Bank Math

PrepBank · পাতা ১২১ / ১৬১ · ১২,০০১–১২,১০০ / ১৬,১২৪

১২,০০১.

With an uniform speed, a car covers a distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered?

ক
ক) 320 km
খ
খ) 410 km
গ
গ) 480 km
ঘ
ঘ) 490 km

ব্যাখ্যা

Let the speed of car be x km/hr
Distance= Speed × Time
Distance = 8x km
According to the question,
⇒ (x+4)×7.5= 8x
⇒ 7.5x+30= 8x
⇒ 8x−7.5x= 30
⇒ 0.5x= 30
⇒x= (30/0.5)= 60 km/hr
Required distance: = 8 × 60 = 480 km

১২,০০২.

What is the smallest number of apples that can be distributed equally (without cutting any apple) among 6, 10, 14 and 18 boys?

ক
1260
খ
360
গ
315
ঘ
630

ব্যাখ্যা

Question: What is the smallest number of apples that can be distributed equally (without cutting any apple) among 6, 10, 14 and 18 boys?

Solution:
6, 10, 14, 18 এর লসাগু = 630
অতএব, সর্বনিম্ন ৬৩০টি আপেল ৬, ১০, ১৪ এবং ১৮ জন বালককে সমানভাবে ভাগ করে দেয়া যাবে।

১২,০০৩.

A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?

ক
15 min
খ
20 min
গ
25 min
ঘ
30 min

ব্যাখ্যা

Question: A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?

Solution:
Downstream speed = {(20/24) × 60} km/hr
= 50 km/hr

Let,
speed of water and stream is 4a and a.
Downstream speed = (4a + a) = 5a
and upstream speed = (4a - a) = 3a

ATQ,
5a = 50
∴ a = 10
So, upstream speed = (3 × 10) = 30 km/hr.
∴ Time taken to go 15 km upstream = (15 × 60)/30 = 30 min.

১২,০০৪.

If A travels to his school from his house at the speed of 5 km/hr, then he reaches the school 5 minutes late. If he travels at the speed of 6 km/hr, he reaches the school 5 minutes earlier than school time. The distance of his school from his house is:

ক
ক) 2 km
খ
খ) 3 km
গ
গ) 5 km
ঘ
ঘ) 6 km

ব্যাখ্যা

Question: If A travels to his school from his house at the speed of 5 km/hr, then he reaches the school 5 minutes late. If he travels at the speed of 6 km/hr, he reaches the school 5 minutes earlier than school time. The distance of his school from his house is:

Solution:
Let the distance between school and home be x km.
The difference of time when A goes school to school with these two different speed is 10 min
= 10/60 hour.
Now,
x/5 - x/6 = 10/60
Or, (6x - 5x)/30 = 1/6
Or, x/30 = 1/6
Or, x = 30/6
∴ x = 5 km

∴ The distance between school and home 5 km.

১২,০০৫.

Two numbers P and Q are such that the sum of 10% of P and 15% of Q is three-fourths of the sum of 20% of P and 18% of Q. Find the ratio of P : Q.

ক
10 : 3
খ
3 : 7
গ
5 : 12
ঘ
3 : 10

ব্যাখ্যা

Question: Two numbers P and Q are such that the sum of 10% of P and 15% of Q is three-fourths of the sum of 20% of P and 18% of Q. Find the ratio of P : Q.

Solution:
10% of P + 15% of Q = 3/4 × (20% of P + 18% of Q)
⇒ 10P/100 + 15Q/100 = 3/4 × (20P/100 + 18Q/100)
⇒ P/10 + 3Q/20 = 3/4 × (P/5 + 9Q/50)
⇒ 2P/20 + 3Q/20 = 3/4 × (10P + 9Q)/50
⇒ (2P + 3Q)/20 = (30P + 27Q)/200
⇒ 10(2P + 3Q) = 30P + 27Q
⇒ 20P + 30Q = 30P + 27Q
⇒ 30Q - 27Q = 30P - 20P
⇒ 3Q = 10P
⇒ P/Q = 3/10
∴ P : Q = 3 : 10

১২,০০৬.

A profit of 25% could have been made if an item was sold for Tk.750. It was sold for a loss of 5% instead. What is the actual selling price?

ক
ক) Tk. 720
খ
খ) Tk. 570
গ
গ) Tk. 450
ঘ
ঘ) Tk. 620

ব্যাখ্যা

Question: A profit of 25% could have been made if an item was sold for Tk.750. It was sold for a loss of 5% instead. What is the actual selling price?

Solution:

Let be assume cost price of the item is 100x
⇒ 125x = 750
⇒ x = 6

⇒ Now, the actual selling price of the item was 5% less the cost price of the items
⇒ The actual selling price of item = 100x - 5x = 95x
⇒ 95 × 6 = 570

∴ The required result will be 570.

১২,০০৭.

If 2 : 5 :: 6 : x, then x is equal to:

ক
25
খ
15
গ
20
ঘ
30
ঙ
None of the above

ব্যাখ্যা

Question: If 2 : 5 :: 6 : x, then x is equal to:

Solution:
2 : 5 :: 6 : x
⇒ 2/5 = 6/x
⇒ 30 = 2x
∴ x = 15

১২,০০৮.

A man can swim a distance of 360 m in still water in 4 minutes. If the speed of the current is 1 m / sec, how much time will he take to cover the distance of 180 m upstream?

ক
ক) 5 minutes
খ
খ) 6 minutes
গ
গ) 7 minutes
ঘ
ঘ) 8 minutes

ব্যাখ্যা

Distance covered by a man by swimming in still water = 360 m
Time taken by man = 4 minutes = 240 seconds
Speed of man = 360/240 = (3/2) m/sec
Speed of stream is = 1 m/sec.

Time taken in upstream
= 180/[(3/2) - 1)]
= 180/(1/2)
= 360 seconds
⇒ Time = 6 minutes

∴ He will cover 150 m upstream in 6 minutes

১২,০০৯.

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
ক) 11%
খ
খ) 19%
গ
গ) 17%
ঘ
ঘ) 21%

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

১২,০১০.

If 15% of a number is 4.5, then 55% of the same number is -

ক
ক) 15
খ
খ) 9.5
গ
গ) 17.5
ঘ
ঘ) 16.5

ব্যাখ্যা

Question: If 15% of a number is 4.5, then 55% of the same number is -

Solution:
মনে করি,
সংখ্যাটি x

প্রশ্নমতে,
x এর 15% = 4.5
বা, 15x/100 = 4.5
বা, 15x = 4.5 × 100
বা, x = 450/15
∴ x = 30

সংখ্যাটির 55% = 30 এর 55%
= (30 × 55)/100
= 16.5

∴ নির্ণেয় সংখ্যাটি 16.5

১২,০১১.

