Bank Math

PrepBank · পাতা ২০ / ১৬১ · ১,৯০১–২,০০০ / ১৬,১২৪

১,৯০১.

The time taken for the tail end of a train to cross a pole is 43 seconds. If the length of the train is 110 m and speed of the train is 54 km/hr. find the initial distance of the pole from the front end of the train.

ক
ক) 435 m
খ
খ) 525 m
গ
গ) 535 m
ঘ
ঘ) 565 m

ব্যাখ্যা

⇒ Speed of train = 54 × (5/18) = 15m/s
⇒ Distance covered in 43 seconds = 15 × 43 = 645 m
⇒ Length of train = 110m

∴ The initial distance of the pole from the front end of the train = 645 - 110 = 535 m

১,৯০২.

A man and a boy can finish a job working together for 4 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?

ক
3 days
খ
4 days
গ
6 days
ঘ
8 days

ব্যাখ্যা

Question: A man and a boy can finish a job working together for 4 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?

Solution:
1 man and 1 boy can do in 1 day 1/4 part
2 man and 2 boy can do in 1 day 2/4 part = 1/2 part

Now 1 man = 2 boys
(2 + 1) man can do in 1 day is 1/2 part
3 man can do in 1 day is 1/2 part
1 man can do in 1 day is 1/(2 × 3) part = 1/6 part

∴ Man alone can do the work in 6 days.

১,৯০৩.

Z, U, Q, ?, L

ক
ক) K
খ
খ) M
গ
গ) N
ঘ
ঘ) I

ব্যাখ্যা

a b c d e f g h i j k l m n o p q r s t u v w x y z

১,৯০৪.

How much must 1 pay for Tk. 1365 stock at 104? (brokerage 1%)

ক
Tk 1514.75
খ
Tk 1435.50
গ
Tk 1433.25
ঘ
None of these

ব্যাখ্যা

Question: How much must 1 pay for Tk. 1365 stock at 104? (brokerage 1%)

Solution:
Required answer = Tk. 1365 × (104 + 1)/100
= Tk. (1365 × 105)/100
= Tk. 1433.25

১,৯০৫.

If machine A polishes x units in 12 minutes and machine B polishes 5x units in 40 minutes, in how many minutes will A and B, working together, polish 50x units?

ক
ক) 240
খ
খ) 300
গ
গ) 350
ঘ
ঘ) 120

ব্যাখ্যা

In 1 minute A polishes x/12 unit and B polishes 5x/40 = x/8 minute
A and B together polishes x/12 + x/8 = 5x/24 units in 1 minute
5x/24 unites requires 1 minute
So, 50x units require = (24 × 50x) / 5x = 240 minutes

১,৯০৬.

Every day a mango seller sells half his stock, 10% of the stock overnight gets spoiled. If 1983 mangoes rotted over 3 nights then what did he start with on the first day?

ক
20,000
খ
22,000
গ
24,000
ঘ
27,000

ব্যাখ্যা

Let x be the starting number of mangoes.
In the day, he sold x/2 mangoes.
Mango left = x/2

Over the 1st night, x/20 mangoes rotted
Therefore, next day he had mangoes available for sale
= (x/2) - (x/20)
= (10x -x)/20
= 9x/20 .
Then, he sold 9x/40 mangoes.
Mango left for next day = 9x/40

Over the 2nd night, mangoes rotted = (9x/40)/10
= 9x/400
So, next day, he had mangoes available = (9x/40) - (9x/400)
= 81x/400 .
Then, he sold 81x/800 mangoes. Mango left for next day = 81x/800 mangoes .

Over the 3rd night, mangoes rotted = (81x/800)/10
= 81x/8000 .
Now, we will stop here, since the bottom line is about number of mangoes which rotted over 3 nights
So, total number of mangoes which rotted over 3 nights are;
(x/20)+(9x/400)+(81x/8000)
= 661x/8000
We get the equation,
661x/8000 = 1983
We get, x=24000
He started with 24000 mangoes

১,৯০৭.

A museum has an average of 510 visitors on Sunday and 240 on other days. Find the average number of visitors per day in a month of 30 days beginning with a Sunday.

ক
285
খ
275
গ
237
ঘ
245

ব্যাখ্যা

Question: A museum has an average of 510 visitors on Sunday and 240 on other days. Find the average number of visitors per day in a month of 30 days beginning with a Sunday.

Solution:
Since, the month begins with a Sunday, so there will be 5 Sundays and 25 other days in this month.

Total visitors in Sundays = 5 × 510 = 2550
Total visitors in other days = 25 × 240 = 6000

∴ Total visiotors in the whole month = (2550 + 6000) = 8550

∴ Average number of visitors per day of the month = 8550/30 = 285

১,৯০৮.

Solve: (81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?

ক
- 0.8
খ
0.6
গ
0. 7
ঘ
- 0.6

ব্যাখ্যা

Question: Solve: (81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?

Solution:
Given that,
(81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?
⇒ 200 ÷ 5³ = 1.2 × 2 + ?
⇒ 200 ÷ 125 = 1.2 × 2 +?
⇒ 1.6 = 2.4 + ?
∴ ? = - 0.8

১,৯০৯.

When 0.232323..... is converted into a fraction, then the result is-

ক
1/5
খ
2/9
গ
23/99
ঘ
23/100

ব্যাখ্যা

Question: When 0.232323..... is converted into a fraction, then the result is-

Solution:

১,৯১০.

A train 150 meters long passes a signal post in 15 seconds. How long will it take to pass a bridge that is 450 meters long?

ক
1 minute
খ
3 minutes
গ
1 minute 30 seconds
ঘ
2 minutes

ব্যাখ্যা

Question: A train 150 meters long passes a signal post in 15 seconds. How long will it take to pass a bridge that is 450 meters long?

Solution:
Train's speed = Distance/Time
= 150/15 = 10 m/s

Total distance to pass the bridge,
= Length of train + Length of bridge
= 150 m + 450 m
= 600 m

∴ Required time = Distance/Speed
= 600/10
= 60 seconds
= 1 minute

∴ The train will take 60 seconds or 1 minute to pass platform.

১,৯১১.

An train travels 10 miles at a speed of 50 miles per hour. How fast must the train travel on the return trip if the round-trip travel time is to be 20 minutes?

ক
ক) 55 miles/hours
খ
খ) 75 miles/hours
গ
গ) 65 miles per hour
ঘ
ঘ) 78 miles per hour

ব্যাখ্যা

We know speed = distance/time
Given distance = 10 miles
Speed = 50 miles per hour
Time = distance/speed = ⅕ hours = 12 min
Total time = 20 min
Time left = 20 – 12 = 8 min = 2/15 hour

So the train has to cover 10 miles in 8 minutes.
Speed = distance/time
= 10/(2/15)
= 10(15/2)
= 75 miles per hour

Hence option b is the answer.

১,৯১২.

A mixture of 50 liters of milk and water contains 10% of water. How much water must be added to make the water 20% in the new mixture?

ক
ক) 6.25 litres
খ
খ) 7 litres
গ
গ) 7.25 litres
ঘ
ঘ) 8.25 litres

ব্যাখ্যা

Quantity of water in given mixture
=10 / 100 x 50=5 litres.

Quantity of milk in given mix.
= 50 - 5= 45 litres.

Let x litres of water be added to it.
Milk : 45 litres, water (5 + x) litres
Total mix = (50 + x) litres
(5+x)/ (50+ x ) = 20/100
⇒ (5 + x)5 = 50 + x
⇒ 4x = 25
⇒ x= 6.25
6.25 litres of water must be added.

১,৯১৩.

Find the value of x, if 3^{(2x + 1)}= 243.

ক
2
খ
3
গ
1/2
ঘ
4

ব্যাখ্যা

Question: Find the value of x, if 3^{(2x + 1)} = 243.

Solution:
3^{(2x + 1)} = 243
⇒ 3^{(2x + 1)} = 3⁵ (since 243 = 3⁵)
⇒ 2x + 1 = 5
⇒ 2x = 5 - 1
⇒ 2x = 4
⇒ x = 4/2
∴ x = 2

১,৯১৪.

1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

ক
52%
খ
48%
গ
45%
ঘ
42%

ব্যাখ্যা

Question: 1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

Solution:
Number of students failed = 40% of boys (1200) + 60% of girls (800)
= (40 × 1200)/100 + (60 × 800)/100
= 480 + 480
= 960

Total number of students = 1200 + 800 = 2000

∴ Percentage of candidates failed = (960/2000) × 100
= 48%

১,৯১৫.

