Bank Math

PrepBank · পাতা ৫০ / ১৬১ · ৪,৯০১–৫,০০০ / ১৬,১২৪

৪,৯০১.

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

ক
420 meters
খ
210 meters
গ
240 meters
ঘ
280 meters

ব্যাখ্যা

Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:
Speed = (54 × 1000)/3600
= 15 m/sec

Length of the train = (15 × 20) m = 300 m
Let
the length of the platform be x meters.

Then,
(x + 300)/36 = 15
⇒ x + 300 = 540
∴ x = 240 meters

৪,৯০২.

If the height of a vertical pole is √3 times the length of its shadow on the ground, then the angle of elevation of the sun at that time is -

ক
30°
খ
60°
গ
45°
ঘ
75°

ব্যাখ্যা

Let AB be a vertical pole and let its shadow be BC
Let BC = x m, then length of pole = √3x

Θ be the angle of elevation.
∴ tanΘ = AB/BC = √3x/x
= √3
= tan60°
Θ = 60°.

৪,৯০৩.

Tk.1500 is invested at 5% per year simple interest. In how many years the investment will be Tk.1800?

ক
ক) 5 years
খ
খ) 4 years
গ
গ) 6 years
ঘ
ঘ) 3 years

ব্যাখ্যা

প্রশ্ন: Tk. 1500 is invested at 5% per year simple interest. In how many years the investment will be Tk. 1800?

সমাধান:
Here,
P = Tk. 1500
I = 1800 - 1500 = Tk. 300
r = 5% = 5/100
n = ?

We know that,
∴ I = Pnr
⇒ n = I/(Pr)
= (300 × 100)/(1500 × 5)
= 4

∴ The investment will be Tk. 1800 in 4 years.

৪,৯০৪.

The diameter of a wheel is 1.26m. How far will it travel in 600 revolutions?

ক
ক) 2676 m
খ
খ) 7623 m
গ
গ) 2637 m
ঘ
ঘ) 2376 m

ব্যাখ্যা

Diameter of the wheel =1.26m
Radius of the wheel r=1.26/2m
=0.63m

The distance traveled in one revolution = perimeter of the wheel
=2πr
= 2 × (22/7) × 0.63 m
= 99/25 m
distance traveled in 600 revolutions = (99/25) × 600
= 2376 m

৪,৯০৫.

The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is:

ক
30
খ
28
গ
25
ঘ
20

ব্যাখ্যা

Question: The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is:

Solution:
Given that,
Average of 6 numbers = 30
∴ Sum of 6 numbers = 6 × 30 = 180

Average of first 4 numbers = 25
∴ Sum of first 4 numbers = 4 × 25 = 100

And, Average of last 3 numbers = 35
∴ Sum of last 3 numbers = 3 × 35 = 105

∴ Fourth number is = (Sum of first 4 + Sum of last 3) - Total sum
= (100 + 105) - 180
= 205 - 180
= 25

So the fourth number is 25.

৪,৯০৬.

Working individually, A would finish a project in 3 days. B takes double the time as taken by A, C takes one more day in addition to the time taken by B. If all three of them decide to work together on the project, how much time would they take to finish it?

ক
ক) 15/16 days
খ
খ) 11/10 days
গ
গ) 14/9 days
ঘ
ঘ) 16/7 days

ব্যাখ্যা

A can do the work in 3 days. So, in 1 day a does 1/3 amount of work.

B takes double the time as A. So, B can do the work in 6 days. So, in 1 day B does 1/6 amount of work

C takes one more day in addition to the time taken by B. So, C can do the work in 7 days. So, in 1 day C does 1/7 amount of work

When they work together, in 1 day they complete how much work?
In 1 day A, B and C together complete = 1/3 + 1/6 + 1/7 = 9/14 amount of work
A, B and C together complete the entire work in 14/9 days.

৪,৯০৭.

The surface area of a cube is 150 square units. What is the length of the longest stick that can be placed inside the cube?

ক
25√2
খ
5
গ
6√3
ঘ
25
ঙ
5√3

ব্যাখ্যা

Question: The surface area of a cube is 150 square units. What is the length of the longest stick that can be placed inside the cube?

Solution:
Given that,
Surface area of a cube = 150 square units

We know,
Surface area of a cube, S = 6a²
⇒ 6a² = 150
⇒ a² = 150/6
⇒ a²= 25 = 5²
∴ a = 5

The longest stick that can fit inside the cube runs along the space diagonal.
So the space diagonal of a cube, d = a√3
= 5√3 ; [a = 5]

So the length of the longest stick that can be placed inside the cube is 5√3 units.

৪,৯০৮.

A computer can perform 30 identical tasks in 6 hour. At that rate, what is the minimum number of computers that should be assigned to complete 80 of the tasks within 3 hours?

ক
ক) 12
খ
খ) 7
গ
গ) 6
ঘ
ঘ) 16

ব্যাখ্যা

We Know
Total work = rate × Time
Therefore, Rate = 30/6 = 5 task/hr

Now we need to find the number of computers
Given, total work = 80 task and total time = 3 hrs

So, No. of computers = 80 / (5×3) = 5.33, but no. of computers cannot be fraction, so we have to consider it as 1.
∴ Total no. of computers = 5+1 = 6.

৪,৯০৯.

In a certain code, MOUSE is written as 51438 and SEND is written as 3826, how is SOUND written in that code?

ক
62143
খ
41362
গ
35642
ঘ
31426

ব্যাখ্যা

Question: In a certain code, MOUSE is written as 51438 and SEND is written as 3826, how is SOUND written in that code?

Solution:
Given,
M = 5
O = 1
U = 4
S = 3
E = 8

and,
S = 3
E = 8
N = 2
D = 6

So SOUND is written in that code:
S = 3
O = 1
U = 4
N = 2
D = 6

৪,৯১০.

Last year Jaman bought two lamps. This year he sold them for BDT 2000 each. On one lamp, he made 25% profit and on the other lamp he had 25% loss. What was his net loss or profit?

ক
ক) Loss BDT 1000
খ
খ) Profit BDT 100
গ
গ) LOSS BDT 100
ঘ
ঘ) No profit loss
ঙ
ঙ) None

ব্যাখ্যা

প্রথম ল্যাম্পের ক্রয়মূল্য ১২৫ক/১০০=২০০০ টাকা
বা, ক = ১৬০০ টাকা।
অর্থাৎ, প্রথম ল্যাম্প থেকে তার লাভ হয় ৪০০ টাকা।
দ্বিতীয় ল্যাম্পের ক্রয়মূল্য ৭৫ক/১০০=২০০০
বা, ক= ২৬৬৬.৬৭ টাকা।
অর্থাৎ, দ্বিতীয় ল্যাম্প থেকে তার ক্ষতি হয় ৬৬৬.৬৭ টাকা।
তাহলে তার সর্বমোট ক্ষতি হয় ৬৬৬.৬৭ - ৪০০ = ২৬৭.৬৭ টাকা যা প্রশ্নের অপশনে নেই।

৪,৯১১.

The average wages of a worker during a fortnight comprising 15 consecutive working days was Tk. 90 per day. During the first 7 days, his average wages was Tk. 87 per day and the average wages during the last 7 days was Tk. 92 per day. What was his wage on the 8^th day?

ক
Tk. 97
খ
Tk. 89
গ
Tk. 92
ঘ
Tk. 101
ঙ
Tk. 94

ব্যাখ্যা

Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was Tk. 90 per day. During the first 7 days, his average wages was Tk. 87 per day and the average wages during the last 7 days was Tk. 92 per day. What was his wage on the 8^th day?

Solution:
The total wages earned during the 15 days that the worker worked ,
= 15 × 90
= Tk. 1350

The total wages earned during the first 7 days
= 7 × 87
= Tk. 609

The total wages earned during the last 7 days
= 7 × 92
= Tk. 644

Total wages earned during the 15 days,
= wages during first 7 days + wage on 8th day + wages during the last 7 days.