Mr.X gives 1/2 of his property to his wife and 1/2 of the rest to his son. The remainder is divided equally between his two daughters. The share of each daughter is-

ক
ক) 1/12
খ
খ) 1/2
গ
গ) 1/4
ঘ
ঘ) 1/8

ব্যাখ্যা

Let
The whole property be 1
Share of wife =1/2
Remaining share= 1/2
Share of son = 1/2 of 1/2
= 1/4
Remaining share= (1/2) - (1/4)
= (2 - 1)/4
= 1/4
Share for each daughter =1/2 of 1/4
=1/8

১২,০১২.

If Mario was 32 years old 8 years ago, how old was he x years ago?

ক
ক) X-40
খ
খ) X-24
গ
গ) 40-x
ঘ
ঘ) 24-x

ব্যাখ্যা

Mario was 32 years old 8 years ago
Therefore, Mario's present age = 32 + 8 = 40 years
x years ago, his age = (40 - x) years

১২,০১৩.

If the average of 'a' numbers is b² and the average of 'b' numbers is a², what is the average of the combined (a + b) numbers?

ক
a - 1
খ
a + 1
গ
ab
ঘ
1

ব্যাখ্যা

Question: If the average of 'a' numbers is b² and the average of 'b' numbers is a², what is the average of the combined (a + b) numbers?

Solution:
দেওয়া আছে:
'a' সংখ্যার গড় = b²
∴ a সংখ্যার সমষ্টি = a × b²

'b' সংখ্যার গড় = a²
∴ 'b' সংখ্যার সমষ্টি = b × a²

∴ মোট সমষ্টি = (a × b²) + (b × a²)
= ab(a + b)

∴ তাদের গড় = মোট সমষ্টি/(a + b)
= ab(a + b)/(a + b)
= ab

১২,০১৪.

Jihan types 450 words in half an hour. How many words would he type in 7 minutes?

ক
ক) 95 words
খ
খ) 105 words
গ
গ) 115 words
ঘ
ঘ) 125 words

ব্যাখ্যা

Question: Jihan types 450 words in half an hour. How many words would he type in 7 minutes?

Solution:
Words per minute= (Number of words) / (Time in minutes)
Words per minute = 450 words / 30 minutes
= 15 words/minute

number of words in 7 minutes:
Number of words = Words per minute × Time in minutes
= 15 words/minute × 7 minutes
= 105 words

Jihan would type 105 words in 7 minutes.

১২,০১৫.

A boy runs opposite to that of a train at a speed of 20 km/hr. If the relative speed between the train and the boy running in the opposite direction is 50 km/hr. What is the length of the train, if it takes 20 seconds to cross the boy, when he is at rest?

ক
159.1 m
খ
160.23 m
গ
166.6 m
ঘ
154.12 m

ব্যাখ্যা

Speed = Distance/Time

Relative speed = Speed of train + Speed of boy
50 = Speed of train + 20

Speed of train = 50 – 20 = 30 km/hr

Convert km/hr into m/s
30 km/hr = 30 × (5/18) = 8.33 m/s

Distance = Speed x Time
= 8.33 x 20 = 166.6 m.

১২,০১৬.

If (x + y) > 5 and (x – y) > 3, then which of the following gives all and only possible value of x?

ক
ক) x < 3
খ
খ) x > 3
গ
গ) x > 4
ঘ
ঘ) x < 5

ব্যাখ্যা

(x + y > 5
(x – y > 3
^___________
2x > 8
∴ x > 4

১২,০১৭.

In a mixture of milk and water, the proportion of water by weight was 75%. If in the 60 gm mixture, 15 gm of water was added, what would be the percentage of water?

ক
70%
খ
75%
গ
80%
ঘ
90%

ব্যাখ্যা

Question: In a mixture of milk and water, the proportion of water by weight was 75%. If in the 60 gm mixture, 15 gm of water was added, what would be the percentage of water?

Solution:
Weight of water in 60 gm mixture = 75% of 60 gm
= {(75/100) × 60} gm
= 45 gm.

Weight of water in 75 gms mixture = (45 + 15) gm
= 60 gm.

∴ Required percentage = {(60/75) × 100}%
= 80%.

১২,০১৮.

Rajib purchased a car for Tk. 2,60,000 and sold it for Tk. 3,50,000. What is the percent profit she made on the car?

ক
24.73%
খ
34.62%
গ
44.25%
ঘ
28.53%

ব্যাখ্যা

Question: Rajib purchased a car for Tk. 2,60,000 and sold it for Tk. 3,50,000. What is the percent profit she made on the car?

Solution:
Profit = Selling Price - Cost Price = 3,50,000 - 2,60,000 = 90,000 Tk.

We know that,
Percent Profit = (Profit/Cost Price) × 100
= (90000/260000) × 100
= (9 × 100)/26
= 34.615
= 34.62%

∴ Rajib made a 34.62% profit on the car.

১২,০১৯.

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red is :

ক
1/2
খ
2/5
গ
3/10
ঘ
7/10

ব্যাখ্যা

Question: A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red is :

Solution:
There are 2 possible cases: the first ball drawn is red or black.
P(first ball black) = 6/10
P(first ball red) = 4/10

P(second ball red | first ball drawn is black) = 4/12
P(second ball red | first ball drawn is red) = 6/12 = 1/2

The probability of the second ball being red, P(R) = (4/10)×(1/2) + (6/10) ×(4/12)
= (1/5) + (1/5)
= 2/5

১২,০২০.

A sum becomes Tk. 10760 in 5 years. and Tk. 11186 in 6 years. at simple interest. What is the sum?

ক
ক) Tk. 8,530
খ
খ) Tk. 8,030
গ
গ) Tk. 8,630
ঘ
ঘ) Tk. 8,730

ব্যাখ্যা

A sum becomes Tk. 10760 in 5 years. and Tk. 11186 in 6 years.
at simple interest of 1 year = 11186 - 10760
= Tk. 426
Interest of 5 year = 426 × 5 = 2130

∴ Required principal = 10760 - 2130 = Tk. 8,630

১২,০২১.

3 litre of water is added to 11 litres of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is -

ক
20%
খ
33%
গ
30%
ঘ
25%

ব্যাখ্যা

We have an 11-liter solution containing 42% of alcohol in the water.
=> quantity of alcohol in the solution = (11 × 42)/100
Now 3 liter of water is added to the solution.
=> Total quantity of the new solution = 11 + 3 = 14
Percentage of alcohol in the new solution = {(11 × 42)/100}/14 × 100
= (11 × 3)/100
= 33%

১২,০২২.

If p × q = p + q + (p/q), then the value of 5 × 3 is?