A trader buys some goods for Tk. 150. If the overhead expenses are 12% of cost price, then at what price should it be sold to earn 10%?

ক
ক) Tk. 188.80
খ
খ) Tk. 185.80
গ
গ) Tk. 187.80
ঘ
ঘ) Tk. 184.80

ব্যাখ্যা

দ্রব্যের ক্রয়মূল্য 150 টাকা
অতিরিক্ত ব্যয়ভার (150 এর 12%) = (150 × 12/100) = 18 টাকা
∴ মোট খরচ (150 + 18) = 168 টাকা
10% লাভে বিক্রয়মূল্য (168 + 168 এর 10%) = 168 + 16.8 = 184.80 টাকা

১,৯১৬.

If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

ক
46 meters
খ
47 meters
গ
48 meters
ঘ
49 meters
ঙ
50 meters

ব্যাখ্যা

Question: If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

Solution:
Let the required length be x meters

More men, More length built (Direct proportion)
Less days, Less length built (Direct Proportion)

∴ (20 × 6 × x)=(35 × 3 × 56)
∴ x = 49

Hence, the required length is 49 m.

১,৯১৭.

On a certain airline, the price of a ticket is directly proportional to the number of miles to be traveled. If the ticket for a 900-mile trip on this airline costs Tk. 120, which of the following gives the number of money charged for a k-mile trip on this airline?

ক
(2k)/15
খ
2/(15k)
গ
15/(2k)
ঘ
(15k)/2
ঙ
(40k)/3

ব্যাখ্যা

Question: On a certain airline, the price of a ticket is directly proportional to the number of miles to be traveled. If the ticket for a 900-mile trip on this airline costs Tk. 120, which of the following gives the number of money charged for a k-mile trip on this airline?

Solution:
900 mile trip cost Tk. 120
∴ 1 mile trip costs Tk. 120/900 = 2/15
∴ k mile trip will cost Tk. (2k)/15

১,৯১৮.

How many real roots does the polynomial 2x³ + 8x - 7 have?

ক
ক) None
খ
খ) One
গ
গ) Two
ঘ
ঘ) Three

ব্যাখ্যা

Every polynomial of the form ax³ + bx + c with a, b > 0 has exactly one real roots.
Hence, 2x³ + 8x - 7 or 2x³ + 8x + (-7) has one real root.

১,৯১৯.

A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is-

ক
100 m
খ
200 m
গ
250 m
ঘ
300 m

ব্যাখ্যা

Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is-

Solution:
Let the length of the train is x m and speed is s.
ATQ,
s = (x + 800)/100 and,
s = (x + 400)/60

∴ (x + 800)/100 = (x + 400)/60
or, 60x + 48000 = 100x + 40000
or, 40x = 8000
or, x = 200 m

১,৯২০.

Six bells commence tolling together and toll at intervals of 3, 5, 6, 9, 10, and 15 seconds respectively. In 45 minutes, how many times do they toll together?

ক
29
খ
31
গ
33
ঘ
39

ব্যাখ্যা

Question: Six bells commence tolling together and toll at intervals of 3, 5, 6, 9, 10, and 15 seconds respectively. In 45 minutes, how many times do they toll together?

Solution:
3 = 3¹
5 = 5¹
6 = 2 × 3
9 = 3²
10 = 2 × 5
15 = 3 × 5

∴ ল.সা.গু. = 2¹ × 3² × 5¹
= 2 × 9 × 5
= 90

সুতরাং, ঘণ্টাগুলো প্রতি 90 সেকেন্ড পর পর একসাথে বাজবে।

এখন,
45 মিনিট = 45 × 60 = 2700 সেকেন্ড

মোট 2700 সেকেন্ডে ঘণ্টাগুলো যতবার একসাথে বাজবে = 2700/90 = 30 বার

যেহেতু ঘণ্টাগুলো প্রথমে একবার একসাথে বাজা শুরু করেছিল, তাই মোট সংখ্যাটি হবে 30 এর সাথে সেই প্রথমবারটি যোগ করে।
∴ মোট সংখ্যা = 30 + 1 = 31 বার।

সুতরাং, 45 মিনিটে ঘণ্টাগুলো মোট 31 বার একসাথে বাজবে।

১,৯২১.

In a survey of 1,000 consumers it is found that 720 consumers liked product A and 450 liked product B. What is the least number that must have liked both the products?

ক
270
খ
70
গ
170
ঘ
None of these

ব্যাখ্যা

Question: In a survey of 1,000 consumers it is found that 720 consumers liked product A and 450 liked product B. What is the least number that must have liked both the products?

Solution:
Given that,
Total consumers = 1000
Consumers who like product A = 720
Consumers who like product B = 450

We know,
n(A U B) = n(A) + n(B) - n(A ∩ B)
⇒ 1000 = 720 + 450 - n(A ∩ B)
⇒ 1000 = 1170 - n(A ∩ B)
⇒ n(A ∩ B) = 1170 - 1000
∴ n(A ∩ B) = 170

So 170 consumers like both the products A and B.

১,৯২২.

A boat takes 4 hours to cover a certain distance running downstream, while running upstream it requires 8 hours 48 minutes to cover the same distance. Find the ratio between the speed of the current and the speed of the boat?

ক
ক) 1 : 2
খ
খ) 3 : 8
গ
গ) 2 : 3
ঘ
ঘ) 4 : 3

ব্যাখ্যা

Question: A boat takes 4 hours to cover a certain distance running downstream, while running upstream it requires 8 hours 48 minutes to cover the same distance. Find the ratio between the speed of the current and the speed of the boat?

Solution:
ধরি
দূরত্ব x কি.মি.
নৌকার বেগ + স্রোতের বেগ = x/4................(1)
নৌকার বেগ - স্রোতের বেগ = x/{8(48/60)}
= x/(44/5)
= 5x/44 ...............(2)

2(নৌকার বেগ) = (x/4) + (5x/44)
= (11x + 5x)/44
= 16x/44
= 4x/11
(নৌকার বেগ) = 2x/11

2(স্রোতের বেগ ) = (x/4) - (5x/44)
= (11x - 5x)/44
=6x/44
= 3x/22

(স্রোতের বেগ) =3x/44
স্রোতের বেগ : নৌকার বেগ = 3x/44 : 2x/11
= 3 : 8

১,৯২৩.

From the figure, which of the following must be true?
(I) x + y = 90
(II) x is 35 units greater than y
(III) x is 35 units less than y

ক
I only
খ
II only
গ
III only
ঘ
I and III only

ব্যাখ্যা

Question: From the figure, which of the following must be true?
(I) x + y = 90
(II) x is 35 units greater than y
(III) x is 35 units less than y

Solution:
চিত্রে কোণ x হলো ত্রিভুজটির একটি বহিঃস্থ কোণ। সুতরাং, এর মান বিপরীত অন্তঃস্থ কোণ দুটি, 35 এবং y-এর সমষ্টির সমান।

অর্থাৎ, x = y + 35

এই সমীকরণ থেকে বোঝা যায় যে x এর মান y এর চেয়ে 35 একক বেশি। তাই, (II) বিবৃতিটি সত্য এবং (III) মিথ্যা।

এখন, যদি x একটি স্থূলকোণ (x > 90) হয়, তাহলে x + y এর মান 90 এর চেয়ে বেশি হবে। সুতরাং, x + y যে অবশ্যই 90 এর সমান হবে, এমন কোনো কথা নেই। তাই, (I) বিবৃতিটি অনিবার্যভাবে সত্য নয়।

অতএব, শুধুমাত্র (II) অবশ্যই সঠিক।

১,৯২৪.

Which of the following digits will replace the M marks in the following equation ?
9M + M8 + M6 = 251

ক
6
খ
7
গ
8
ঘ
5
ঙ
None

ব্যাখ্যা

Question: Which of the following digits will replace the M marks in the following equation ?
9M + M8 + M6 = 251

9M+ M8 + M6 = 251
⇒ {(9 × 10) + M} + (10M + 8) + (10M + 6) = 251
⇒ 21M + 104 = 251
⇒ 21M = 251 - 104
⇒ 21M = 147
⇒ M = 7

১,৯২৫.

18 men bind 900 books in 10 days. Find how many binders will be required to bind 600 books in 12 days?

ক
9
খ
10
গ
12
ঘ
15

ব্যাখ্যা

Question: 18 men bind 900 books in 10 days. Find how many binders will be required to bind 600 books in 12 days?

Solution:
To bind 900 books in 10 days binders needed 18 men
To bind 1 books in 1 days binders needed 180/900 men
To bind 600 books in 12 days binders needed (180 × 600)/(900 × 12) men
= 10 men

১,৯২৬.