ATQ,
1350 = 609 + wage on 8^th day + 644
⇒ wage on 8^th day = 1350 - 609 - 644 = Tk. 97
∴ wage on 8^th day = Tk. 97

৪,৯১২.

If x = 2 + √3 and y = 2 - √3, find the value of (x² + y²)²

ক
169
খ
196
গ
16
ঘ
144

ব্যাখ্যা

Question: If x = 2 + √3 and y = 2 - √3, find the value of (x² + y²)²

Solution:
We are given:
x = 2 + √3, y = 2 - √3

Now,
x + y
= (2 + √3) + (2 - √3)
= 4

And,
⇒ xy
= (2 + √3)(2 - √3)
= 2² - (√3)²
= 4 - 3 = 1

We know,
x² + y² = (x + y)² - 2xy
⇒ x² + y² = (4)² - 2(1) [Substitute the values]
⇒ x² + y² = 16 - 2
⇒ x² + y² = 14

∴ (x² + y²)² = 14² = 196

৪,৯১৩.

What value will come in place of question mark in the following equations 0.006 ÷ ? = 0.6

ক
0.01
খ
0.001
গ
0.002
ঘ
0.0001

ব্যাখ্যা

Question: What value will come in place of question mark in the following equations 0.006 ÷ ? = 0.6

Solution:
Let
? = x

Now
0.006 ÷ x = 0.6
0.006/x = 0.6
x = 0.006/0.6
x = 0.01

৪,৯১৪.

The average age of seven boys sitting in a row facing South is 27 years. If the average age of the first three boys is 25 years and the average age of the last three boys is 29 years, what is the age of the boy who is sitting in the middle of the row?

ক
24 years
খ
28 years
গ
26 years
ঘ
27 years
ঙ
None

ব্যাখ্যা

Question: The average age of seven boys sitting in a row facing South is 27 years. If the average age of the first three boys is 25 years and the average age of the last three boys is 29 years, what is the age of the boy who is sitting in the middle of the row?

Solution:
7 জন বালকের মোট বয়স = (27 × 7) বছর
= 189 বছর

১ম 3 জন বালকের মোট বয়স = (25 × 3) বছর
= 75 বছর

শেষ 3 জন বালকের মোট বয়স = (29 × 3) বছর
= 87 বছর

6 জন বালকের মোট বয়স = (87 + 75) বছর
= 162 বছর

মাঝখানের বালকের বয়স = (189 - 162) বছর
= 27 বছর

৪,৯১৫.

The average of six consecutive numbers A, B, C, D, E and F is 62. What is the sum of B and F?

ক
122
খ
123
গ
124
ঘ
125

ব্যাখ্যা

Question: The average of six consecutive numbers A, B, C, D, E and F is 62. What is the sum of B and F?

Solution:
Let the Numbers A, B, C, D, E, F be x, x + 1, x + 2, x + 3, x + 4, x + 5.
According to question,
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 62 × 6
⇒ 6x + 15 = 372
⇒ 6x = 372 - 15 = 357
⇒ 6x = 357
⇒ x = 59.5

∴ B = x + 1 = 60.5
∴ F = x + 5 = 64.5

∴ B + F = 60.5 + 64.5 = 125

৪,৯১৬.

A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?

ক
7/8
খ
3/11
গ
5/12
ঘ
9/19

ব্যাখ্যা

Question: A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?

Solution:
Given that,
Number of black balls = 5
Number of white balls = 6

Now,
Favorable event = ⁶C₂ = 15
Total possible events = ¹¹C₂ = 55

∴ Probability = 15/55 = 3/11

৪,৯১৭.

After fillings the car's fuel tank, a driver drove from A to B and then to C. He used 2/3 portion of the fuel driving from A to B. If he used another 7 liters to drive from B to C and still had 1/4 of the tank left, how many liters does the tank hold?

ক
84 liters
খ
72 liters
গ
66 liters
ঘ
88 liters

ব্যাখ্যা

Question: After fillings the car's fuel tank, a driver drove from A to B and then to C. He used 2/3 portion of the fuel driving from A to B. If he used another 7 liters to drive from B to C and still had 1/4 of the tank left, how many liters does the tank hold?

Solution:
Let full capacity x liters
Fuel used from B to C = x - {(2x/3) + (1x/4)}
= (12x - 8x - 3x)/12
= x/12

Now,
x/12 of capacity = 7 liters
∴ x of capacity = 7 × 12 = 84 liters

৪,৯১৮.

A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 25 meters apart, then at what speed is the train travelling?

ক
60 km/h
খ
50 km/h
গ
40 km/h
ঘ
30 km/h

ব্যাখ্যা

Question: A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 25 meters apart, then at what speed is the train travelling?

Solution:
Number of gaps between 21 telephone posts = 20

∴ Distance travelled in 1 minute or 60 sec = (25 × 20) meter
= 500 m

∴ Speed of the train = (500 ÷ 60) m/sec
= 25/3 m/sec
= {(25/3) × (18/5)} km/h
= 30 km/h

৪,৯১৯.

If -1 ≤ 3 - 2x ≤ 3, then -

ক
ক) 0 ≤ x ≤ 2
খ
খ) -2 ≤ x ≤ 0
গ
গ) x ≤ 2
ঘ
ঘ) x ≥ 0

ব্যাখ্যা

Given, -1 ≤ 3 - 2x ≤ 3
⇒ -4 ≤ - 2x ≤ 0 [Adding - 3 in every section]
⇒ 2 ≥ x ≥ 0
⇒ 0 ≤ x ≤ 2

৪,৯২০.

The compound interest on 300 tk. at 7% per annum is 21 taka. The period is:

ক
1 year
খ
2 years
গ
3 years
ঘ
4 years

ব্যাখ্যা

Question: The compound interest on 300 tk. at 7% per annum is 21 taka. The period is:

Solution:
চক্রবৃদ্ধি সুদাসল = P (1 + r)ⁿ
= 300 + 21
= 321 tk.

321 = 300 × (1 + 7/100)ⁿ
⇒ (1 + 7/100)ⁿ = 321/300
⇒ (107/100)ⁿ = 107/100
⇒ (107/100)ⁿ= (107/100)¹
∴ n = 1 year

৪,৯২১.

In a circle, O is the center, ∠AOB = 60°. If the radius of the circle is 4 cm, then what is the value of AB?

ক
ক) 2 cm
খ
খ) 4 cm
গ
গ) 4√2 cm
ঘ
ঘ) 6 cm

ব্যাখ্যা

Question: In a circle, O is the center, ∠AOB = 60°. If the radius of the circle is 4 cm, then what is the value of AB?

Solution:
O কেন্দবিশিষ্ট বৃত্তে, ∠AOB = 60°
ব্যাসার্ধ OA = ব্যাসার্ধ OB = 4cm
∠OAB = ∠OBA = 60°

অতএব, AOB একটি সমবাহু ত্রিভুজ।
OA = OB = AB = 4 cm

৪,৯২২.

A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. His average speed is?

ক
12 kmph
খ
6 kmph
গ
5 kmph
ঘ
9 kmph
ঙ
4 kmph

ব্যাখ্যা

Question: A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. His average speed is?

Solution:
Given that,
A man covers half of his journey at 6 km/h
And The remaining half at 3 km/h.

We know that,
Average speed = 2xy/(x + y)
= (2 × 6 × 3)/(6 + 3)
= 36/9
= 4 kmph

৪,৯২৩.

A shirt is being sold for Tk. 1350 after a 10% discount. Determine its original price.

ক
Tk. 1400
খ
Tk. 1450
গ
Tk. 1500
ঘ
Tk. 1550

ব্যাখ্যা

Question: A shirt is being sold for Tk. 1350 after a 10% discount. Determine its original price.

Solution:
Given,
Let the original price be x Tk.

Discount = 10% of x
= 10x/100
= x/10

∴ Selling Price = Original Price - Discount
= x - (x/10)
= 9x/10

Now,
9x/10 = 1350
⇒ 9x = 1350 × 10
⇒ 9x = 13500
⇒ x = 13500/9
∴ x = 1500

∴ Original price = 1500 Tk.