ক
15
খ
29/3
গ
24/3
ঘ
5/3

ব্যাখ্যা

p × q = p + q + (p/q)
5 × 3 = 5 + 3 + (5 / 3)
= 8 + 5/3
= 29/3

১২,০২৩.

If a person invests Tk. 900 at 12% simple interest and Tk. 700 at 8% simple interest, how much interest will he receive after four years?

ক
428 Tk
খ
480 Tk
গ
520 Tk
ঘ
656 Tk

ব্যাখ্যা

Question: If a person invests Tk. 900 at 12% simple interest and Tk. 700 at 8% simple interest, how much interest will he receive after four years?

Solution:
এখানে,
I₁ = p₁n₁r₁
= (900 × 4 × 12)/100
= 432 টাকা

আবার,
I₂ = p₂n₂r₂
= (700 × 4 × 8)/100
= 224 টাকা

∴ মোট সুদ = (432 + 224) টাকা
= 656 টাকা

১২,০২৪.

Two bikes start at the same time from two destination 300 km apart and travel towards each other. If they cross each other at a distance of 130 km from one of the destinations, what is the ratio of their speeds?

ক
17 : 13
খ
7 : 3
গ
1 : 3
ঘ
2 : 3

ব্যাখ্যা

Solution: Two bikes start at the same time from two destination 300 km apart and travel towards each other. If they cross each other at a distance of 130 km from one of the destinations, what is the ratio of their speeds?

Solution:
ধরি,
প্রথম বাইকারের গতি = V₁
দ্বিতীয় বাইকারের গতি = V₂

প্রথম বাইকার অতিক্রম করে = 130 km
দ্বিতীয় বাইকার অতিক্রম করে = 300 - 130 = 170 km

এখন
130/V₁ =170/V₂
130V₂ = 170V₁
V₂/V₁ = 170/130
V₂ : V₁ = 17 ; 13

১২,০২৫.

Diagonal of a square is 16 inches long. What is the area of the square?

ক
256 square inch
খ
128 square inch
গ
64 square inch
ঘ
132 square inch

ব্যাখ্যা

If the length of the square is 'a', then diagonal = a√2
Therefore, a√2 = 16
⇒ a = 16/√2
⇒ a² = (16/√2)² = 128

১২,০২৬.

The line y = 2x - 1 cuts the x-axis at P. The coordinates of P are

ক
(0, - 1)
খ
(1/2, 0)
গ
(- 1/2, 0)
ঘ
(- 1, 0)

ব্যাখ্যা

Question: The line y = 2x - 1 cuts the x-axis at P. The coordinates of P are

Solution:
প্রদত্ত সমীকরণ,
y = 2x - 1 ............(১)

এখন, x অক্ষকে ছেদ করলে y = 0 হয়।
(১) নং সমীকরণ হতে পাই,
⇒ y = 2x - 1
⇒ 2x - 1 = 0
⇒ 2x = 1
∴ x = 1/2

∴ P বিন্দুটি x-অক্ষকে যেবিন্দুতে ছেদ করেছে ঐ ছেদবিন্দুর স্থানাঙ্ক হলো = (1/2, 0)

১২,০২৭.

Wendy has 5 pairs and 8 shirts. How many different combinations can she make with these items?

ক
ক) 13
খ
খ) 24
গ
গ) 40
ঘ
ঘ) 21

ব্যাখ্যা

Wendy can make = 5 × 8 = 40 different combinations.

১২,০২৮.

If log₃{log₂(x² - 4x - 24)} = 1, where ‘x’ is a natural number, find the value of x.

ক
10
খ
4
গ
6
ঘ
8

ব্যাখ্যা

Question: If log₃{log₂(x² - 4x - 24)} = 1, where ‘x’ is a natural number, find the value of x.

Solution:
Given,
log₃{log₂(x² - 4x - 24)} = 1
⇒ log₂(x² - 4x - 24) = 3
⇒ x² - 4x - 24 = 8
⇒ x² - 4x - 32 = 0
⇒ (x - 8) (x + 4) = 0
⇒ x = 8, - 4
Since x is a natural number, so x = 8.

১২,০২৯.

The difference between the length and breadth of a rectangle is 23m . If its perimeter is 206m, then its area is:

ক
2520 m²
খ
2720 m²
গ
2250 m²
ঘ
2270 m²

ব্যাখ্যা

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103
Solving the two equations, we get: l = 63 and b = 40
∴ Area = (l x b) = (63 x 40) m² = 2520 m²

১২,০৩০.

The cost price of 60 articles is the same as the selling price of 'q' articles. If the profit is 20%, then the value of 'q' is -

ক
40
খ
45
গ
50
ঘ
56

ব্যাখ্যা

Question: The cost price of 60 articles is the same as the selling price of 'q' articles. If the profit is 20%, then the value of 'q' is -

Solution:
Let,
The cost price of each article be = Tk. 1
The cost price of 'q' articles = Tk. q
The selling price of 'q' articles = Tk. 60

∴ Profit = Tk. (60 - q)

According to the question,
(60 - q)/q = 20%
⇒ 100(60 - q)/q = 20
⇒ 6000 - 100q = 20q
⇒ 120q = 6000
⇒ q = 6000/120
∴ q = 50

১২,০৩১.

A group of 30 employees of Cadre A has a mean age of 27. A different group of 70 employees of Cadre B has a mean age of 23. What is the mean age of the employees of the two groups together?

ক
26.2
খ
23.2
গ
24
ঘ
24.2

ব্যাখ্যা

Question: A group of 30 employees of Cadre A has a mean age of 27. A different group of 70 employees of Cadre B has a mean age of 23. What is the mean age of the employees of the two groups together?

Solution:
• Cadre A has a mean age = 27
- Total employees = 30
- Total age = 27×30 = 810 years

On the other hand,
• Cadre B has a mean age = 23
- Total employees = 70
- Total age = 1610 years

• From both the A and B cadre groups,
- Total employees = 100
- Total age = 2420 years
Now, Mean or Average = 2420/100 = 24.2 years.

১২,০৩২.

Find the cost price of a product. It is marked up by 45% more than the cost price and then a discount of 20% of marked price is given. Selling price is Tk. 4060.

ক
Tk. 3500
খ
Tk. 3600
গ
Tk. 3200
ঘ
Tk. 3800

ব্যাখ্যা

Question: Find the cost price of a product. It is marked up by 45% more than the cost price and then a discount of 20% of marked price is given. Selling price is Tk. 4060.

Solution:
Let,
Cost price be Tk. 100

Marked price = Tk. 100 + Tk. 45
= Tk. 145

Discount = 20% of marked price
∴ Selling price = (100 - 20) % of marked price = 80% of of marked price
= 80% of Tk. 145
= Tk. 116

Selling price 116 when cost price 100
∴ Selling price 1 when cost price 100/116
∴ Selling price 4060 when cost price (100 × 4060)/116
= Tk. 3500

১২,০৩৩.