If a^2x+2=1, where a is a positive real number other than 1, then x = ?

ক
ক) -2
খ
খ) -1
গ
গ) 0
ঘ
ঘ) 1

ব্যাখ্যা

Given that, a^2x+2=1
=> a^2x+2=a⁰=> 2x+2=0
=> x=−2/ 2 =−1

১,৯২৭.

A tank is 1/4 parts full with water. If 15 liters of water is added, the tank becomes 2/3 parts full. What is the capacity of the tank?

ক
42 liters
খ
36 liters
গ
30 liters
ঘ
28 liters

ব্যাখ্যা

Question: A tank is 1/4 parts full with water. If 15 liters of water is added, the tank becomes 2/3 parts full. What is the capacity of the tank?

Solution:
Let the total capacity of the tank be x liters

ATQ,
(x/4) + 15 = 2x/3
⇒ (2x/3) - (x/4) = 15
⇒ (8x - 3x)/12 = 15
⇒ 5x = 12 × 15
⇒ x = 180/5
∴ x = 36

So the total capacity of the tank is 36 liters.

১,৯২৮.

A square and a circle have the same perimeter. The length of the side of the square is 22 cm. What is the area of the circle?

ক
576 square cm
খ
616 square cm
গ
720 square cm
ঘ
784 square cm

ব্যাখ্যা

Question: A square and a circle have the same perimeter. The length of the side of the square is 22 cm. What is the area of the circle?

Solution:
বর্গের পরিসীমা = 4 × বাহুর দৈর্ঘ্য
= 4 × 22 সেমি
= 88 সেমি

প্রশ্নমতে, বর্গ এবং বৃত্তের পরিসীমা সমান।
সুতরাং, বৃত্তের পরিধি = 88 সেমি

আমরা জানি,
বৃত্তের পরিধি = 2πr
⇒ 2πr = 88
⇒ 2 × (22/7) × r = 88
⇒ (44/7) × r = 88
⇒ r = 88 × (7/44)
∴ r = 14 সেমি

এখন, বৃত্তের ক্ষেত্রফল = πr²
= (22/7) × (14)²
= (22/7) × 196
= 22 × 28
= 616 বর্গ সেমি

১,৯২৯.

Two bicycles start at the same time from points P and Q, moving toward each other. If the distance between P and Q is 120 km and their speeds are 12 km/h and 8 km/h respectively then after how much time will they meet each other?

ক
6 hours
খ
5.5 hours
গ
6.5 hours
ঘ
7 hours

ব্যাখ্যা

Question: Two bicycles start at the same time from points P and Q, moving toward each other. If the distance between P and Q is 120 km and their speeds are 12 km/h and 8 km/h respectively then after how much time will they meet each other?

Solution:
Given,
The distance between P and Q = 120 km
Speed of 1^st bicycle = 12 km/h
Speed of 2^nd bicycle = 8 km/h

The bicycles are moving toward each other,
So their relative speed = (Speed of 1^st bicycle + Speed of 2^nd bicycle)
= (12 + 8) km/h
= 20 km/h

Time = (Distance ÷ relative speed)
= (120 ÷ 20)
= 6 h

১,৯৩০.

Find the value of k if (x - 1) is a factor of 4x{x + (k/4x) - (1/4)}.

ক
3
খ
- 3
গ
- 2
ঘ
2

ব্যাখ্যা

Question: Find the value of k if (x - 1) is a factor of 4x{x + (k/4x) - (1/4)}.

Solution:
4x{x + (k/4x) - (1/4)}
= 4x² + k - x
= 4x² - x + k

As x - 1 is a factor,
4 × 1² - 1 + k = 0
⇒ 3 + k = 0
⇒ k = -3

১,৯৩১.

The difference between the greatest and least prime numbers which are less than 80 is-

ক
71
খ
75
গ
77
ঘ
79

ব্যাখ্যা

Question: The difference between the greatest and least prime numbers which are less than 80 is-

Solution:
Greatest prime number = 79
Least prime number = 2
So, their difference = 79 - 2 = 77

১,৯৩২.

Find the missing number:

ক
2
খ
5
গ
7
ঘ
9

ব্যাখ্যা

Question: Find the missing number:

Solution:
We can see that,
The elements of the 3rd row are 8, 6, and a missing element.
8 is equal to the summation of 2 and 6.
6 is equal to the summation of 1 and 5.

∴ So the rest of the missing element is the summation of 3 and 4, which is 7.

১,৯৩৩.

Find the odd number out
6, 9, 15, 21, 24, 28, 30

ক
21
খ
28
গ
30
ঘ
9

ব্যাখ্যা

Question: Find the odd number out
6, 9, 15, 21, 24, 28, 30

Solution:
6, 9, 15, 21, 24, 30 সবগুলো সংখ্যাই 3 দ্বারা বিভাজ্য।
28, 3 দ্বার বিভাজ্য নয়।

১,৯৩৪.

The ratio of present ages of A and B is 6 : 7. Five years hence, this ratio would become 7 : 8. Find the present age of A.

ক
30 years
খ
33 years
গ
35 years
ঘ
36 years

ব্যাখ্যা

Question: The ratio of present ages of A and B is 6 : 7. Five years hence, this ratio would become 7 : 8. Find the present age of A.

Solution:
Let
A’s present age = 6n years
B’s present age = 7n years

So, according to the question
(6n + 5)/(7n + 5) = 7/8
⇒ 48 n + 40 = 49 n + 35
⇒ n = 5

Thus, A’s present age = 6n = 30 years

১,৯৩৫.

A train crosses platform in 50 seconds travelling with a speed of (x + 6) km/hr. If the length of the train be 250 m and the length of the platform be (x + 220) m, then find the value of x?

ক
30
খ
35
গ
40
ঘ
50

ব্যাখ্যা

Question: A train crosses platform in 50 seconds travelling with a speed of (x + 6) km/hr. If the length of the train be 250 m and the length of the platform be (x + 220) m, then find the value of x?

Solution:
Speed of train = (x + 6) km/hr
= (x + 6) × (5/18) m/s

Length of train = 250 m
Length of platform = (x + 220) m

Distance = Length of train + Length of platform
= (250 + x + 220) m
= (470 + x) m

Time = 50 seconds

ATQ,
(x + 6) × (5/18) = (470 + x)/50
⇒ 5 × 50 (x + 6) = 18(470 + x)
⇒ 125(x + 6) = 9(470 + x)
⇒ 125x + 750 = 4230 + 9x
⇒ 125x - 9x = 4230 - 750
⇒ 116x = 3480
⇒ x = 3480/116
⇒ x = 30

∴ The value of x is 30

১,৯৩৬.

7⁶ⁿ - 6⁶ⁿ, where n is an integer > 0, is divisible by-

ক
13
খ
127
গ
559
ঘ
All of these

ব্যাখ্যা

Question: 7⁶ⁿ - 6⁶ⁿ, where n is an integer > 0, is divisible by-

Solution:
7⁶ⁿ - 6⁶ⁿ

Assume that n = 1
= 7⁶ - 6⁶
= (7³)² - (6³)²
= (7³ - 6³)(7³ + 6³)
= (343 - 216) × (343 + 216)
= 127 × 559
= 127 × 13 × 43

Clearly, it is divisible by 127, 13 as well as 559

১,৯৩৭.

5.4 is 45 percent of 20 percent of a certain number. What is the number?

ক
30
খ
60
গ
90
ঘ
120

ব্যাখ্যা

Question: 5.4 is 45 percent of 20 percent of a certain number. What is the number?

Solution:
ধরি, সংখ্যাটি = x

প্রশ্নমতে,
45% of (20% of x) = 5.4
⇒ (45/100) × {(20/100) × x} = 5.4
⇒ (9/20) × (1/5) × (x )= 5.4
⇒ 9x/100 = 5.4
⇒ 9x = 5.4 × 100
⇒ 9x = 540
⇒ x = 540/9
∴ x = 60

১,৯৩৮.

What sum of money will amount to Tk. 2,500 in 4 years and to Tk. 2,900 in 6 years at simple interest?

ক
Tk. 1,700
খ
Tk. 1,900
গ
Tk. 2,100
ঘ
Tk. 2,300

ব্যাখ্যা

Question: What sum of money will amount to Tk. 2,500 in 4 years and to Tk. 2,900 in 6 years at simple interest?

Solution:
Increase in 2 years = 2,900 - 2,500
= Tk. 400

∴ Simple interest for 2 years = Tk. 400
∴ Simple interest for 4 years = Tk. (400 × 4/2)
= Tk. 800

Principal, P = 2,500 - 800
= Tk. 1,700

১,৯৩৯.