৪,৯২৪.

If the number of workers is doubled, how many times more time will be required to complete the task?

ক
0.5 times
খ
2 times
গ
3 times
ঘ
None of these

ব্যাখ্যা

Question: If the number of workers is doubled, how many times more time will be required to complete the task?

Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর দিগুণ = 2x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
২x জন কাজটি করে = xn/২x
= n/২ সময়ে বা ১/২ সময়ে।

৪,৯২৫.

For a geometric sequence, the first term a = 7 and the common ratio r = 2 . What is the sum of the first 5 terms?

ক
264
খ
225
গ
217
ঘ
198

ব্যাখ্যা

Question: For a geometric sequence, the first term a = 7 and the common ratio r = 2 . What is the sum of the first 5 terms?

Solution:
Given,
a = 7
r = 2 > 1
n = 5

S = {a(rⁿ - 1)}/(r - 1)
= {7(2⁵ - 1)}/(2 - 1)
= 7 × 31
= 217

৪,৯২৬.

A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 144 minutes, will be covered by A in:

ক
12 minutes
খ
24 minutes
গ
18 minutes
ঘ
15 minutes

ব্যাখ্যা

Question: A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 144 minutes, will be covered by A in:

Solution:
Let,
The speed of C = x
So the speed of B = 3x
and the speed of A = 3x × 2
= 6x

Ratio of speed A : B : C = 6x : 3x : x
= 6 : 3 : 1

Then ratio of time taken = 1/6 : 1/3 : 1
= 1 : 2 : 6

Hence, time taken by A = 144/6 minutes
= 24 minutes

৪,৯২৭.

A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562 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
Tk. 4991
খ
Tk. 5991
গ
Tk. 6001
ঘ
Tk. 6991

ব্যাখ্যা

Question: A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562 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. (6435 + 6927 + 6855 + 7230 + 6562)
= Tk. 34009.

Required sale = Tk. [ (6500 x 6) - 34009 ]
= Tk. (39000 - 34009)
= Tk. 4991.

৪,৯২৮.

If x ≥ 15 and y ≤ 9 , which of the following must be true?

ক
x + y ≤ 6
খ
x - y ≥ 6
গ
x + y ≤ 24
ঘ
x - y ≥ 24

ব্যাখ্যা

Question: If x ≥ 15 and y ≤ 9 , which of the following must be true?

Solution:
Here,
x ≥ 15 ..............(1)
and,
y ≤ 9
⇒ - y ≥ - 9 .............(2)

From (1) + (2) we get,
x - y ≥ 15 - 9
∴ x - y ≥ 6

৪,৯২৯.

If 2√(2x + 1) + 5 = 8, then x =

ক
ক) 5/4
খ
খ) 2.5
গ
গ) 5/8
ঘ
ঘ) 5

ব্যাখ্যা

Question: If 2√(2x + 1) + 5 = 8, then x =

Solution:
Given that,
2√(2x + 1) + 5 = 8
⇒ 2√(2x + 1) = 3
⇒ √(2x + 1) = 3/2
⇒ 2x + 1 = 9/4
⇒ 2x = (9/4) - 1
⇒ 2x = 5/4
∴ x = 5/8

৪,৯৩০.

On multiplying a number by 7 all the digit in the product appear as 3's , the smallest such numbers is -

ক
48619
খ
47619
গ
47719
ঘ
47649

ব্যাখ্যা

Question: On multiplying a number by 7 all the digit in the product appear as 3's , the smallest such numbers is -

Solution:
Let's check the options one by one:
47649 × 7 = 333543; This result is not all 3's.
47719 × 7 = 333033; This result is not all 3's.
47619 × 7 = 333333; This result is all 3's!
48619 × 7 = 340333; This result is not all 3's.

৪,৯৩১.

A motorcycle covers 40km with a speed of 20km/hr. Find the speed of the motorcycle for the next 40km journey so that the average speed of the whole journey will be 30km/hr.

ক
ক) 70 km/hr
খ
খ) 52.5 km/hr
গ
গ) 60 km/hr
ঘ
ঘ) 60.5 km/hr

ব্যাখ্যা

Question: A motorcycle covers 40km with a speed of 20km/hr. Find the speed of the motorcycle for the next 40km journey so that the average speed of the whole journey will be 30km/hr.

Solution:
ধরি
পরবর্তী 40km ভ্রমণের গতিবেগ = x km/hr

প্রশ্নমতে,
(40/20) + (40/x) = 80/30
⇒ (1/20) + (1/x) = 2/30
⇒ 1/x = (1/15) - 1/20
⇒ 1/x = (4 - 3)/60
⇒ 1/x =1/60
x = 60

৪,৯৩২.

If a set has 5 elements, then the power set of that set has ______ elements.

ক
5
খ
125
গ
10
ঘ
32

ব্যাখ্যা

Question: If a set has 5 elements, then the power set of that set has ______ elements.

Solution:
The number of elements in the power set of a set with n elements is 2ⁿ.
Here, n = 5
∴ Number of elements in the power set = 2⁵ = 32

So the power set has 32 elements.

৪,৯৩৩.

Find the determinant of the matrix:

ক
2
খ
4
গ
- 2
ঘ
- 6

ব্যাখ্যা

Question: Find the determinant of the matrix:

Solution:
2 × 2 ম্যাট্রিক্সের জন্য:

⇒ det(A) = ad - bc

Given matrix,

∴ det(A) = 1 × 4 - 2 × 3 = 4 - 6 = - 2

৪,৯৩৪.

A gardener has to plant trees in rows containing equal number of trees. If he plants in rows of 6, 8, 10 or 12 then five trees are left unplanted. But if he plants in rows of 13 trees each, then no tree is left. What is the number of trees that the gardener plants?

ক
ক) 485
খ
খ) 845
গ
গ) 725
ঘ
ঘ) 625

ব্যাখ্যা

LCM of 6, 8, 10, 12 = 120
∴ Required number is of the from 120k + 5
Least value of k for which (120k + 5) is divisible by 13 is k = 7
∴ Required number
= (120 × 7 + 5)
= 845

৪,৯৩৫.

A husband and wife have six married sons. Each of them has four children. The total number in the family is:

ক
32
খ
34
গ
36
ঘ
38

ব্যাখ্যা

Question: A husband and wife have six married sons. Each of them has four children. The total number in the family is:

Solution:
A husband and wife = 2
six married sons = 6 + 6 (wives) = 12
Each of them has four children = 6 × 4 = 24

∴ The total number in the family is = 2 + 12 + 24
= 38

৪,৯৩৬.

What will come at the place of question mark?
6, 24, 60, 120, 210, ?

ক
336
খ
343
গ
350
ঘ
380

ব্যাখ্যা

Question: What will come at the place of question mark?
6, 24, 60, 120, 210, ?

Solition:
2³ - 2 = 6
3³ - 3 = 24
4³ - 4 = 60
5³ - 5 = 120
6³ - 6 = 210
7³ - 7 = 336

৪,৯৩৭.

A boat can travel from point A to point B and return back to point A in 10 hours. Speed of the boat in still water is 8 km/h and the speed of the stream is 4 km/h. Find the distance between A and B.

ক
ক) 25 km
খ
খ) 27 km
গ
গ) 30 km
ঘ
ঘ) 29 km

ব্যাখ্যা

Speed of boat along the stream = 8 + 4 = 12 km/h
Speed of boat against stream = 8 - 4 = 4 km/h
ATQ,
x/12 + x/4 = 10
⇒ (x+3x)/12 = 10
⇒ 4x = 120
⇒ x = 30 km

৪,৯৩৮.

A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 52 years now, the son's age five years back was-

ক
19 year
খ
23 year
গ
18 year
ঘ
21 year
ঙ
None

ব্যাখ্যা

Question: A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 52 years now, the son's age five years back was-

Solution:
let, at present son is x years old
so, at time of his birth the father was x years old

∴ at present the age of father is = x + x year
= 2x year

2x = 52
⇒ x = 52/2
= 26 year

∴ the son's age five years back was = 26 - 5
= 21 year

৪,৯৩৯.