The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:

ক
5√3 m
খ
7√3 m
গ
9√3 m
ঘ
10√3 m

ব্যাখ্যা

Question: The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:

Solution:

let, x is the height of the building.

Hence,
tan 30° = perpendicular/base = x/30
⇒ 1/√3 = x/30
⇒ x = 30/√3 m
⇒ x = (30√3)/(√3 × √3)
⇒ x = (30√3)/3
⇒ x = 10√3 m

১২,০৩৪.

What type of polynomial equation is 5x³ + 9x² - 4 = 0?

ক
cubic equation
খ
linear equation
গ
quadratic equation
ঘ
biquadratic equation

ব্যাখ্যা

Question: Which of the following is the polynomial equation 5x³ + 9x² - 4 = 0

Solution:
The given polynomial equation is in terms of x.
The highest power of x is 3 and hence the degree of the equation is 3.
Hence, it is a cubic equation.

The highest degree of the polynomial is 2 is a quadratic equation.
The highest degree of the polynomial is 1 is a linear equation.
The highest degree of the polynomial is 4 is a biquadratic equation.

১২,০৩৫.

A and B started a business investing Tk. 18,000 and Tk. 27,000 respectively. Out of a total profit of Tk. 15,000, what is B’s share?

ক
Tk. 9,000
খ
Tk. 5,000
গ
Tk. 7,000
ঘ
Tk. 1,000

ব্যাখ্যা

Question: A and B started a business investing Tk. 18,000 and Tk. 27,000 respectively. Out of a total profit of Tk. 15,000, what is B’s share?

Solution:
Investment of A = Tk. 18,000
Investment of B = Tk. 27,000

Ratio of investments = 18,000 : 27,000
= 2 : 3

Total profit = Tk. 15,000

B’s share of profit
= 3/(2 + 3) × 15,000
= 3/5 × 15,000
= 9,000

Therefore, B’s share of the profit is Tk. 9,000.

১২,০৩৬.

Today is Karim's 18th birthday and his father's 48th birthday. How many years from today will Karim's father be twice as old as Karim at that time?

ক
12 years
খ
15 years
গ
10 years
ঘ
16 years

ব্যাখ্যা

Question: Today is Karim's 18th birthday and his father's 48th birthday. How many years from today will Karim's father be twice as old as Karim at that time?

Solution:
Given that, Today Karim is 18 years old
And his Father is 48 years old
Age difference = 48 - 18 = 30 years (constant)

Let After x years, father's age = 2 × Karim's age

Now, Karim's age after x years = 18 + x
Father's age after x years = 48 + x

ATQ,
48 + x = 2(18 + x)
⇒ 48 + x = 36 + 2x
⇒ 2x - x = 48 - 36
⇒ x = 12

So, in 12 years, Karim's father will be twice as old as Karim.

১২,০৩৭.

Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Tk. 4160, then how much is the salary of A now?

ক
Tk.1200
খ
Tk.1400
গ
Tk.1600
ঘ
Tk.1800
ঙ
Tk.2000

ব্যাখ্যা

Question: Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Tk. 4160, then how much is the salary of A now?

Solution:
Let,
the salaries of A and B last year be Tk. 3x and Tk. 4x respectively.

Then,
A's present salary = Tk. (5/4) × 3x
= Tk. 15x/4

B's present salary = Tk.(3/2) × 4x
= Tk. 6x.

According to the question,
(15x/4) + 6x = 4160
⇒ 39x = 4160 × 4
⇒ x = (4160 × 4)/39

So, A's present salary = Tk. (15/4) × (4160 × 4)/39
= Tk.1600

১২,০৩৮.

In a cash box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?

ক
100
খ
200
গ
220
ঘ
150

ব্যাখ্যা

Question: In a cash box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?

Solution:

let, there are x numbers of 10 paisa, 25 paisa and 50 paisa coins.

1 tk = 100 paisa

x {(10/100) + (25/100) + (50/100)} = 170

⇒ x (1/10 + 1/4 + 1/2) = 170

⇒ 17x/20 = 170

⇒ x = 200

১২,০৩৯.

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

ক
3 : 59 p.m.
খ
4 : 00 p.m.
গ
3 : 58 p.m.
ঘ
4 : 03 p.m.

ব্যাখ্যা

Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

Solution:
Time from 7 a.m. to 4 : 15 p.m. = 9 hrs 15 min. = 37/4 hrs.
Now,
3 min. 5 sec. of this clock = 3 min. of the correct clock.
⇒ 37/720 hrs. of this clock = 1/20 hrs. of the correct clock.
⇒ 37/4 hrs. of this clock = {(1/20) × (720/37) × (37/4)} hrs. of the correct clock.
= 9 hrs.

∴ The correct time is 9 hrs. after 7 a.m. = 4 p.m.

১২,০৪০.

If five students run a mile in 5 minutes, then how much time will 50 students take to run a mile?

ক
ক) 50 min
খ
খ) 5 min
গ
গ) 10 min
ঘ
ঘ) 250 min

ব্যাখ্যা

Question: If five students run a mile in 5 minutes, then how much time will 50 students take to run a mile?

Solution:
এখানে দূরত্ব মুখ্য। যেহেতু দূরত্ব দুই ক্ষেত্রেই একই, তবে সময়ও একই লাগবে।

৫ জন ছাত্রের এক মাইল যেতে সময় লাগে ৫ মিনিট।
৫০ জন ছাত্র যদি একই বেগে দৌড়ায় তবে একসাথে তারা ৫ মিনিটেই ১ মাইল অতিক্রম করে।

১২,০৪১.

The value of 5^1/4 × (125)^0.25 =?

ক
ক) √5
খ
খ) 5
গ
গ) √5
ঘ
ঘ) 25

ব্যাখ্যা

Question: The value of 5^1/4 × (125)^0.25 =?

Solution:
5^1/4 × (125)^0.25
= 5^0.25 × (5³)^0.25
= 5^0.25 × 5^0.75
= 5¹
= 5

১২,০৪২.

A dishonest milkman profess to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is-

ক
4%
খ
6.25%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: A dishonest milkman profess to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is-

Solution:
Let, the cost price of 1 liter of milk be = 100 Tk
So, the selling price of 1 liter mixture is also = 100 Tk

Here, in 100 Tk, SP gain = 25%
So, cost price of the mixture = (100 × 100)/125 = 80 Tk

So, water in the mixture = 100 - 80 = Tk 20

১২,০৪৩.

Find the mother age after 8 years, if the ratio of age of mother and son is 5 ∶ 2 and the product of their ages in years is 1000.

ক
52 years
খ
58 years
গ
42 years
ঘ
None of these

ব্যাখ্যা

Question: Find the mother age after 8 years, if the ratio of age of mother and son is 5 ∶ 2 and the product of their ages in years is 1000.