A vessel contains milk and water in the ratio 7 : 4. If 15 liters of milk are added to it, the ratio of milk to water becomes 10 : 4. Find the final amount of milk in the new mixture.

ক
50 liters
খ
68 liters
গ
75 liters
ঘ
78 liters

ব্যাখ্যা

Question: A vessel contains milk and water in the ratio 7 : 4. If 15 liters of milk are added to it, the ratio of milk to water becomes 10 : 4. Find the final amount of milk in the new mixture.

Solution:
Let the initial amount of milk be 7x liters
and the amount of water 4x liters.

According to the question,
(7x + 15)/4x = 10/4
⇒ 4(7x + 15) = 10 × 4x
⇒ 28x + 60 = 40x
⇒ 60 = 12x
⇒ x = 60/12
⇒ x = 5

∴ Final amount of milk in mixture = 7x + 15
= 7 × 5 + 15
= 35 + 15
= 50 liters.

১,৯৪০.

In a geometric sequence, the third term is 16 and the sixth term is 128. What is the first term?

ক
4
খ
6
গ
8
ঘ
3

ব্যাখ্যা

Question: In a geometric sequence, the third term is 16 and the sixth term is 128. What is the first term?

Solution:
Let the first term of the geometric sequence be a
and the common ratio be r.
Third term = 16
∴ ar² = 16 ....... (1)
Again,
Sixth term = 128
∴ ar⁵ = 128 ....... (2)

Now, divide equation (2) by equation (1),
ar⁵/ar² = 128/16
⇒ r³ = 8
⇒ r³ = 2³
∴ r = 2
Substitute the value of r into equation (1).
a(2)² = 16
⇒ 4a = 16
∴ a = 4

Therefore, the first term of the geometric sequence is 4.

১,৯৪১.

If P/Q < 1, and P and Q are positive integers, which of the following must be greater than 1?

ক
ক) P/Q
খ
খ) Q/P²
গ
গ) P/2Q
ঘ
ঘ) P/Q²
ঙ
ঙ) Q/P

ব্যাখ্যা

Question: If P/Q < 1, and P and Q are positive integers, which of the following must be greater than 1?

Solution:
If P/Q < 1 then Q/p > 1
So, option 5 is the correct answer.

১,৯৪২.

In a simultaneous throw of two coins, the probability of getting at least one head is:

ক
ক) 1/2
খ
খ) 1/4
গ
গ) 3/4
ঘ
ঘ) 1/3

ব্যাখ্যা

Question: In a simultaneous throw of two coins, the probability of getting at least one head is:

Solution:
Here S= {HH,HT,TH,TT}
Let E= event of getting at least on head ={HH,HT,TH}

∴P(E)= n(E)/n(S) = 3/4

১,৯৪৩.

সকাল 7 টায় দুটি ট্রেন 300 কিলোমিটার দূরত্বের দুটি স্টেশন থেকে একে অপরের দিকে যাত্রা শুরু করে। সকাল 11 টায় তারা একে অপরকে অতিক্রম করে। যদি দ্রুতগামী ট্রেনের গড় গতি ধীরগতির ট্রেনের তুলনায় 7 কিমি বেশি হয়, তবে দ্রুততর ট্রেনের গতি কিমি/ঘন্টায় কত?

ক
ক) 45 কি.মি./ঘণ্টা
খ
খ) 44 কি.মি./ঘণ্টা
গ
গ) 43 কি.মি./ঘণ্টা
ঘ
ঘ) 41 কি.মি./ঘণ্টা

ব্যাখ্যা

প্রশ্ন: সকাল 7 টায় দুটি ট্রেন 300 কিলোমিটার দূরত্বের দুটি স্টেশন থেকে একে অপরের দিকে যাত্রা শুরু করে। সকাল 11 টায় তারা একে অপরকে অতিক্রম করে। যদি দ্রুতগামী ট্রেনের গড় গতি ধীরগতির ট্রেনের তুলনায় 7 কিমি বেশি হয়, তবে দ্রুততর ট্রেনের গতি কিমি/ঘন্টায় কত?

সমাধান:
ধরি
দ্রুতগতির ট্রেন এর গতিবেগ = x কি.মি./ঘণ্টা
ধীরগতির ট্রেন এর গতিবেগ =y কি.মি./ঘণ্টা

যাত্রার মোট সময় = 11 - 7 = 4 ঘণ্টা
এখানে
x + y = 300/4 = 75...............(1)
আবার
x - y = 7 .................(2)

(1) + (2) ⇒
x + y + x - y = 75 + 7
2x = 82
x = 41 কি.মি./ঘণ্টা

১,৯৪৪.

Jamal ranks 12th out of 46 students in a class. What is his position from the end?

ক
32
খ
33
গ
34
ঘ
35
ঙ
36

ব্যাখ্যা

শেষ থেকে জামালের অবস্থান (৪৬ - ১২ + ১) = ৩৫।

১,৯৪৫.

45 toymakers can prepare 30 toys per day. Rifat wants 360 toys. How many toymakers should he employ to get the job done in 12 days?

ক
38
খ
55
গ
35
ঘ
45

ব্যাখ্যা

Question: 45 toymakers can prepare 30 toys per day. Rifat wants 360 toys. How many toymakers should he employ to get the job done in 12 days?

Solution:
Let, the required number of toymakers x
45 toymakers make 30 toys per day
So, 1 toymaker makes = 30/45 = 2/3 toys per day
Each toymaker in 12 days makes = (2/3) × 12 = 8 toys
So, x toymakers will make = 8x toys

ATQ,
8x = 360
⇒ x = 360 × (1/8)
∴ x = 45

১,৯৪৬.

An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

ক
356 cm²
খ
576 cm²
গ
27342/23 cm²
ঘ
22275/28 cm²
ঙ
None of the above

ব্যাখ্যা

Question: An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Solution:

The area between two consecutive ribs is subtending = 360/8 = 45° at the center of the assumed flat circle.

Area between two consecutive ribs of circle

১,৯৪৭.

The banker’s discount on a certain sum due 2 years hence is 11/10 of the true discount. The rate percent is

ক
ক) 11%
খ
খ) 10%
গ
গ) 5%
ঘ
ঘ) 5.5%

ব্যাখ্যা

Let
True Discount be Tk.1
Then, Banker's Discount = Tk. 11/10 = Tk. 1.10
∴ Sum = Tk {(1.10 × 1)/(1.10 - 1)}
= Tk (110/10)
= Tk. 11
Simple interest on Tk. 11 for 2 years is Tk 1.10
∴ Rate = {(100 × 1.10)/(11 × 2)%
= 5%

১,৯৪৮.

The average of x, y, z is 6 and x - y = 4 xy = 21 what is the value of z?

ক
6
খ
7
গ
8
ঘ
9

ব্যাখ্যা

Question: The average of x, y, z is 6 and x - y = 4 xy = 21 what is the value of z?

Solution:
Given that,
The average of x, y, and z is 6.
⇒ (x + y + z)/3 = 6
⇒ x + y + z = 18 ...........(1)

x - y = 4
x = y + 4 ..........(2)

And
xy = 21 ......... (3)

From (3),
⇒ (y + 4)y = 21
⇒ y² + 4y - 21 = 0
⇒ y² + 7y - 3y - 21 = 0
⇒ y(y + 7) - 3(y + 7) = 0
⇒ (y + 7)(y - 3) = 0
⇒ y = 3, - 7 [Neglecting the negative value]
∴ y = 3

If y = 3, Then x = y + 4 = 3 + 4 = 7

From (2),
∴ x = y + 4 = 3 + 4 = 7

From (1),
⇒ x + y + z = 18
⇒ z = 18 - (7 + 3) = 18 - 10
∴ z = 8

১,৯৪৯.

Which one of the following fractions is closest to 1/4?

ক
ক) 1/5
খ
খ) 3/10
গ
গ) 3/20
ঘ
ঘ) 4/15

ব্যাখ্যা

question: Which one of the following fractions is closest to 1/4?

solution:
1/4 = 0.25

given options,
1/5 = 0.2
3/10 = 0.3
3/20 = 0.15
4/15 = 0.266

so, the closest fraction to 1/4 is 4/15

১,৯৫০.

If 7 - 2x ≤ 15, then what is the value of x?

ক
[-4, ∞)
খ
(-∞, -4]
গ
[4, ∞)
ঘ
(-∞, 4]

ব্যাখ্যা

Question: If 7 - 2x ≤ 15, then what is the value of x?