In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5 ?

ক
24 lit
খ
16 lit
গ
32 lit
ঘ
8 lit
ঙ
None of the above

ব্যাখ্যা

Given mixture = 48 lit
Milk in it = 48 x 5/8 = 30 lit
=> Water in it = 48 - 30 = 18 lit
Let 'L' lit of water is added to make the ratio as 3:5
=> 30/(18+L) = 3/5
=> 150 = 54 + 3L
=> L = 32 lit.

৪,৯৪০.

In a survey of 100 people, 60 people like coffee, 50 people like tea, and 20 people like both coffee and tea. How many people like only coffee?

ক
10
খ
20
গ
30
ঘ
40
ঙ
60

ব্যাখ্যা

Question: In a survey of 100 people, 60 people like coffee, 50 people like tea, and 20 people like both coffee and tea. How many people like only coffee?

Solution:
Total number of people surveyed = 100
People who like coffee = 60
People who like tea = 50
People who like both coffee and tea = 20
People who like only coffee can be calculated as follows:

People who like only coffee = People who like coffee - People who like both coffee and tea
= 60 - 20
= 40

Therefore, the number of people who like only coffee is 40.

৪,৯৪১.

A shopkeeper sells two articles for Tk. 900 each. On one, he gains 20% and on the other, he loses 20%. What is his overall gain or loss percentage?

ক
2% gain
খ
4% loss
গ
No gain, no loss
ঘ
5% loss

ব্যাখ্যা

Question: A shopkeeper sells two articles for Tk. 900 each. On one, he gains 20% and on the other, he loses 20%. What is his overall gain or loss percentage?

Solution:
Sells price of two books = (900 × 2) = Tk. 1800

Cost price of first book = (100/120) × 900
= Tk. 750

Cost price of second book = (100/80) × 900
= Tk. 1125

∴ Loss = (1125 + 750) - 1800
= 1875 - 1800
= Tk. 75

∴ loss percentage = (75/1875) × 100%
= 4%

৪,৯৪২.

If it is 250 miles from Dhaka to Dinajpur and 120 miles from Dhaka to Pabna, what percentage of the distance from Dhaka to Dinajpur is the distance from Dhaka to Pabna?

ক
ক) 12
খ
খ) 24
গ
গ) 36
ঘ
ঘ) 48

ব্যাখ্যা

ঢাকা থেকে পাবনার দূরত্ব = 120 মাইল
ঢাকা থেকে দিনাজপুরের দূরত্ব = 250 মাইল

নির্ণেয় শতাংশ = (ঢাকা থেকে পাবনার দূরত্ব/ঢাকা থেকে দিনাজপুরের দূরত্ব) × 100%
= (120/250) × 100%
= 48%

৪,৯৪৩.

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

ক
ক) 1
খ
খ) 3
গ
গ) 7
ঘ
ঘ) 14
ঙ
ঙ) 16

ব্যাখ্যা

Let the required number of days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders 1:7 and Webs 7:1 } :: 7:x
=> 1 × 7 × x = 7 × 1 × 7
=> x = 7

৪,৯৪৪.

The sum of all prime numbers between 60 and 80 is:

ক
523
খ
272
গ
351
ঘ
414

ব্যাখ্যা

Question: The sum of all prime numbers between 60 and 80 is:

Solution:
According to the list of prime numbers, we know that—
prime numbers between 60 and 80 are:
61, 67, 71, 73, 79

Sum of these number = (61 + 67 + 71 + 73 + 79) = 351

৪,৯৪৫.

The number nearest to 320, which is exactly divisible by each of 2, 3, 5 is-

ক
ক) 305
খ
খ) 330
গ
গ) 310
ঘ
ঘ) 270

ব্যাখ্যা

প্রশ্ন: 320 এর নিকটবর্তী কোন সংখ্যাটি 2, 3, 5 দ্বারা নিঃশেষে বিভাজ্য?

সমাধান:
2, 3, 5 এর ল.সা.গু = 30
320 এর কাছাকাছি 30 দ্বারা বিভাজ্য সংখ্যা হলো 300 এবং 330.
এরমধ্যে নিকটবর্তী সংখ্যা 330

৪,৯৪৬.

ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A = ?

ক
50°
খ
30°
গ
100°
ঘ
120°

ব্যাখ্যা

According to the property,
∠A = 2∠D
= 2 × 50°
= 100°
Therefore, the angle, ∠BAC = ∠A = 100°

৪,৯৪৭.

The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number.

ক
44
খ
47
গ
49
ঘ
51

ব্যাখ্যা

Question: The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number.

Solution:
ধরি, সপ্তম সংখ্যাটি x

প্রথম সাতটি সংখ্যার গড় ৬৩
প্রথম সাতটি সংখ্যার সমষ্টি (৬৩ × ৭) = ৪৪১
প্রথম ছয়টি সংখ্যার সমষ্টি = ৪৪১ - x

শেষ সাতটি সংখ্যার গড় ৭০
শেষ সাতটি সংখ্যার সমষ্টি (৭০ × ৭) = ৪৯০
শেষ ছয়টি সংখ্যার সমষ্টি = ৪৯০ - x

সাতটি সংখ্যার সমষ্টি = ৪৪১ - x + ৪৯০ - x + x
= ৯৩১ - x

গড়, (৯৩১ - x)/১৩ = ৬৮
⇒ ৯৩১ - x = ৬৮ × ১৩
⇒ ৯৩১ - x = ৮৮৪
⇒ x = ৯৩১ - ৮৮৪
∴ x = ৪৭

অতএব, সপ্তম সংখ্যাটি ৪৭

৪,৯৪৮.

The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?

ক
12
খ
16
গ
18
ঘ
22

ব্যাখ্যা

Question: The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?

Solution:
PW = Tk. 1800
TD = Tk. 180

PW (present worth) = FV (face value) - TD (true discount)
⇒ Face value = present worth + true discount
= 1800 + 180
= 1980

True discount is the simple interest on the present value for the unexpired time.
Now, simple interest on Tk. 1800 for unexpired time = Tk. 180
The rate of simple interest = (180/1800) × 100% = 10%

Banker's discount is the simple interest on the face value of the bill for unexpired time.
simple interest on Tk. 1980 for unexpired time or remaining time.
R = 10%
Banker's discount = 1980 × (10/100) = 198

Banker's gain = Banker's discount - True discount
= 198 - 180
= 18

Alternative Solution:
Banker's gain = (True discount)²/Present worth
= (180)²/1800
= 18

৪,৯৪৯.

A boat takes 6 hours to move downstream from point P to Q and to return to point P moving upstream. If the speed of the stream is 4 km/hr and speed of the boat in still water is 6 km/hr, what is the distance between point P and Q?

ক
11 km
খ
10 km
গ
9 km
ঘ
8 km

ব্যাখ্যা

Question: A boat takes 6 hours to move downstream from point P to Q and to return to point P moving upstream. If the speed of the stream is 4 km/hr and speed of the boat in still water is 6 km/hr, what is the distance between point P and Q?

Solution:
Let the distance between points P and Q = X km
Speed downstream = 6 + 4= 10 km/hr
Speed upstream = 6 - 4 = 2 km/hr

ATQ,
X/10 + X/2 = 6
⇒ (X + 5X)/10 = 6
⇒ 6X = 10
∴ X = 10

৪,৯৫০.

Robinson crosses a street 500 m long in 6 minutes. His speed in km, per hour is:

ক
ক) 10 km
খ
খ) 8 km
গ
গ) 4 km
ঘ
ঘ) 5 km

ব্যাখ্যা

Question: Robinson crosses a street 500 m long in 6 minutes. His speed in km, per hour is:

Solution:
৬ মিনিটে যায় ৫০০ মিটার
∴ ১ মিনিটে যায় ৫০০/৬ মিটার
∴ ৬০ মিনিট বা ১ ঘণ্টায় যায় (৫০০ × ৬০)/৬ মিটার
= ৫০০০ মিটার বা ৫ কিলোমিটার।

৪,৯৫১.