Solution:
Given that,
Mother : Son = 5 ∶ 2
Product of ages = 1000

Let ages of mother and son be 5x, 2x

According to problem,
5x × 2x = 1000
⇒ 10x² = 1000
⇒ x² = 100 = 10²
∴ x = 10

So, age of mother after 8 years = (5x + 8)
= (5 × 10 + 8)
= 50 + 8
= 58 years

∴ The mother age is 58 years.

১২,০৪৪.

If t is an odd integer, which of the following must be an even integer?

ক
ক) t - 2
খ
খ) 2t+3
গ
গ) 4t+1
ঘ
ঘ) 3t+1

ব্যাখ্যা

If t is odd, then 3t will always be odd
Thus, odd + odd = even (3t + 1 = even number)

১২,০৪৫.

Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

ক
ক) 11
খ
খ) 13
গ
গ) 15
ঘ
ঘ) 17

ব্যাখ্যা

Let
The three integers be x, x + 2 and x + 4.

Then,
3x = 2(x + 4) + 3
3x = 2x + 8 + 3
3x - 2x = 11
x = 11.

Third integer = x + 4 = 11 + 4 = 15

১২,০৪৬.

Hasan is two years older than Halim, who is twice as old as Habib. If the total of ages of Hasan, Halim, and Habib is 72, how old is Hasan?

ক
30 years
খ
32 years
গ
28 years
ঘ
34 years

ব্যাখ্যা

Question: Hasan is two years older than Halim, who is twice as old as Habib. If the total of ages of Hasan, Halim, and Habib is 72, how old is Hasan?

Solution:
Let,
Habib's age be = a years
Then, Halim's age = 2a years
Hasan's age = (2a + 2) years

ATQ,
(2a + 2) + 2a + a = 72
⇒ 5a = 70
∴ a = 14

Hence, Hasan's age = (2 × 14) + 2 = 30 years.

১২,০৪৭.

In an examination, Pankaj scored certain marks and failed by 48 marks. In the same examination, Rajan scored 56% marks, thus scored 84 marks above passing marks. Find the percentage of marks obtained by Pankaj if Rajan scored 224 marks.

ক
22%
খ
23%
গ
24%
ঘ
25%

ব্যাখ্যা

Question: In an examination, Pankaj scored certain marks and failed by 48 marks. In the same examination, Rajan scored 56% marks, thus scored 84 marks above passing marks. Find the percentage of marks obtained by Pankaj if Rajan scored 224 marks.

Solution:
Rajan scored 224 marks.
∴ Pass marks 224 - 84 = 140

∴ Pankaj scored 140 - 48 = 92

56% of Total marks = 224
∴ Total marks = (224 × 100)/56 = 400

Percentage of marks obtained by Pankaj = (92/400) × 100 %
= 23%

১২,০৪৮.

Puja has 60 Tk more than Titu and 90 Tk more than Pavel. If their total is 330 Tk, what is Puja's share?

ক
100 Tk.
খ
160 Tk.
গ
180 Tk.
ঘ
190 Tk.

ব্যাখ্যা

Question: Puja has 60 Tk more than Titu and 90 Tk more than Pavel. If their total is 330 Tk, what is Puja's share?

Solution:
let,
Puja has x Tk.
Titu has (x - 60)Tk.
Pavel has (x - 90)Tk.

x + x - 60 + x - 90 = 330
or, 3x - 150 = 330
or, 3x = 330 + 150
or, x = 480/3
∴ x = 160

So, Puja's share is 160 Tk.

১২,০৪৯.

A fisherman can row his boat to the market for 80 km along the stream. For this he takes 1 hour 20 minutes. His son says that his father’s rowing speed in still water is 45 km/hr. How much time should he take to row the same distance back, against the stream?

ক
ক) 3 hours 10 minutes
খ
খ) 2 hours 40 minutes
গ
গ) 2 hours 30 minutes
ঘ
ঘ) 3 hours 50 minutes

ব্যাখ্যা

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

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

X+Y = (45+Y) km/hr
1 hour 20 munites = 1 hour + 20/60 = (1 + 1/3) = (4/3) hours
Downstream speed = Distance covered/Time taken

∴ 45 + y = 80/(4/3)
∴ Y = 15 km/hr
X - Y = 45 - 15 = 30 km/hr

Time is taken to go against the stream = 80/30 hours = 2 Hours 40 minutes.

১২,০৫০.

The perimeter of the base of a cube is 48 cm. What is its volume?

ক
1728 cm³
খ
1232 cm³
গ
2744 cm³
ঘ
4096 cm³

ব্যাখ্যা

Question: The perimeter of the base of a cube is 48 cm. What is its volume?

Solution:
Let the side length of the cube be x.
So, 4x = 48
∴ x = 12 cm

Volume = (12)³
= 1728 cm³

১২,০৫১.

ক
0
খ
- 1
গ
- 2
ঘ
- 3
ঙ
- 4

ব্যাখ্যা

Question:

Solution:

১২,০৫২.

Pipe X can fill a cistern in 2 hours, and Pipe Y can empty it in 3 hours. If both pipes are opened at 8 : 15 A. M., when will the cistern be full?

ক
3 : 05 P. M.
খ
2 : 30 P. M.
গ
1 : 55 P. M.
ঘ
2 : 15 P. M.

ব্যাখ্যা

Question: Pipe X can fill a cistern in 2 hours, and Pipe Y can empty it in 3 hours. If both pipes are opened at 8 : 15 A. M., when will the cistern be full?

Solution:
Given that,
Pipe X can fill the cistern in 2 hours
Pipe Y can empty the cistern in 3 hours
Both pipes are opened at 8:15 A.M.

Let the total capacity of the cistern = 1 unit
Pipe X fills 1/2 unit/hour
Pipe Y empties 1/3 unit/hour

∴ Net rate = (1/2) - (1/3) = (3 - 2)/6 = 1/6 unit/hour

∴ Time to fill the cistern = 1/Net rate = 1/(1/6) = 6 hour

If both pipes are opened at 8:15 A.M., then the cistern will be full at = 8 : 15 A.M. + 6 hours
= 2 : 15 P. M.

১২,০৫৩.

The average of the largest and smallest 3 digits numbers formed by 0, 2, and 4 would be:

ক
212
খ
303
গ
232
ঘ
312

ব্যাখ্যা

Question: The average of the largest and smallest 3 digits numbers formed by 0, 2, and 4 would be:

Solution:
ATQ,
Largest number = 420
Smallest number = 204

∴ Average = (420 + 204)/2
= 624/2
= 312

১২,০৫৪.