Solution:
Given inequality:
7 - 2x ≤ 15

Subtract 7 from both sides:
-2x ≤ 8

Divide both sides by -2 (and reverse the inequality sign):
x ≥ -4

So, the solution set is x ∈ [-4, ∞)

১,৯৫১.

In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 15° & ∠EOA = 85°, then find the value of ∠ECA.

ক
60°
খ
45°
গ
40°
ঘ
35°

ব্যাখ্যা

Question: In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 15° & ∠EOA = 85°, then find the value of ∠ECA.
(প্রদত্ত চিত্র অনুসারে, AB বৃত্তের ব্যাস এবং O কেন্দ্র। ∠BOD = ১৫° এবং ∠EOA = ৮৫° হলে, ∠ECA এর মান কত?)

Solution:
∠EOA = 85°, ∠BOD = 15°
∠EOD = 180° - (85° + 15°) = 80°

In ΔOED,
OE = OD (ব্যাসার্ধ)
∠OED = ∠ODE = 50°

In ΔOEC,
∠EOC = 80°+15° = 95°, ∠OEC =50°
∴ ∠ECA = 180°- (95 + 50°) = 35°

১,৯৫২.

A 280 metre long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?

ক
85.54 km/h
খ
80.64 km/h
গ
82.75 km/h
ঘ
79.25 km/h

ব্যাখ্যা

Question: A 280 metre long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?

Solution:
Given that,
Length of the train = 280 m
Length of the platform = 3 × 280 = 840 m

∴ Total distance to be covered
= Train length + Platform length
= 280 + 840
= 1120m
And, Time taken = 50 seconds

∴ Speed = Distance/Time
= 1120/50
= 22.4 m/s
= 22.4 × 3.6 ;[1 m/s = 3.6 km/h]
= 80.64 km/h

∴ The speed of the train is 80.64 km/h.

১,৯৫৩.

If 10% of x is equal to 25% of y, and y = 16, what is the value of x?

ক
ক) 4
খ
খ) 6.4
গ
গ) 24
ঘ
ঘ) 40

ব্যাখ্যা

ATQ, x×10% = y×25%
⇒ x = (25×16)/10
∴ x = 40

১,৯৫৪.

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

ক
120
খ
240
গ
360
ঘ
720
ঙ
None

ব্যাখ্যা

Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

Solution:
The word 'OPTICAL' contains 7 different letters.

When the vowels OIA are always together, they can be supposed to form one letter.

Then, we have to arrange the letters PTCL (OIA).

Now, 5 letters can be arranged in 5! = 120 ways.

The vowels (OIA) can be arranged among themselves in = 3! = 6 ways.

Required number of ways = (120 × 6) = 720.

১,৯৫৫.

A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq.ft per day, they approximately what time will be taken by the cow to graze the whole field ?

ক
4.86 days
খ
5.2 days
গ
6.16 days
ঘ
8 days

ব্যাখ্যা

Question: A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq.ft per day, they approximately what time will be taken by the cow to graze the whole field ?

Solution:
Area of the field = π 14² sq.ft
= 616 sq.ft

Time required =616/100
= 6.16 days

১,৯৫৬.

A, B, C, D and E are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers was deleted?

ক
A
খ
B
গ
C
ঘ
D

ব্যাখ্যা

Question: A, B, C, D and E are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers was deleted?

Solution:
Let, the numbers are A = x, B = x + 1, C = x + 2, D = x + 3, E = x + 4

sum = x + x + 1 + x + 2 + x + 3 + x + 4 = 5x + 10

Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%.

new sum = sum - 0.2 sum
= 0.8 sum
= 0.8 (5x + 10)
= 4x + 8

deleted number = 5x + 10 - 4x - 8 = x + 2 = C

১,৯৫৭.

Which of the following is the lowest ratio?

ক
ক) 15 : 23
খ
খ) 7 : 15
গ
গ) 17 : 25
ঘ
ঘ) 21 : 39

ব্যাখ্যা

Question: Which of the following is the lowest ratio?

Solution:
15 : 23 = 15/23 = 0.652
7 : 15 = 7/15 = 0.467
17 : 25 = 17/25 = 0.68
21 : 39 = 21/39 = 0.538

এখানে, 7 : 15 = 7/15 = 0.467 এর মান সবচেয়ে ক্ষুদ্রতম।

১,৯৫৮.

There are two squares S₁ and S₂. The ratio of their areas is 4 : 25. If the side of S₁ is 6 cm. What is the side of S₂?

ক
20 cm
খ
5 cm
গ
15 cm
ঘ
12 cm

ব্যাখ্যা

Question: There are two squares S₁ and S₂. The ratio of their areas is 4 : 25. If the side of S₁ is 6 cm. What is the side of S₂?

Solution:
Let,
The Area of S₁ = 4x²
The Area of S₂ = 25x²

∴ Side of S₁ = 2x
∴ Side of S₂ = 5x

ATQ,
2x = 6
∴ x = 3

∴ Side of S₂ = 5 × 3 = 15 cm

১,৯৫৯.

The floor of a company's office has an area of 20,000 square feet. If the floor is in the shape of a square, approximately how many feet long is each side?

ক
140
খ
450
গ
500
ঘ
1000
ঙ
None of these

ব্যাখ্যা

Question: The floor of a company's office has an area of 20,000 square feet. If the floor is in the shape of a square, approximately how many feet long is each side?

Solution:
The floor is in the shape of a square
Area of the floor 20000 square feet

∴ Length of each side = √20000 feet
= 141.42 feet

∴ We can say Length of each side is approximately 140 feet

১,৯৬০.

If x - 1/x = √3 then x + 1/x = ?

ক
ক) 3√3
খ
খ) √7
গ
গ) 2√3
ঘ
ঘ) 7

ব্যাখ্যা

Given,
x - 1/x = √3
⇒ (x - 1/x)² = (√3)²⇒ (x + 1/x)² - 4.x.(1/x) = 3
⇒ (x + 1/x)² = 3 + 4 = 7
∴ x + 1/x = √7

১,৯৬১.

The set of points defined by the equation x² + y² + z² = 4 is -

ক
ক) a point
খ
খ) a circle
গ
গ) a line
ঘ
ঘ) a sphere

ব্যাখ্যা

The general equation of a sphere is: (x - a)² + (y - b)² + (z - c)² = r², where (a, b, c) represents the center of the sphere
As, here x² + y² + z² = 4
or, (x - 0)² + (y - 0)² + (z - 0)² = 2²,
So, it's an equation of a sphere where (0, 0, 0) represents the center of the sphere and '2' is it's radius

১,৯৬২.

There are 5 red and 3 black balls in a bag. Probability of drawing a black ball is -

ক
ক) 5/8
খ
খ) 1/2
গ
গ) 3/8
ঘ
ঘ) 1/4

ব্যাখ্যা

মোট বলের সংখ্যা = (5 + 3) = 8 টি
কালো বলের সংখ্যা = 3 টি
একটি কালো বল উঠার সম্ভাব্যতা = 3/8 টি

১,৯৬৩.

A man is now 3 times as old as his son. In 10 years' time, the sum of their ages will be 84. How old was the man when his son was born?

ক
ক) 26 years
খ
খ) 28 years
গ
গ) 32 years
ঘ
ঘ) 36 years

ব্যাখ্যা

Question : A man is now 3 times as old as his son. In 10 years' time, the sum of their ages will be 84. How old was the man when his son was born?

Solution:
ধরি,
বর্তমানে পুত্রের বয়স = x বছর
পিতার বয়স 3x বছর

প্রশ্নমতে,
10 + x + 10 + 3x = 84
4x =84 - 20
4x =64
x=16
পুত্রের বয়স 16 বছর
পিতার বয়স = 3 × 16 = 48 বছর

জন্মের সময় পিতার বয়স ছিলো = 48 - 16= 32 বছর

১,৯৬৪.

If 283P is divisible by 9, what is the value of P?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 5

ব্যাখ্যা

Question: If 283P is divisible by 9, what is the value of P?

Solution:
একটি সংখ্যা ৯ দ্বারা বিভাজ্য হবে যদি সংখ্যাটির অঙ্কগুলোর সমষ্টি ৯ দ্বারা বিভাজ্য হয়।

২ + ৮ + ৩ = ১৩; এর সাথে ৫ যোগ করলে ১৮ হয়, যা ৯ দ্বারা বিভাজ্য।
∴ P = ৫

১,৯৬৫.