From the top of a lighthouse which is 90 m above the sea, the angle of depression of a ship is 60°. How far is the ship from the lighthouse?

ক
30√3 m
খ
30 m
গ
17.34 m
ঘ
20.5 m

ব্যাখ্যা

Question: From the top of a lighthouse which is 90 m above the sea, the angle of depression of a ship is 60°. How far is the ship from the lighthouse?

Solution:

Let the height of the lighthouse above sea be AC and it is given 90 m.
Ship is at point B so the distance between the base of lighthouse A and ship is AB.
In ΔABC,
tan60° = AC/AB
⇒ √3 = 90/AB
⇒ AB = 90/√3 = 30√3

৪,৯৫২.

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

ক
ক) 3 hr 45 min
খ
খ) 3 hr 30 min
গ
গ) 4 hr 45 min
ঘ
ঘ) 3 hr 30 min

ব্যাখ্যা

Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
Time is taken by one tap to fill half the tank = 3 hr
Remaining part = 1 - 1/2 = 1/2

Part filled by four taps in one hr = 4 × (1/6) = 2/3

2/3 part filled by four taps in 1 hr
1 part filled by four taps in 3/2 hr
1/2 part filled by four taps in (3/2) × (1/2) hr
= 3/4 hr
= 45 min

So, total time taken = 3 + 45 min = 3 hr 45 min

৪,৯৫৩.

A garden of 100 meter length and 60 meter width has a walkway of 2 meter width on every side. What is the area of the garden, in square meters, excluding the walkway?

ক
ক) 5684
খ
খ) 6000
গ
গ) 624
ঘ
ঘ) 5376
ঙ
ঙ) 312

ব্যাখ্যা

Question: A garden of 100 meter length and 60 meter width has a walkway of 2 meter width on every side. What is the area of the garden, in square meters, excluding the walkway?

Solution:
The length of garden excluding the walkway = 100 - 4 meter
= 96 meter

The width of garden excluding the walkway = 60 - 4 meter
= 56 meter

∴ The are of the garden excluding the walkway = 96 × 56 square meter
= 5376 square meter

৪,৯৫৪.

A train passes a man at 110 kmph running towards the train at the speed of 10 kmph. If it took 3 seconds to cross the man, what would be the length of the train?

ক
80 m
খ
100 m
গ
150 m
ঘ
200 m

ব্যাখ্যা

Question: A train passes a man at 110 kmph running towards the train at the speed of 10 kmph. If it took 3 seconds to cross the man, what would be the length of the train?

Solution:
As both of them are facing towards each other.
total speed will be = 110 + 10 kmph
= 120 kmph

length of the train = 120 × (3/3600) km
= 0.1 km
= 100 m

৪,৯৫৫.

If x² - 6x + 8 < 0, then solve the inequality.

ক
x < 2 or x > 4
খ
2 ≤ x ≤ 4
গ
2 < x < 4
ঘ
x > 4

ব্যাখ্যা

Question: If x² - 6x + 8 < 0, then solve the inequality.

Solution:
x² - 6x + 8 < 0
⇒ x² - 2x - 4x + 8 < 0
⇒ x(x - 2) - 4(x - 2) < 0
⇒ (x - 2)(x - 4) < 0

দুটি রাশির গুণফল শূন্যের চেয়ে ছোট হওয়ার শর্ত হলো, একটি রাশি ধনাত্মক এবং অন্যটি ঋণাত্মক হতে হবে।
∴ অসমতাটি সত্য হবে যদি x - 2 > 0 এবং x - 4 < 0 হয়।

x - 2 > 0 অর্থাৎ, x > 2
x - 4 < 0 অর্থাৎ, x < 4

∴ অসমতার সমাধান হলো 2 < x < 4

৪,৯৫৬.

There are 2 bags. One has 5 white and 3 black napkins. The other one has 4 white and 2 black napkins. Find the probability of picking up a white napkin.

ক
9/14
খ
31/48
গ
1/2
ঘ
1

ব্যাখ্যা

Here, one probability is to find which bag is selected AND the other is for a white napkin from the selected bag.
Probability of selecting 1 bag out of 2 bags = 1/2

Say it has 4 white and 2 black napkins.

So, white napkins probability = 4/(4 + 2) = 4/6
So Probability 1 = (1/2) × (4/6) = 4/12

Similarly, Probability 2 = (1/2) × {5/(5 + 3)} = 5/16

Total probability of white napkin = (4/12) + (5/16) = 31/48

৪,৯৫৭.

How many 8 letter words can be formed by rearranging the letters of the word TRENDING such that T and G occupy the first and last positions respectively?

ক
6!
খ
6!/2!
গ
8! × 2!
ঘ
8!
ঙ
None

ব্যাখ্যা

Question: How many 8 letter words can be formed by rearranging the letters of the word TRENDING such that T and G occupy the first and last positions respectively?

Solution:
As T and G should occupy the first and last position, the first and last position can be filled in only one following way.
T _ _ _ _ _ _ G.

The remaining 6 positions can be filled in the remaining words (R, E, N, D, I, N) where "N" comes twice.

Total permutations of these 6 letters with one letter repeating = 6!/2! ways

৪,৯৫৮.

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

ক
8
খ
9
গ
10
ঘ
11

ব্যাখ্যা

Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Solution:
Let.
C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.

ATQ,
(2x + 2) + 2x + x = 27
⇒ 5x = 25
∴ x = 5.

Hence, B's age = 2x = 10 years.

৪,৯৫৯.

Two tailors X and Y are paid a total of Tk. 550 per week by their employer. If X is paid 20 percent more than the sum paid to Y, how much is Y paid per week?

ক
ক) Tk. 200
খ
খ) TK. 250
গ
গ) TK. 300
ঘ
ঘ) Tk 400

ব্যাখ্যা

Let,
the sum paid to Y per week be Tk. x
Then, sum paid to X per week
= 120% of Tk. x
= Tk. (120/100) × x
= Tk. (6/5) x.
∴ x + (6x/5) = 550
⇒ 11x/5 = 550
⇒ x = (550 × 5)/11
= Tk. 250.

৪,৯৬০.

If m and n are in the domain of the function g and g(m) > g(n), which of the following must be true?

ক
ক) Mn ≠ 0
খ
খ) M > n
গ
গ) M < n
ঘ
ঘ) m ≠ n

ব্যাখ্যা

If g(m) > g(n)
∴ m > n
So, m ≠ n

৪,৯৬১.

A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the savings is 61 : 6. If his monthly income is Tk. 8710, the amount of his monthly savings is-

ক
Tk. 660
খ
Tk. 780
গ
Tk. 810
ঘ
Tk. 840

ব্যাখ্যা

Question: A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the savings is 61 : 6. If his monthly income is Tk. 8710, the amount of his monthly savings is-

Solution:
Expenditure : Savings = 61 : 6

∴ Sum of the terms of ratio = (61 + 6) = 67

Given,
Total monthly salary = Tk. 8710

∴ Monthly savings = Tk.{(6/67) × 8710}
= Tk. 780

৪,৯৬২.

Find the square of a positive number which when decreased by 17 is equal to 60 times the reciprocal of the number.

ক
169
খ
196
গ
225
ঘ
400

ব্যাখ্যা

Question: Find the square of a positive number which when decreased by 17 is equal to 60 times the reciprocal of the number.

Solution:
Let the number be x

Then, x - 17 = 60/x
⇒ x² - 17x − 60 = 0
⇒ x² - 20x + 3x − 60 = 0
⇒ (x - 20)(x + 3) = 0
∴ x = 20, - 3

The positive number = 20
Hence, the square of the positive number = 400

৪,৯৬৩.

If a 20-meter tall pole creates a shadow of length 20√3 meters, what is the angle of elevation of the sun?

ক
20°
খ
30°
গ
45°
ঘ
60°

ব্যাখ্যা

Question: If a 20-meter tall pole creates a shadow of length 20√3 meters, what is the angle of elevation of the sun?