The ratio of the areas of two squares is 225 : 196, then the ratio of their perimeters-

ক
ক) 17 : 18
খ
খ) 15 : 17
গ
গ) 14 : 15
ঘ
ঘ) 15 : 14

ব্যাখ্যা

Let
the sides of the two squares be x and y respectively.
Then,
Reqd. ratio of areas

x²/y²= 225/196
x²/y² =15²/14²
(x/y)² = (15/14)²
x/y = 15/14
4x/4y = 15 × 4 /14 × 4
4x/4y = 15/14
4x : 4y = 15 : 14

১২,০৫৫.

If ‘a’ is an integer, then which of the following must be divisible by 3?

ক
ক) a² + 1
খ
খ) a² - 1
গ
গ) a² - 4
ঘ
ঘ) a² + 4
ঙ
ঙ) None of the above

ব্যাখ্যা

Assume a = 3 and test the options.

১২,০৫৬.

The ratio of two numbers is 3 : 4 and their H.C.F is 4. The smallest number is-

ক
ক) 8
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 16

ব্যাখ্যা

ধরি,
সংখ্যা দুটি 3ক ও 4ক
3ক ও 4ক এর গ ,সা,গু = ক
প্রশ্নমতে
ক = 4

ছোট সংখ্যাটি = 3 × 4 = 12

১২,০৫৭.

A tank is filled in 10 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
70 hour
খ
35 hour
গ
50 hour
ঘ
33 hour

ব্যাখ্যা

Suppose pipe A can fill the tank in x hours. Then,
pipe B can fill the tank in x/2 hours,
pipe C can fill the tank in x/4 hours.
Part filled by pipe A in 1 hour = 1/x
Part filled by pipe B in 1 hour = 2/x
Part filled by pipe C in 1 hour = 4/x
Therefore, partly filled by pipe A, pipe B, and pipe C together in 1 hour
= 1/x + 2/x + 4/x
= 7/x
i.e., pipe A, pipe B, and pipe C together can fill the tank in x/7 hours.
Given that pipe A, pipe B, and pipe C together can fill the tank in 10 hours
x/7 = 10
⇒ x = 70.

১২,০৫৮.

In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is-

ক
3 : 5
খ
1 : 3
গ
3 : 4
ঘ
1 : 2

ব্যাখ্যা

Question: In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is-

Solution:
Let the number of boys be 5k.
Then the number of girls = 20% more than the boys = 5k × 1.2 = 6k

Total students = 66
5k + 6k = 66
⇒ 11k = 66
⇒ k = 66/11
∴ k = 6

∴ Number of boys = 5 × 6 = 30
∴ Number of girls = 6 × 6 = 36

Now, when 4 more girls are admitted than New number of girls = 36 + 4 = 40

∴ Ratio of boys to girls = 30 : 40 = 3 : 4 (dividing both by 10)

So the ratio of the number of boys to girls is 3 : 4

১২,০৫৯.

8597 - ? = 7429 - 4358

ক
5426
খ
5706
গ
5526
ঘ
5476

ব্যাখ্যা

Question: 8597 - ? = 7429 - 4358

Solution:
Let
? = x

Now
8597 - x = 7429 - 4358
or, 8597 - 7429 + 4358 = x
x = 5526

১২,০৬০.

How many kgs of sugar costing Tk 9 per kg must be mixed with 27 kg of sugar costing Tk 7 per kg so that may be a gain of 10% by selling the mixture at Tk 9.24 per kg?

ক
ক) 63 kg
খ
খ) 58 kg
গ
গ) 72 kg
ঘ
ঘ) 49 kg

ব্যাখ্যা

Question: How many kgs of sugar costing Tk 9 per kg must be mixed with 27 kg of sugar costing Tk 7 per kg so that may be a gain of 10% by selling the mixture at Tk 9.24 per kg?

Solution:
Let, the sugar of Tk 9 per kg is = x kg

ATQ,
110% of (7 × 27 + 9 × x) = 9.24(27 + x)
⇒ (11/10) × (189 + 9x) = 249.48 + 9.24x
⇒ 2079 + 99x = 2494.8 + 92.4x
⇒ 6.6x = 415.8
⇒ x = 63

১২,০৬১.

If 3/(x - 1) = 2/ (x + 1), what is the value of x?

ক
ক) - 5
খ
খ) - 1
গ
গ) 0
ঘ
ঘ) 1

ব্যাখ্যা

question: If 3/(x - 1) = 2/ (x + 1), what is the value of x?

solution:
3/(x -1) = 2/(x + 1)
⇒ 3(x + 1) = 2(x -1)
⇒ 3x + 3 = 2x - 2
x = - 5

১২,০৬২.

The members of a club participate in at least one game. Twenty of them play football, 10 play cricket, 12 play hokey. Three of them play cricket only, 4 of them play both the cricket and football but not hockey, 2 of them participate all games. How many people play both cricket and hockey but not football?

ক
1
খ
2
গ
3
ঘ
None of these

ব্যাখ্যা

Question: The members of a club participate in at least one game. Twenty of them play football, 10 play cricket, 12 play hokey. Three of them play cricket only, 4 of them play both the cricket and football but not hockey, 2 of them participate all games. How many people play both cricket and hockey but not football?

Solution:
ফুটবল খেলে = 20 জন
ক্রিকেট খেলে = 10 জন
হকি খেলে = 12 জন
শুধু ক্রিকেট খেলে = 3 জন
ক্রিকেট ও ফুটবল খেলে = 4 জন
ক্রিকেট, ফুটবল ও হকি খেলে = 2 জন

হকি ও ক্রিকেট খেলে কিন্তু ফুটবল খেলে না এদের সংখ্যা = { 10 - ( 3 + 4 + 2)}
= 1 জন।

১২,০৬৩.

In a university, 80 percent of the students lived in hostel, and 60 percent of the hostel students are lucky to get a single room. If number of lucky students is 1200, then how many students were there in the university?

ক
ক) 1800
খ
খ) 2000
গ
গ) 2400
ঘ
ঘ) 2500

ব্যাখ্যা

Question: In a university, 80 percent of the students lived in hostel, and 60 percent of the hostel students are lucky to get a single room. If number of lucky students is 1200, then how many students were there in the university?

Solution:
ধরি, বিশ্ববিদ্যালয়ে ছাত্র সংখ্যা x
হোস্টেলে বাস করে = x এর ৮০%
= ০.৮x জন ছাত্র

হোস্টেলে বাস করা ছাত্রদের মধ্যে ৬০% ভাগ্যবান ছাত্র সিঙ্গেল রুম পায়।

০.৮x এর ৬০% = ১২০০
⇒ ০.৪৮x = ১২০০
⇒ x = ১২০০/০.৪৮
∴ x = ২৫০০

অতএব, বিশ্ববিদ্যালয়ে ২৫০০ জন ছাত্র আছে।

১২,০৬৪.