A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-

ক
ক) 20years
খ
খ) 25 years
গ
গ) 30 years
ঘ
ঘ) 45 years

ব্যাখ্যা

Question: A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-

Solution:
let the sum P

2P = P (1 + r)¹⁵
⇒ (1 + r)¹⁵ = 2

let, sum will 4 times in n years
4P = P(1 + r)ⁿ
⇒ 4 = (1 + r)ⁿ
⇒ 2² = (1 + r)ⁿ
⇒ ((1 + r)¹⁵)² = (1 + r)ⁿ
⇒ (1 + r)³⁰ = (1 + r)ⁿ
∴ n = 30 years

১,৯৬৬.

A, B, and C are boxes containing marbles in the ratio 2 : 3 : 4. Total number of marbles is 90. The above ratio can be changed to 4 : 5 : 6 by transferring-

ক
4 marbles from C to A
খ
3 marbles from A to C
গ
6 marbles from B to C
ঘ
3 marbles from C to B

ব্যাখ্যা

Question: A, B, and C are boxes containing marbles in the ratio 2 : 3 : 4. Total number of marbles is 90. The above ratio can be changed to 4 : 5 : 6 by transferring-

Solution:
A's share = 90 × (2/9) = 20
B's share = 90 × (3/9) = 30
C's share = 90 × (4/9) = 40

When marbles are shared in the ratio of 4 : 5 : 6

A's share = 90 × (4/15) = 24
B's share = 90 × (5/15) = 30
C's share = 90 × (6/15) = 36

Clearly,
From C (40 - 4) = 36 marbles have been transferred from to A (20 + 4) = 24

So, The above ratio can be changed to 4 : 5 : 6 by transferring 4 marbles from C to A.

১,৯৬৭.

If ∠XYZ in the figure above is a right angle, what is the value of x?

ক
155°
খ
145°
গ
125°
ঘ
110°

ব্যাখ্যা

Question:

If ∠XYZ in the figure above is a right angle, what is the value of x?

Solution:

∠XYZ = 90°

∠XYA = 90° - 55° = 35°

∠x + ∠XYA = 180°

⇒ ∠x = 180° - 35°
∴ ∠x = 145°

১,৯৬৮.

A bonus of TK. 1000 is to be divided among three people so that Rohit receives twice as much as Sachin, who receives one-fifth as much as Gagan. How much money should Gagan receive?

ক
ক) TK. 625
খ
খ) TK. 525
গ
গ) TK.725
ঘ
ঘ) TK. 325

ব্যাখ্যা

Let
Gagan receive TK. x.
then Sachin receive one fifth of Gagan =x/5
Rohit receive twice of Sachin =2x/5
x + (x/5) + (2x/5) = 1000
(5x + x + 2x)/5 = 1000
8x/5 = 1000
x = (1000 × 5)/8
x = 625

১,৯৬৯.

When I was married 10 years ago my wife became the 6th member of the family. Today my father died and a baby born to me. The average age of my family during my marriage is the same as today. What was the age of Father when he died?

ক
ক) 50 yrs
খ
খ) 60 yrs
গ
গ) 70 yrs
ঘ
ঘ) 65 yrs
ঙ
ঙ) 70 yrs

ব্যাখ্যা

Let the Father be x years when he died.
Average Age 10 years ago be A.
Total Age 10 years ago = 6 × A
Total Age after 10 years(Just before father's Death) = 6A + 6 × 10 = 6A + 60
Father Died and Baby was born => the Total number of people in the family is Same (6)
Baby born today so age of baby = 0
(6A + 60 - x)/6 = 6A/6
=> A + 10 -(x/6) = A
=> x/6 = 10
=> x = 60
Therefore we can conclude that the father was 60 years old when he died.

১,৯৭০.

If set A = {1, 2} and B = {3, 4}, then A × B (Cartesian product of set A and B) is

ক
ক) {1, 2, 3, 4}
খ
খ) {(1, 3), (2, 4)}
গ
গ) {(1, 3), (2, 4), (1, 4), (2, 3)}
ঘ
ঘ) {(3, 1), (4, 1)}

ব্যাখ্যা

প্রশ্ন: If set A = {1, 2} and B = {3, 4}, then A × B (Cartesian product of set A and B) is

সমাধান:
দেওয়া আছে,
A = {1, 2}
B = {3, 4}

∴ A × B = {1, 2} × {3, 4}
= {(1, 3), (2, 4), (1, 4), (2, 3)}

১,৯৭১.

A garrison of 500 men had food for 50 days. After 10 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?

ক
20 days
খ
22 days
গ
25 days
ঘ
28 days

ব্যাখ্যা

Question: A garrison of 500 men had food for 50 days. After 10 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?

Solution:
After 10 days, food having for = 50 - 10 = 40 days
After arriving 300 men, total men = 500 + 300 = 800 men

500 men can eat the food for 40 days
∴ 1 man can eat the food for (40 × 500) days
∴ 800 men can eat the food for (40 × 500)/800 days
= 25 days

১,৯৭২.

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than him. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

ক
23
খ
24
গ
25
ঘ
None

ব্যাখ্যা

Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than him. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?

Solution:
Let the average age of the whole team by x years

Now
∴ 11x - (26 + 29) = 9(x - 1)
⇒ 11x - 9x = 46
⇒ 2x = 46
⇒ x = 23

Average age of the team is 23 years

১,৯৭৩.

The ratio of milk to water in 84 liters of mixture is 5 : 2. The water (in liters) to be added to it to make the the ratio 2 : 1 is -

ক
ক) 3 liters
খ
খ) 6 liters
গ
গ) 8 liters
ঘ
ঘ) 10 liters

ব্যাখ্যা

Question: The ratio of milk to water in 84 liters of mixture is 5 : 2. The water (in liters) to be added to it to make the the ratio 2 : 1 is -

Solution:
Quantity of milk = {84 × (5/7)} litres = 60 liters
Quantity of water = 84 - 60 = 24 liters

Let the quantity of water to be added be x liters

Then,
{60/(24 + x)} = 2/1
⇒ 2x + 48 = 60
⇒ 2x = 60 - 48
⇒ 2x = 12
∴ x = 6

১,৯৭৪.

The area of the triangle whose vertices are given by the coordinates (1, 2), (- 4, -3) and (4, 1) is:

ক
10 sq. units
খ
14 sq. units
গ
8 sq. units
ঘ
12 sq. units

ব্যাখ্যা

Question: The area of the triangle whose vertices are given by the coordinates (1, 2), (- 4, -3) and (4, 1) is:

Solution:
Given that,
Vertices of triangle = (1, 2), (- 4, -3), (4, 1)

We know,
Area of triangle = (1/2) × |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)| [whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃)]
= (1/2) × |1(- 3 - 1) + (- 4) (1 - 2) + 4{2 - (- 3)}|
= (1/2) × |(- 4) + 4 + 20|
= 20/2
= 10 sq. units

So the area of the triangle is 10 sq. units.

১,৯৭৫.

The marked price of a DVD is Tk. 250. It is sold for Tk. 225. The rate of discount is = ?

ক
20%
খ
25%
গ
10%
ঘ
30%
ঙ
None

ব্যাখ্যা

Question: The marked price of a DVD is Tk. 250. It is sold for Tk. 225. The rate of discount is = ?

Solution:
Here,

Marked Price = Tk. 250

Selling Price = Tk. 225

Difference = 250 - 225 = Tk. 25

∴ Discount = (25/250) × 100
= 10%

১,৯৭৬.

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. What is the volume of the cone so formed?

ক
7π cm³
খ
8π cm³
গ
9π cm³
ঘ
10π cm³
ঙ
12π cm³

ব্যাখ্যা

Given that, radius, r = 3 cm and height, h = 4 cm
Therefore, volume, V = (1/3) × πr²h
= (1/3) × π × 3² × 4
= 12π cm³

১,৯৭৭.

Two lots of onions with equal quantity, one costing Tk.10 per kg and the other costing Tk.15 per kg. are mixed together and whole lot is sold at Tk.15 per kg. What is the profit or loss?

ক
ক) 10% loss
খ
খ) 10% profit
গ
গ) 20% loss
ঘ
ঘ) 20% profit

ব্যাখ্যা

ধরি
প্রতি বস্তায় রসুন আছে x কেজি

প্রথম বস্তার x কেজি রসুন প্রতি কেজি 10 টাকা দরে ক্রয় করে।
প্রথম বস্তা রসুনের ক্রয়মূল্য 10x টাকা

দ্বিতীয় বস্তার x কেজি রসুন 15 টাকা দরে ক্রয় করে।
দ্বিতীয় বস্তা রসুনের ক্রয়মূল্য 15x টাকা

মোট ক্রয়মূল্য= 10x + 15x = 25x টাকা
আবার
(x + x) বা 2x কেজি রসুন বিক্রয় করা হয় প্রতি কেজি 15 টাকা দরে
মোট বিক্রয়মূল্য = 15 × 2x = 30x টাকা

লাভ = 30x - 25x = 5x টাকা

শতকরা লাভ = {(5x/25x) × 100}% = 20%

১,৯৭৮.