Solution:

ধরি,
খুঁটির উচ্চতা AB = 20 m
খুঁটির ছায়ার দৈর্ঘ্য BC = 20√3 m

এখন,
ΔABC হতে পাই,
tanθ = লম্ব/ভূমি
⇒ tanθ = AB/BC
⇒ tanθ = 20/(20√3)
⇒ tanθ = 1/√3
⇒ tanθ = tan30°
∴ θ = 30°

৪,৯৬৪.

Four people are running around a circular ground from a point on the circumference at 9.00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again?

ক
5.00 pm
খ
6.00 pm
গ
7.00 pm
ঘ
9.00 pm

ব্যাখ্যা

Question: Four people are running around a circular ground from a point on the circumference at 9.00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again?

Solution:
L.C.M. of 40, 50, 60 and 30
= 600 minutes
= 10 hours
So, they meet again 10 hours after they start.
They meet together again = 9.00 am + 10 hours
= 7.00 pm

৪,৯৬৫.

Kamrul bought a house, whose sale price was Tk. 8 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and the lawn of the house. At what price should he sell the house to earn a profit of 25%?

ক
7,90,000 Tk
খ
8,90,000 Tk
গ
8,92,000 Tk
ঘ
7,92,000 Tk

ব্যাখ্যা

Question: Kamrul bought a house, whose sale price was Tk. 8 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and the lawn of the house. At what price should he sell the house to earn a profit of 25%?

Solution:
Here, original price = 8,00,000 Tk

After 20% early bird discount,
8,00,000 × (1 - 0.20) = 6,40,000 Tk

After 10% cash discount,
6,40,000 × (1 - 0.10) = 5,76,000 Tk

Renovation cost = 10% of 5,76,000
= (10/100) × 5,76,000
= 57,600 Tk

∴ Total CP = 5,76,000 + 57,600 = 6,33,600 Tk

Now,
Profit amount = 25% of 6,33,600
= (25/100) × 6,33,600
= 1,58,400 Tk

∴ Required SP = 6,33,600 + 1,58,400 = 7,92,000 Tk

৪,৯৬৬.

A pole of 60 metre long breaks into two parts without complete separation and makes an angle 30° with the ground. Find the length of the broken part of the pole.

ক
40 m
খ
30 m
গ
45 m
ঘ
50 m

ব্যাখ্যা

Question: A pole of 60 metre long breaks into two parts without complete separation and makes an angle 30° with the ground. Find the length of the broken part of the pole.

Solution:

sin30° = x/(60 - x)
⇒ 1/2 = x/(60 - x)
⇒ 60 - x = 2x
⇒ 3x = 60
⇒ x = 60/3 = 20

∴ The length of the broken part of the pole = 60 - 20 = 40 m

৪,৯৬৭.

The efficiency of A, B and C is in the ratio 4 : 5 : 6. Together they can complete a piece of work in 32 days. In how many days will B alone complete the work?

ক
ক) 96 days
খ
খ) 90 days
গ
গ) 98 days
ঘ
ঘ) 92 days

ব্যাখ্যা

Efficiency of A, B and C is in the ratio 4 : 5 : 6
They can complete a work in 32 days by working together

Calculation:
Total efficiency of all three working together = 4 + 5 + 6 = 15
Total work done in 32 days = 15 × 32

Let B will complete the work in n days, working alone
⇒ 5n = 15 × 32
⇒ n = 96

∴ B alone will complete the work in 96 days

৪,৯৬৮.

Four dice (six-faced) are rolled. The number of possible outcomes in which at least one die shows 2 is

ক
621
খ
631
গ
641
ঘ
671

ব্যাখ্যা

Question: Four dice (six-faced) are rolled. The number of possible outcomes in which at least one die shows 2 is

Solution:
Total possible outcomes = 6 × 6 × 6 × 6
= 1296

Total possible outcomes without 2 = 5 × 5 × 5 × 5
= 625

The number of possible outcomes in which at least one die shows 2 is = 1296 - 625
= 671

৪,৯৬৯.

Payel is taller than Belal, who is shorter than Priyamani. Utshob is taller then Priyanka but shorter than Belal. Priyamani is shorter than Payel. Who is the tallest?

ক
Priyanka
খ
Belal
গ
Priyamani
ঘ
Payel

ব্যাখ্যা

প্রশ্ন: Payel is taller than Belal, who is shorter than Priyamani. Utshob is taller then Priyanka but shorter than Belal. Priyamani is shorter than Payel. Who is the tallest?

সমাধান:
Arranging,
Payel > Priyamani > Belal > Utshob > Priyanka

So, Payel is the tallest.

৪,৯৭০.

If m and n are natural numbers, then ^m√n is

ক
ক) always irrational
খ
খ) irrational unless n is the mth power of an integer
গ
গ) irrational unless m is the nth power of an integer
ঘ
ঘ) irrational unless m and n are coprime

ব্যাখ্যা

irrational unless n is the mth power of an integer. If m and n are natural numbers, then ^m√n is irrational unless n is mth power of an integer

৪,৯৭১.

Which number is odd one in oval A and B respectively?

ক
ক) 42,18
খ
খ) 48, 52
গ
গ) 36, 6
ঘ
ঘ) 42, 52

ব্যাখ্যা

In the first oval every number is divisible by 12 except 42 and in the second oval every number is divisible by 6 except 52.

৪,৯৭২.

Three sets of English, Mathematics, and Science books containing 336, 240, and 96 books, respectively, have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The total number of stacks will be -

ক
18
খ
14
গ
22
ঘ
24

ব্যাখ্যা

Question: Three sets of English, Mathematics, and Science books containing 336, 240, and 96 books, respectively, have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The total number of stacks will be -

Solution:
প্রত্যেক তাকে বইয়ের সংখ্যা হবে ৩৩৬, ২৪০ এবং ৯৬ এর গ.সা.গু. এর সমান।
৩৩৬, ২৪০ এবং ৯৬ এর গ.সা.গু = ৪৮

মোট তাক হবে = (৩৩৬ + ২৪০ + ৯৬)/৪৮
= ১৪টি

৪,৯৭৩.

The price of a certain book is discounted by 10% and the reduced price is then discounted by 10%. The series of successive discounts is equivalent to a single discount of

ক
15%
খ
18%
গ
19%
ঘ
20%

ব্যাখ্যা

Question: The price of a certain book is discounted by 10% and the reduced price is then discounted by 10%. The series of successive discounts is equivalent to a single discount of

Solution:
10% ছাড়ে মূল্য = (100 - 10) = 90 টাকা
পুনরায়, 10% ছাড়ে মূল্য = {90 - 90 × (10/100)} টাকা
= (90 - 9) টাকা
= 81 টাকা

এককালীন ছাড় = (100 - 81) টাকা
= 19 টাকা

৪,৯৭৪.

If each edge of a cube is increased by 25%, then the percentage increase in its surface area is?

ক
ক) 30%
খ
খ) 43.75%
গ
গ) 56.25%
ঘ
ঘ) 61%

ব্যাখ্যা

Question: If each edge of a cube is increased by 25%, then the percentage increase in its surface area is?

Solution:
Let the original edge = a
Then, the surafce area = 6a²
New edge = 125a/100 = 5a/4
New surafce area = 6 × (5a/4)² = 75a²/8
Increase in surface area = (75a²/8 - 6a²) = 27a²/8
The percentage increase in its surface area = (27a² × 1/6a² × 100)% = 56.25%

৪,৯৭৫.

Given that the diagonal of a square measures 10√2 units, find the area of the square in square units.

ক
80 square units
খ
100 square units
গ
144 square units
ঘ
169 square units

ব্যাখ্যা

Question: Given that the diagonal of a square measures 10√2 units, find the area of the square in square units.