A is twice fast as B and B is thrice fast as C is. The journey covered by C in 3/2 hours will be covered by A is-

ক
ক) 15 minutes
খ
খ) 20 minutes
গ
গ) 30 minutes
ঘ
ঘ) 1 hour

ব্যাখ্যা

Let speed of C = X
Then Speed of B = 3X
Then Speed of A = 6X
Ratio of the speed of A and C = 1:6
So, Greater the speed less time taken in journey.
C’s speed is 6 times less than A So A will take
1/6 of the total time taken C to covered same distance.
So, Time taken by A
= 3/(2×6)
= 1/4 hours
= 15minutes

১২,০৬৫.

ক
0.03
খ
0.3
গ
0.43
ঘ
None of these

ব্যাখ্যা

Question:

Solution:

১২,০৬৬.

A litre of water evaporates from 6L of sea water containing 4% salt. Find the percentage of salt in the remaining solution.

ক
ক) 5(1/2)%
খ
খ) 3(1/2)%
গ
গ) 3%
ঘ
ঘ) 4(4/5)%
ঙ
ঙ) 5%

ব্যাখ্যা

Quantity of salt in 6L of sea water,
= (6×4)/100 = 0.24
Percentage of salt in 5L of sea water,
= (0.24×100)/5
= 4(4/5)%

১২,০৬৭.

In the figure AC and BC are radii of circles. The length of AB is 8. If AC = 4, what is BC? (BC is tangent to the circle with center A.)

ক
5
খ
5/2
গ
4√3
ঘ
3

ব্যাখ্যা

Question: In the figure AC and BC are radii of circles. The length of AB is 8. If AC = 4, what is BC? (BC is tangent to the circle with center A.)

Solution:
Since BC is tangent to circle with centre A
∴ BC is perpendicular to AC.
ΔABC is right angled triangle.
So,
BC = √(AB² - AC²)
= √(8² - 4²)
= √(64 - 16)
= √48
= √(16 × 3)
= 4√3

১২,০৬৮.

A person paid Tk. 17000 for a motor-car after a single discount of 15%. If he is given successive discount of 5% and 10% then how much he would pay?

ক
ক) 17000
খ
খ) 17010
গ
গ) 17100
ঘ
ঘ) 18900

ব্যাখ্যা

Cost price of motor-car = Tk. 17000
Mark price of motor-car
= Tk 17000 × 100/85 = Tk. 20000
After successive discount,Cost price
= Tk. 20000 × 95/100×90/100
= Tk. 17100

১২,০৬৯.

Which of the numbers below is not equivalent to 20%?

ক
1/5
খ
20/100
গ
0.5
ঘ
0.2

ব্যাখ্যা

20% = 20/100 = 1/5 = 0.2

১২,০৭০.

The total population of a village increased from 18000 to 22500 in a decade. The average percentage increase of population per year of that village is-

ক
2.37%
খ
2.5%
গ
3.6%
ঘ
6.75%

ব্যাখ্যা

Question: The total population of a village increased from 18000 to 22500 in a decade. The average percentage increase of population per year of that village is-

Solution:
Population increase in 10 years = (22500 - 18000) = 4500.
Increase% of ten year = (4500/18000) × 100% = 25%
∴ Required average = (25/10)% = 2.5%

১২,০৭১.

A shopkeeper marks his goods 40% above the cost price and offers a discount of 20% on the marked price. What is his gain percent?

ক
12%
খ
17%
গ
9%
ঘ
15%

ব্যাখ্যা

Question: A shopkeeper marks his goods 40% above the cost price and offers a discount of 20% on the marked price. What is his gain percent?

Solution:
Let,
the cost price (CP) be Tk. 100

Marked Price = 40% more than cost price
= 100 + 40
= 140 Tk.

Discount = 20% of 140
= (20/100) × 140
= 28 Tk.

Selling Price (SP)= 140 - 28 = 112 Tk.

∴ Profit = SP - CP = 112 - 100 = 12 Tk.

∴ Gain percent = 12%

১২,০৭২.

Three numbers are in ratio 1 : 2 : 3 and HCF is 17. The largest number is:

ক
17
খ
34
গ
51
ঘ
63

ব্যাখ্যা

Question: Three numbers are in ratio 1 : 2 : 3 and HCF is 17. The largest number is:

Solution:
let, the numbers are x, 2x, 3x
HCF is x
x = 17

largest number = 17 × 3
= 51

১২,০৭৩.

If (5x - 2y) ∶ (x - 2y) = 9 ∶ 17, then find the value of x/y = ?

ক
4/19
খ
5/17
গ
8/15
ঘ
9/17

ব্যাখ্যা

Question: If (5x - 2y) ∶ (x - 2y) = 9 ∶ 17, then find the value of x/y = ?

Solution:
Given that,
(5x - 2y) ∶ (x - 2y) = 9 ∶ 17

Now,
⇒ (5x - 2y)/(x - 2y) = 9/17
⇒ 17 × (5x - 2y) = 9 × (x - 2y)
⇒ 85x - 34y = 9x - 18y
⇒ 76x = 16y
⇒ x/y = 16/76
∴ x/y = 4/19

১২,০৭৪.

A committee of 4 members is to be formed by selecting out of 6 man and 5 women. In how many different ways the committee can be formed if it should have 2 men and 2 women?

ক
110
খ
80
গ
150
ঘ
170

ব্যাখ্যা

Question: A committee of 4 members is to be formed by selecting out of 6 man and 5 women. In how many different ways the committee can be formed if it should have 2 men and 2 women?

Solution:
2 men can be selected out of 6 men in ⁶C₂ = 6!/2!(6 - 2)! = 15 ways
And
2 women can be selected out of 5 women in ⁵C₂ = 5!/2!(5 - 2)! = 10 ways

∴ Required number of ways = 15 × 10 = 150

∴ 150 different ways to form the committee with 2 men and 2 women.

১২,০৭৫.

If selling 12 items brings in the same amount as buying 15 items, what's the profit or loss percentage?

ক
20% profit
খ
12% loss
গ
25% profit
ঘ
32% loss

ব্যাখ্যা

Question: If selling 12 items brings in the same amount as buying 15 items, what's the profit or loss percentage?

Solution:
মনে করি,
প্রতিটি পণ্যের ক্রয়মূল্য = 1 টাকা
15 টি পণ্যের ক্রয়মূল্য = 15 টাকা

প্রশ্নমতে,
12 টি পণ্যের বিক্রয়মূল্য = 15 টাকা
1 টি পণ্যের বিক্রয়মূল্য = 15/12 টাকা
= 5/4 টাকা

∴ লাভ/ক্ষতি = বিক্রয়মূল্য - ক্রয়মূল্য = ( 5/4 ) - 1 = (5 - 4) / 4= 1/4

এখন,
1 টাকায় লাভ হয় = 1/4 টাকা
∴ 100 টাকায় লাভ হয় = ( 1/4 ) × 100 = 25 টাকা

সুতরাং, লাভের শতকরা পরিমাণ = 25%

১২,০৭৬.