An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 minutes. What is the ratio of lunch breaks to the total period in the office?

ক
1 : 3
খ
1 : 6
গ
1 : 9
ঘ
1 : 17

ব্যাখ্যা

Question: An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 minutes. What is the ratio of lunch breaks to the total period in the office?

Solution:
The ratio of lunch breaks to the total period in the office = 30/{(8 × 60) + 30}
= 30/510
= 1/17

১,৯৭৯.

The distance from the centre of a circle of radius 5 cm to a chord of lengh 8 cm is-

ক
ক) 5 cm
খ
খ) 4 cm
গ
গ) 3 cm
ঘ
ঘ) 2 cm

ব্যাখ্যা

Let AB = 8 cm. And, be the chord of the circle with radius AO = 5 cm

Draw OP⊥AB, join OA
according to the theorem
AP = 1/2 AB = 1/2 × 8 = 4 cm
In △APO, ∠A = 90°
∴ (AO)² = (AP)² + (OP)²
OP = (AO)² − (AP)²
= √(5² − 4²)
= √9
∴ OP = 3cm

১,৯৮০.

In how many ways can the letters of the word "AUTHOR" be arranged such that the vowels are only in the odd positions?

ক
36
খ
72
গ
18
ঘ
108

ব্যাখ্যা

Question: In how many ways can the letters of the word "AUTHOR" be arranged such that the vowels are only in the odd positions?

Solution:
এখানে
মোট বর্ণ আছে 6টি
স্বরবর্ণ অর্থাৎ Vowel আছে (A, O, U) 3টি
ব্যঞ্জনবর্ণ অর্থাৎ Consonant আছে (T, H, R) 3টি

স্বরবর্ণ 3টি বিজোড় স্থানে রেখে বিন্যাস সংখ্যা = 3! = 6
বাকি 3টি ব্যঞ্জনবর্ণ 3টি জোড় স্থানে রেখে বিন্যাস সংখ্যা = 3! = 6

∴ স্বরবর্ণগুলোকে কেবল বিজোড় স্থানে রেখে মোট বিন্যাস সংখ্যা = 6 × 6
= 36

অতএব, AUTHOR শব্দটিকে স্বরবর্ণগুলোকে কেবল বিজোড় স্থানে রেখে মোট 36 উপায়ে সাজানো যাবে।

১,৯৮১.

The area of a square and rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 6 cm and the breadth is less than 4 cm. Find the perimeter of the rectangle.

ক
66 cm
খ
52 cm
গ
48 cm
ঘ
42 cm
ঙ
None

ব্যাখ্যা

Question: The area of a square and rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 6 cm and the breadth is less than 4 cm. Find the perimeter of the rectangle.

Solution:
Let,
the length of each side of the square be x cm.
Then, the length of rectangle = (x + 6) cm
and its breadth = (x - 4) cm

ATQ,
(x + 6)(x - 4) = x²
⇒ x² + 6x - 4x - 24 = x²
⇒ 2x = 24
∴ x = 12

Length = 12 + 6 = 18 cm
Breadth = 12 - 4 = 8 cm

∴ Perimeter = 2(length + breadth) = 2 (18 + 8) = 2 × 26 = 52 cm

১,৯৮২.

Rahim can hammer 20 nails in 6 minutes. Charlie can do the same job in only 5 minutes. How long will it take them to hammer 22 nails if Rahim hammers the first 5 nails, then Charlie hammers for 3 minutes and finally Rahim finished the job?

ক
ক) 4.6 minutes
খ
খ) 5.0 minutes
গ
গ) 5.4 minutes
ঘ
ঘ) 6.0 minutes

ব্যাখ্যা

Question: Rahim can hammer 20 nails in 6 minutes. Charlie can do the same job in only 5 minutes. How long will it take them to hammer 22 nails if Rahim hammers the first 5 nails, then Charlie hammers for 3 minutes and finally Rahim finished the job?

Solution:
In 5 Charlie minutes can hammer 20 nails
In 3 Charlie minutes can hammer (20 × 3)/5 = 12 nails
Rest nails = 22 - 12 = 10 nails

Rahim can hammer 20 nails in 6 minutes
Rahim can hammer 5 nails in (6 × 5) / 20 = 1.5 minutes

Rest nails = 10 - 5 = 5 nails

So, the rest 5 nails can hammer Rahim in 1.5 minutes

So, total time taken = 3 + 1.5 + 1.5 = 6 minutes

১,৯৮৩.

If (1/2)log (11 + 4√7) = log (2 + x), what is the value of x?

ক
√7
খ
11
গ
4
ঘ
2

ব্যাখ্যা

Question: If (1/2)log (11 + 4√7) = log (2 + x), what is the value of x?

Solution:
We have (1/2)log (11 + 4√7) = log (2 + x)
Now, we can write it as (1/2)log (7 + 4 + 4√7) = log (2 + x)
⇒ (1/2)log {2² + (√7)² + 2.2.√7} = log (2 + x)
⇒ (1/2)log(2 + √7)² = log(2 + x)
⇒ 2.(1/2)log (2 +√7) = log (2 + x)
⇒ log (2 +√7) = log (2 + x)
Both side Log will be canceled out
Now, 2 + √7 = 2 + x
Therefore, x = 2 + √7 - 2 = √7

১,৯৮৪.

A beats B by 100 m and C by 150 m in a kilometer race. In the same race, by how many meters does B beat C in that race?

ক
50.00 m
খ
55.55 m
গ
62.50 m
ঘ
45.50 m

ব্যাখ্যা

Question: A beats B by 100 m and C by 150 m in a kilometer race. In the same race, by how many meters does B beat C in that race?

Solution:
Here,
A : B = 1000 : 900
A : C = 1000 : 850

B/C = B/A / C/A
= (B/A) × (A/C)
= (900/1000) × (1000/850)
= 900/850

in 900m B beats C by 50m
∴ in 1000m B beats C by = (50 × 1000)/900 = 50000/900 = 55.55m

১,৯৮৫.

A man sells Tk. 5000, 12 % stock at 156 and invests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby increases his income by Tk. 70. How much of the proceeds were invested in each stock?

ক
ক) Tk. 4000
খ
খ) Tk. 4200
গ
গ) Tk. 4002
ঘ
ঘ) Tk. 4020

ব্যাখ্যা

S.P of Tk. 5000 stock = {(156/100) × 5000}
= Tk. 7800

Income from this stock = tk. {(12/100) × 5000}
= Tk. 600

Let investment in 8 % stock be x and that in 9 % stock = (7800 - x).

Therefore,
x × (8/90) + (7800 - x) × 9/108 = 600 + 70
⇒ 4x/45 + {(7800 - x)/12} = 670
⇒ 16x + 117000 - 15x = 670 × 180
⇒ x = 3600

Money invested in 8% stock at 90 = Tk. 3600
Money invested in 9% at 108 = Tk. (7800 - 3600)
= Tk. 4200.

১,৯৮৬.

A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Tk. 6500 for 6 months, B, Tk. 8400 for 5 months and C, Tk. 10000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Tk. 7400. Calculate the share of B in the profit.

ক
Tk. 2470
খ
Tk. 1900
গ
Tk. 2800
ঘ
Tk. 2660

ব্যাখ্যা

Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Tk. 6500 for 6 months, B, Tk. 8400 for 5 months and C, Tk. 10000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Tk. 7400. Calculate the share of B in the profit.

Solution:
Ratio of their investments = (6500 × 6) : (8400 × 5) : (10000 × 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10

Sum of the ratio = (13 + 14 + 10) = 37

Here,
The profit earned was Tk. 7400

For working, A received = 5% of Tk. 7400
= Tk. (5 × 7400)/100
= Tk. 370

Remaining profit = Tk. (7400 - 370)
= Tk. 7030

∴ B's share = Tk. {7030 × (14/37)}
= Tk. 2660

১,৯৮৭.

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 42, the how old is A?

ক
ক) 16 years
খ
খ) 17 years
গ
গ) 18 years
ঘ
ঘ) 21 years

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 42, the how old is A?

Solution:
Let,
C is = x years old
B is 2x years old
A is (2x + 2) years old

Now,
2x + 2x + 2 + x = 42
⇒ 5x + 2 = 42
⇒ 5x = 40
∴ x = 8
A is (2 × 8) + 2 years old
= 16 + 2 years old
= 18 years old

১,৯৮৮.