Solution:
দেয়া আছে,
বর্গক্ষেত্রের কর্ণের দৈর্ঘ্য = 10√2 একক
আমরা জানি,
বর্গক্ষেত্রের কর্ণের দৈর্ঘ্য = √2 × বাহু

প্রশ্নমতে,
√2 × বাহু = 10√2
⇒ বাহু = 10√2/√2
∴ বাহু = 10 একক

এখন,
বর্গক্ষেত্রের ক্ষেত্রফল = (বাহুর দৈর্ঘ্য)²
= (10)²
= 100 বর্গ একক

৪,৯৭৬.

The factor of x² - 5x - 6 are:

ক
ক) (x - 6)(x + 1)
খ
খ) (x + 6)(x - 1)
গ
গ) (x - 3)(x + 2)
ঘ
ঘ) (x - 3)(x - 2)

ব্যাখ্যা

x² - 5x - 6
x² - 6x + x - 6
x(x - 6) + 1(x - 6)
(x - 6)(x + 1).

৪,৯৭৭.

If a 38 meter ladder is placed against a 19 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is-

ক
20º
খ
30º
গ
40º
ঘ
60º

ব্যাখ্যা

Question: If a 38 meter ladder is placed against a 19 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is-

Solution:
Given that,
Ladder's length = 38 m
Wall's height = 19 m

Perpendicular = Wall's height = 19 m
Hypotenuse = Ladder's length = 38 m

We know,
Sinθ = Perpendicular/Hypotenuse
⇒ Sinθ = 19/38
⇒ Sinθ = 1/2
⇒ Sinθ = sin30º
∴ θ = 30º

৪,৯৭৮.

The mean of 40 observations was 46. Later on it was found that an observation 38 was wrongly taken as 33. find the corrected value of mean.

ক
ক) 40.23
খ
খ) 42.36
গ
গ) 46.12
ঘ
ঘ) 51.23

ব্যাখ্যা

Average = Sum of quantities/Number of quantities
1) Sum of observations = Average x No. of observations
= 46 x 40 = 1840

2) Correct sum = Sum of observations + (38 – 33)
= 1840 + (5)
= 1845.
Corrected Mean Value = Corrected Sum/No. of Observations
= 1845/40
= 46.125

৪,৯৭৯.

A shopkeeper sells a badminton racket, whose marked price is 200 taka, at a discount of 15% and gives a shuttle cock costing 20 taka free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

ক
90 Tk
খ
100 Tk
গ
120 Tk
ঘ
150 Tk

ব্যাখ্যা

Question: A shopkeeper sells a badminton racket, whose marked price is 200 taka, at a discount of 15% and gives a shuttle cock costing 20 taka free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

Solution:
Marked price = 200 tk
After 15% discount selling price = (100 - 15)% of 200
= 85% of 200
= (85/100) × 200
= 170
cost of shuttle cock 20 Tk
so, actual selling price = 170 - 20 tk
= 150 tk

let, cost price per racket is x tk
at 25% profit, selling price = 1.25x tk

So, 1.25x = 150
⇒ x = 150/1.25
= 120 Tk

His cost price per racket is 120 Tk.

৪,৯৮০.

In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?

ক
10.7%
খ
20%
গ
25%
ঘ
33.33%
ঙ
58.33%

ব্যাখ্যা

Question: In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?

Solution:
No of bank customers in 1985 = 45% of 60 = 0.45 × 60 = 27
No of bank customers in 1987 = 25% of 144 = 0.25 × 144 = 36

∴ Custeomer increase 36 - 27 = 9

∴ increase in % = (9/27) × 100% = (100/3)% = 33.33%

৪,৯৮১.

Mr. Hannan was both the 17th highest and the 17th lowest in a badminton tournament. How many participants were in the tournament?

ক
ক) 32
খ
খ) 33
গ
গ) 34
ঘ
ঘ) 27

ব্যাখ্যা

প্রশ্ন : Mr. Hannan was both the 17th highest and the 17th lowest in a badminton tournament. How many participants were in the tournament?

সমাধান :

ব্যাডমিণ্টন প্রতিযোগিতায় অংশগ্রহনকারীর সংখ্যা = 17 + 17 - 1 = 33

৪,৯৮২.

The distance between cities A and B is 120 miles. A car travels from A to B at 60 miles per hour and returns from B to A along the same route at 40 miles per hour. What is the average speed for the round trip?

ক
48
খ
50
গ
52
ঘ
56

ব্যাখ্যা

Question: The distance between cities A and B is 120 miles. A car travels from A to B at 60 miles per hour and returns from B to A along the same route at 40 miles per hour. What is the average speed for the round trip?

Solution:
দেওয়া আছে,
A এবং B শহরের দূরত্ব = 120 মাইল

A থেকে B তে যাওয়ার সময়,
60 মাইল অতিক্রম করে = 1 ঘণ্টায়
∴ 1 মাইল অতিক্রম করে = 1/60
∴ 120 মাইল অতিক্রম করে = 120/60 = 2

B থেকে A তে ফেরার সময়,
40 মাইল অতিক্রম করে1
∴ 1 মাইল অতিক্রম করে 1/40
∴ 120 মাইল অতিক্রম করে 120/40 = 3

মোট সময় = (2 + 3) ঘণ্টা = 5 ঘণ্টা
মোট অতিক্রান্ত দূরত্ব = (120 + 120) মাইল = 240 মাইল

∴ গড় গতিবেগ = মোট দূরত্ব/মোট সময় = (240/5) মাইল/ঘণ্টা = 48 মাইল/ঘণ্টা

• বিকল্প সমাধান:
2xy/(x + y)
= (2 × 60 × 40)/(60 + 40)
= 4800/100 = 48 মাইল/ঘণ্টা

৪,৯৮৩.

An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 5?

ক
1/5
খ
3/5
গ
2/5
ঘ
4/5

ব্যাখ্যা

Question: An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 5?

Solution:
total number = 100
n(n+1) will be divisible by 5 if n or n + 1 is divisible by 5

when n is divisible by 5, there are 20 such number (5, 10, 15, 20, 25,.....,100)
when n + 1 is divisible by 5, there are 20 such number (4, 9, 14,.....,99)

∴ proability = (20 + 20)/100
= 40/100
= 2/5

৪,৯৮৪.

A train passes a man at 110 kmph running towards the train at the speed of 10 kmph. If it took 3 seconds to cross the man, what would be the length of the train?

ক
300 m
খ
100 m
গ
250 m
ঘ
180 m

ব্যাখ্যা

Question: A train passes a man at 110 kmph running towards the train at the speed of 10 kmph. If it took 3 seconds to cross the man, what would be the length of the train?

Solution:
As both of them are facing towards each other.
total speed will be = 110 + 10 kmph
= 120 kmph

length of the train = 120 × (3/3600) km
= 0.1 km
= 100 m

৪,৯৮৫.

A tradesman marks his goods 30% above the cost price. If he allows a discount of 10% Then his gain precent is?

ক
ক) 13%
খ
খ) 15%
গ
গ) 16%
ঘ
ঘ) 17%

ব্যাখ্যা

Question: A tradesman marks his goods 30% above the cost price. If he allows a discount of 10% Then his gain precent is?

Solution:
At 30% above,
Market price of goods = 100 + 30 = Tk. 130

At 10% discount,
Selling price = 130 - 10% of 130
= 130 - 13
= Tk. 117

∴ Gain = 117 - 100 = Tk. 17
Gain % = (17/100) × 100
= 17%

৪,৯৮৬.

What is the miximum number of 3 × 3 squares that can be formed form the squares in the 6 × 6 checker board to the right?

ক
4
খ
12
গ
24
ঘ
16

ব্যাখ্যা

Question: What is the miximum number of 3 × 3 squares that can be formed form the squares in the 6 × 6 checker board to the right?

Solution:
Let's consider the picture above.
For each row we can pick exactly 4 different groups of 3 consecutive boxes.
In the same manner, for each column we can select 4 different groups of 3 consecutive boxes.

Therefore, we find the maximum number of (3 × 3) squares of the chessboard,
4 × 4 = 16

৪,৯৮৭.

