of getting a diamond or a king
Then, n(E) = (13 + 3) = 16
∴P(E) = n(E)/(S) = 16/52 = 4/13

১২,৬০০.

The cost price of 6 oranges equals selling price of five. The profit or loss percent in the transaction is?

ক
20%
খ
25%
গ
30%
ঘ
50%

ব্যাখ্যা

Question: The cost price of 6 oranges equals selling price of five. The profit or loss percent in the transaction is?

Solution:
দেওয়া আছে,
6টি কমলার ক্রয়মূল্য = 5টি কমলার বিক্রয়মূল্য
ধরি, 1টি কমলার ক্রয়মূল্য = x টাকা
তাহলে,
6 টি কমলার ক্রয়মূল্য = 6x টাকা
5 টি কমলার বিক্রয়মূল্য = 6x টাকা

∴ 1টি কমলার বিক্রয়মূল্য = 6x/5 টাকা

∴ লাভ = বিক্রয়মূল্য - ক্রয়মূল্য
= (6x/5) - x
= (6x - 5x)/5
= x/5

∴ x টাকায় লাভ হয় x/5 টাকা
1 টাকায় লাভ হয় = (x/5)/x টাকা
100 টাকায় লাভ হয় = (1 × 100)/5 = 20 টাকা

∴ লাভ হয় 20%