Find the greatest number which divides 34, 90, and 104 and leaves the same remainder in each case.

ক
14
খ
15
গ
17
ঘ
18

ব্যাখ্যা

Question: Find the greatest number which divides 34, 90, and 104 and leaves the same remainder in each case.

Solution:
Difference between numbers = 90 - 34 = 56, and 104 - 90=14

HCF of 56 and 14 = 14

Hence, 14 is the largest number which divides the given number and leaves the same remainder in each case.

১,৯৮৯.

Kalam has three daughters; Shaila, Meena and Tina. Three years ago, when Kalam was twice as old as Tina, he was 30 years older than Meena. Now he is 47 years older than Shaila. In 4 years, Shaila will be half as old as Tina. What is the sum of the current ages of Kalam and his three daughters?

ক
ক) 138
খ
খ) 144
গ
গ) 154
ঘ
ঘ) 180
ঙ
ঙ) None

ব্যাখ্যা

Suppose, three years ago Tina's Age was = x years
So, then Kalam's age was = 2x years, Meena's age was = 2x-30.
Now Kalam's age = 2x+3, Shaila's age = 2x+3 - 47 = 2x-44.
According to the question,
x+7 = 2(2x-44+4)
⇒ x+7 = 4x-80
⇒ 3x = 87
⇒ x = 29
current age of Kalam = 2x+3 = 2×29 + 3 = 61, Tina = 29+3 = 32,
Meena = 61-30 = 31, Shaila = 2×29 - 44 = 14.
Sum of their ages = 61+32+31+14 = 138.

১,৯৯০.

Nibir, while going to school, passes 200m in 2 minutes, waits for his friend for 5 minutes, and then crosses the next 600m in 4kmph. What is his average speed?

ক
3 kmph
খ
3.5 kmph
গ
4 kmph
ঘ
2.56 kmph

ব্যাখ্যা

Question: Nibir, while going to school, passes 200m in 2 minutes, waits for his friend for 5 minutes, and then crosses the next 600m in 4kmph. What is his average speed?

Solution:
600m or, 0.6km was crossed with 4kmph
time = 0.6/4 h = (0.6/4)60 minutes = 9 minutes

total time = (9 + 2 + 5) minutes = 16 minutes

average speed = total distance/total time
= 800m/16 minutes
= 0.8/(16/60) kmph
= 3 kmph

১,৯৯১.

If a * b = 2a - 3b + ab, then (3 * 5) + (5 * 3) is equal to?

ক
22
খ
24
গ
26
ঘ
28

ব্যাখ্যা

Question: If a * b = 2a - 3b + ab, then (3 * 5) + (5 * 3) is equal to?

Solution:
a * b = 2a - 3b + ab
3 ∗ 5 = 2 × 3 - 3 × 5 + 3 × 5
= 6 - 15 + 15
= 6

5 ∗ 3 = 2 × 5 - 3 × 3 + 3 × 5
= 10 - 9 + 15
=16

∴ (3 * 5) + (5 * 3)
= 6 + 16
= 22

১,৯৯২.

A mother is 20 years older than her daughter. In 10 years, her age will be twice the age of her daughter. What is the present age of the daughter?

ক
5 years
খ
10 years
গ
8 years
ঘ
6 years

ব্যাখ্যা

Question: A mother is 20 years older than her daughter. In 10 years, her age will be twice the age of her daughter. What is the present age of the daughter?

Solution:
Let the daughter’s present age be x years.
Then, the mother’s present age is = x + 20 years.

ATQ
In 10 years, the mother’s age will be twice the daughter’s age.
So, (x + 20) + 10 = 2 (x + 10)
⇒ 2x + 20 = x + 30
⇒ 2x - x = 30 - 20
∴ x = 10

Therefore, the present age of the daughter is 10 years.

১,৯৯৩.

একটি সামন্তরিকের দুইটি সন্নিহিত বাহুর দৈর্ঘ্য যথাক্রমে 7 সেন্টিমিটার এবং 5 সেন্টিমিটার হলে, এর পরিসীমার অর্ধেক কত?

ক
12
খ
20
গ
24
ঘ
28

ব্যাখ্যা

প্রশ্ন: একটি সামন্তরিকের দুইটি সন্নিহিত বাহুর দৈর্ঘ্য যথাক্রমে 7 সেন্টিমিটার এবং 5 সেন্টিমিটার হলে, এর পরিসীমার অর্ধেক কত?

সমাধান:
আমরা জানি,
সামান্তরিকের পরিসীমা = 2 × সন্নিহিত বাহুদ্বয়ের সমষ্টি
= 2 × (7 + 5)
= 24 সে.মি.

∴ পরিসীমার অর্ধেক = 24/2 সে.মি.
= 12 সে.মি.

১,৯৯৪.

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

Solution:
Let,
The total distance = 40 + 40 = 80km
The desired speed be x km/hr

ATQ,
40/20 + 40/x = 80/30
⇒ 2 + 40/x = 80/30
⇒ 40/x = (80/30) - 2
⇒ 40/x = 20/30
⇒ 20x = 1200
∴ x = 60

So, the desired speed is 60 km/hr

১,৯৯৫.

Robin can paint 60 walls in 20 minutes. Tara can paint 8 walls in 16 minutes. Working together, how many walls can they paint in 40 minutes?

ক
100 walls
খ
120 walls
গ
40 walls
ঘ
140 walls
ঙ
None

ব্যাখ্যা

Question: Robin can paint 60 walls in 20 minutes. Tara can paint 8 walls in 16 minutes. Working together, how many walls can they paint in 40 minutes?

Solution:
Robin can paint in 1 minute = 60/20 = 3 walls
Tara can paint in 1 minute = 8/16 = 0.5 wall

∴ Working together, they can paint in 1 minute = 3 + 0.5 = 3.5 walls

∴ They can paint in 40 minutes = 3.5 × 40 = 140 walls

∴ Working together, Robin and Tara can paint 140 walls in 40 minutes.

১,৯৯৬.

If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11?

ক
ক) 4x + 6y
খ
খ) x + y + 4
গ
গ) 9x + 4y
ঘ
ঘ) 4x - 9y
ঙ
ঙ) None of the above

ব্যাখ্যা

By hit and trial,
we put x = 5 and y = 1
so that,
(3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.

১,৯৯৭.

A garrison of 400 men had food for 27 days. After 3 days a reinforcement of 200 men arrived. For how many more days will the remaining food last now?

ক
ক) 15 days
খ
খ) 16 days
গ
গ) 20 days
ঘ
ঘ) 22 days

ব্যাখ্যা

Question: A garrison of 400 men had food for 27 days. After 3 days a reinforcement of 200 men arrived. For how many more days will the remaining food last now?

Solution:
After 3 days, food having for = 27 - 3 = 24 days
After arriving 200 men, total men = 400 + 200 = 600 men

400 men can eat the food for 24 days
1 man can eat the food for 24 × 400 days
600 men can eat the food for (24 × 400)/600 days
= 16 days

১,৯৯৮.

Which of the following is the lowest ratio?

ক
ক) 2 : 3
খ
খ) 1 : 3
গ
গ) 1 : 5
ঘ
ঘ) 2 : 5

ব্যাখ্যা

Solution:
2/3 = 0.66
1/3 = 0.33
1/5 = 0.2
2/5 = 0.4

hance the lowest ratio is 1 : 5

১,৯৯৯.

What is the missing number in the sequence:
32, 48, 72, ..., 162, 243.

ক
114
খ
132
গ
96
ঘ
108
ঙ
None

ব্যাখ্যা

Question: What is the missing number in the sequence:
32, 48, 72, ..., 162, 243.

Solution:
Each number is being multiplied by 3/2 to get the next number.
32 × (3/2) = 48
48 × (3/2) = 72
72 × (3/2) = 108
108 × (3/2) = 162
162 × (3/2) = 243

২,০০০.

If x = 1 + √2 and y = 1 - √2, find the value of x² + y².

ক
4
খ
5
গ
6
ঘ
8

ব্যাখ্যা

Question: If x = 1 + √2 and y = 1 - √2, find the value of x² + y².

Solution:
Given that,
x = 1 + √2,
y = 1 - √2

∴ x + y = 1 + √2 + 1 - √2
= 2

And,
xy = (1 + √2)(1 - √2)
= 1² - (√2)²
= 1 - 2
= - 1

Now,
x² + y² = (x + y)² - 2xy
= (2)² - 2(- 1)
= 4 + 2
= 6