The equation x² + ax - b = 0 has equal roots, and one of the roots of the equation x² + ax + 15 = 0 is 3. What is the value of b?

ক
- 12
খ
- 15
গ
- 1/64
ঘ
- 16
ঙ
- 1/32

ব্যাখ্যা

Question: The equation x² + ax - b = 0 has equal roots, and one of the roots of the equation x² + ax + 15 = 0 is 3. What is the value of b?

Solution:
Since one of the roots of the equation x² + ax + 15 = 0 is 3, then substituting we'll get:
3² + 3a + 15 = 0
⇒ 3a = - 15 - 9
⇒ a = - 24/3
∴ a = - 8

Substitute a = - 8 in the first equation: x² - 8x - b = 0
Now, we know that it has equal roots thus its discriminant must equal to zero:
d = (- 8)² + 4b = 0
⇒ 64 + 4b = 0
⇒ 4b = - 64
∴ b = - 16

৪,৯৮৮.

What is the probability of impossible events?

ক
ক) 1
খ
খ) 0
গ
গ) >1
ঘ
ঘ) <1

ব্যাখ্যা

Impossible events can't occur.
The probability of an impossible event is 0.

৪,৯৮৯.

How many liters of oil at Tk.40 per liter should be mixed with 240 liters of a second variety of oil at Tk.60 per liter so as to get a mixture whose cost is Tk.52 per liter?

ক
ক) 120 liters
খ
খ) 180 liters
গ
গ) 110 liters
ঘ
ঘ) 160 liters

ব্যাখ্যা

Apply Allegation Method and first calculate the ratio in which they have to be mixed.
= 8 : 12 = 2 : 3
Thus, the two varieties of oil should be mixed in the ratio 2 : 3. So, if 240 liters of the second variety are taken, then 160 liters of the first variety should be taken.

৪,৯৯০.

Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

ক
70 days days
খ
63/2 days days
গ
75/2 days days
ঘ
None of these

ব্যাখ্যা

Question: Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

Solution:
abir does 80% or 4/5 work in 20 days
in one day, he does 1/25 work
in 3 days, he does 3/25 work

work remaining = 1/5 - 3/25
= 2/25 work

Belal does 2/25 parts in 3 days
he will complete the work 75/2 days

৪,৯৯১.

ক
ক) 30
খ
খ) 32
গ
গ) 22
ঘ
ঘ) None of these

ব্যাখ্যা

(5 × 6 × 4)/10 = 12
and (6 × 7 × 5)/10 = 21
∴ (4 × 8 × 10)/10 = 32

৪,৯৯২.

The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years ?

ক
ক) 4 : 5
খ
খ) 8 : 6
গ
গ) 6 : 9
ঘ
ঘ) 8 : 7

ব্যাখ্যা

Question: The ages of Akash and Belal are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years ?

Solution:
The ages of Akash and Belal are in the ratio 6 : 5
let, akash is 6x years old and belal is 5x years old
5x + 6x = 44
⇒ 11x = 44
∴ x = 4 years old

So, Akash is 24 years old and belal is 20 years old

After 8 years, Akash is (24 + 8) = 32 years old and belal is (20 + 8) years old
∴ their ratio = 32 : 28
= 8 : 7

৪,৯৯৩.

Sabuj sold an item for Tk. 6,384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%?

ক
Tk. 10,879
খ
Tk 12,065
গ
Tk. 11,856
ঘ
Tk. 21,654
ঙ
Tk. 15,400

ব্যাখ্যা

30% ক্ষতিতে দাম, 70% = 6384
30% লাভে দাম, 130% = (6384 × 130)/70
= 11856

৪,৯৯৪.

An outlet pipe can empty a cistern in 5 hours. In what time will it empty 3/5 part of the cistern?

ক
4 hours
খ
3 hours
গ
5 hours
ঘ
2 hours

ব্যাখ্যা

Question: An outlet pipe can empty a cistern in 5 hours. In what time will it empty 3/5 part of the cistern?

Solution:
The outlet pipe empties one complete cistern in 5 hours
Time taken to empty 3/5 Part of the cistern = (3/5) × 5 = 3 hours.

৪,৯৯৫.

A box contains 200 marbles, 25% of which are of black colour. Babu took some marbles from the box and found that 30% of them are black. Of the remaining marbles, 10% were black marbles. How many marbles did Babu take?

ক
120
খ
125
গ
150
ঘ
None of these

ব্যাখ্যা

Question: A box contains 200 marbles, 25% of which are of black colour. Babu took some marbles from the box and found that 30% of them are black. Of the remaining marbles, 10% were black marbles. How many marbles did Babu take?

Solution:
বাক্সে মার্বেল আছে = 200 টি
কালো মার্বেল আছে = 200 এর 25%
= 200 এর 25/100
= 50 টি

ধরি
বাবু বাক্স হতে মার্বেল তুলে ছিলো x টি

প্রশ্নমতে
x এর 30% + (200 - x) এর 10% = 50
⇒ 30x/100 + 10(200 - x)/100 = 50
⇒ (30x + 2000 - 10x)/100 = 50
⇒ 20x + 2000 = 5000
⇒ 20x = 5000 - 2000
⇒ 20x= 3000
∴ x = 150

বাবু বাক্স হতে মার্বেল তুলে ছিলো 150 টি

৪,৯৯৬.

Divide 30 by half and add 37. What do you get?

ক
97
খ
70
গ
83
ঘ
89

ব্যাখ্যা

30/0.5 + 37
= (30 ×10)/5 + 37
= 60 + 37
= 97

৪,৯৯৭.

A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.

ক
ক) 10 km/hr.
খ
খ) 7 km/hr
গ
গ) 5 km/hr
ঘ
ঘ) 2.5 km/hr

ব্যাখ্যা

Given that,
time is taken to travel upstream = 2 × times taken to travel downstream
When the distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream

Let speed upstream = x
Then speed downstream = 2x

we have,
1/2(x + 2x) = speed in still water
⇒ 1/2(3x)=7.5
⇒ 3x = 15
⇒ x = 5
∴ speed upstream = 5 km/hr

∴ Rate of stream = 1/2(2x - x)
= x/2
= 5/2
= 2.5 km/hr.

৪,৯৯৮.

If x - y = 3 then what is the value of x³ - y³ − 9xy?

ক
ক) 12
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 27

ব্যাখ্যা

x³ - y³ − 9xy
= (x - y)³ + 3xy(x - y) - 9xy
= (3)³ + 9xy - 9xy
= 27

৪,৯৯৯.

The perimeter of the base of a cube is 24 cm. What is its volume?

ক
124 cm³
খ
216 cm³
গ
100 cm³
ঘ
150 cm³

ব্যাখ্যা

Question: The perimeter of the base of a cube is 24 cm. What is its volume?

Solution:
Let the side length of the cube be x.
So, 4x = 24
∴ x = 6 cm
Volume = (6)³
= 216 cm³

৫,০০০.

If α and β are roots of the equation x² + x - 1 = 0, then the equation whose roots are α/β and β/α is:

ক
ক) x² + 3x + 1 = 0
খ
খ) x² - 3x + 1 = 0
গ
গ) x² + 3x - 1 = 0
ঘ
ঘ) 2x² - 3x + 1 = 0

ব্যাখ্যা

Question: If α and β are roots of the equation x² + x - 1 = 0, then the equation whose roots are α/β and β/α is:

Solution:
As α and β are roots of x² + x - 1 = 0,
then
⇒ α + β = - ( + 1) = - 1
⇒ αβ = - 1

Now, if (α/β) and (β/α) are roots then,
⇒ Sum of roots = (α/β) + (β/α)
= (α² + β²)/αβ
= [(α + β)² - 2αβ]/αβ
= (- 1)² - 2(-1)]/(-1)
= (1+ 2)/(- 1)
= - 3

Product of roots = (α/β) × (β/α) = 1
Now, then the equation is,
⇒ x² - (Sum of roots)x + Product of roots = 0
⇒ x² - (- 3)x + (1) = 0
⇒ x² + 3x + 1 = 0