Trisha’s grandfather was 8 times older to her 16 years ago. He would be 3 times her age 8 years from now. Eight years ago, what was the ratio of Trisha’s age to that of her grandfather?

ক
3 : 8
খ
1 : 2
গ
1 : 5
ঘ
None of these

ব্যাখ্যা

Question: Trisha’s grandfather was 8 times older to her 16 years ago. He would be 3 times her age 8 years from now. Eight years ago, what was the ratio of Trisha’s age to that of her grandfather?

Solution:
Let, trisha was x years old 16 years ago.

grandfather was 8x years

ATQ,
8x + 16 + 8 = 3 (x + 16 + 8)
⇒ 8x + 24 = 3x + 72
⇒ 8x - 3x = 72 - 24 = 48
⇒ x = 48/5 = 9.6

Eight years ago, trisha was 9.6 + 8 = 17.6
grandfather was = 8 × 9.6 + 8 = 84.8

ratio = 17.6 : 84.8
= 176 : 848
= 11 : 53

১২,০৭৭.

Simplify it.

ক
2.03
খ
2.13
গ
2
ঘ
2.69

ব্যাখ্যা

Question: Simplify it.

Solution:

১২,০৭৮.

In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5 : 3. How many number of girls to be added in the union, so that the number of boys to girls in 6 : 5 ?

ক
5
খ
7
গ
13
ঘ
10

ব্যাখ্যা

Question : In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5 : 3. How many number of girls to be added in the union, so that the number of boys to girls in 6 : 5 is ?

Solution :
Let,
The ratio of numbers of boys to the number of girls is = 5x : 3x

According to the question,
⇒ 5x+3x=48
⇒ 8x=48
∴ x = 6

So the number of boys = 5x
= 5 × 6
= 30

and the number of girls = 3x
= 3 × 6
= 18

Let,
The number of girls to be added in the union = y

So,
30/(18 + y) = 6 : 5
⇒ 6(18 + y) = 30 × 5
⇒ 6(18 + y) = 150
⇒ 18 + y = 150/6
⇒ 18 + y = 25
⇒ y = 25 - 18
∴ y = 7

∴ The number of girls to be added in the union = 7

১২,০৭৯.

A train passes a 254-meter-long bridge in 20 seconds and a 100-meter-long bridge in 13 seconds. Determine the length of the train.

ক
220 meters
খ
104 meters
গ
150 meters
ঘ
186 meters

ব্যাখ্যা

Question: A train passes a 254-meter-long bridge in 20 seconds and a 100-meter-long bridge in 13 seconds. Determine the length of the train.

Solution:

১২,০৮০.

ক
3.2
খ
2.8
গ
1.2
ঘ
None

ব্যাখ্যা

Question:

Solution:

১২,০৮১.

Find the quadratic polynomial if the roots are 4 and 5.

ক
ক) x² + 9x + 20
খ
খ) x² - 9x - 20
গ
গ) x² - 9x + 20
ঘ
ঘ) x² + 7x + 20

ব্যাখ্যা

Question: Find the quadratic polynomial if the roots are 4 and 5.

Solution:
Hence the roots are 4 and 5.
so, the quadratic polynomial is
(x - 4)(x - 5)
= x² - 4x - 5x + 20
= x² - 9x + 20

১২,০৮২.

A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share?

ক
ক) Tk. 18
খ
খ) TK. 15
গ
গ) Tk. 21
ঘ
ঘ) TK. 12

ব্যাখ্যা

Face value of each share = Tk. 20
Dividend per share = 9% of 20 = (9 × 20)/100
= 9/5.
He needs to have an interest of 12% on his money
Money Paid for a share = (9/5) × (12/100)
Money Paid for a share = (9/5) × (100/12)
= 15.
ie, Market Value of the share = Tk. 15.

১২,০৮৩.

Salman converted a 8m length cube to 1m length cube. How many cubes can be formed?

ক
ক) 64
খ
খ) 256
গ
গ) 512
ঘ
ঘ) 1024

ব্যাখ্যা

Question: Salman converted a 8m length cube to 1m length cube. How many cubes can be formed?

Solution:
Here, the length of the big cube, L = 8m
so, the volume of the big cube is, V = 8³= 512m³

the length of the small cubes, l = 1m
so, the volume of one small cube, v = 1³ = 1m³

small cubes can be formed = 512/1 = 512

১২,০৮৪.

A alone can do a work of Tk. 1200 in 6 days. By engaging an assistant, the work is completed in just 4 days. The share the assistant would receive is -

ক
ক) 800Tk.
খ
খ) 400Tk.
গ
গ) 300Tk.
ঘ
ঘ) 600Tk.

ব্যাখ্যা

Question: A alone can do a work of Tk. 1200 in 6 days. By engaging an assistant, the work is completed in just 4 days. The share the assistant would receive is -

Solution:
A alone can do the work in 6 days
in 1 day,
A can do 1/6
both can do 1/4
the assistant can do (1/4) - (1/6)
= (3 - 2)/12
= 1/12

So
A : Assistant = 1/6 : 1/12 = 2 : 1

Hence, the share of the assistant is (1200 × 1/3)
= 400 Tk.

১২,০৮৫.

A rectangular water reservoir contains 48000 liters of water. If the length of the reservoir is 6m and the breadth is 4m, the depth of the reservoir will be -

ক
ক) 1 m
খ
খ) 2 m
গ
গ) 3 m
ঘ
ঘ) 4 m

ব্যাখ্যা

Question: A rectangular water reservoir contains 48000 liters of water. If the length of the reservoir is 6m and the breadth is 4m, the depth of the reservoir will be -

Solution:
1 m³ = 1000 litre
⇒ 48000 litre = 48000/1000
= 48 m³

48 = 6 × 4 × depth
∴ depth = 48/24
= 2 m

১২,০৮৬.

In a rectangle, the diagonal length is 13 and the width is 5. What is the perimeter of the rectangle?

ক
30
খ
34
গ
36
ঘ
48

ব্যাখ্যা

Question: In a rectangle, the diagonal length is 13 and the width is 5. What is the perimeter of the rectangle?

Solution:
Given that,
Diagonal of rectangle, d = 13
Width, w = 5

We know,
Pythagorean theorem, l² + w² = d²
⇒ 13² = l² + 5²
⇒ 169 = l² + 25
⇒ l² = 169 - 25
⇒ l² = 144 = 12²
∴ l = 12
∴ length In a rectangle is, l = 12

Perimeter of a rectangle, P = 2(l + w)
= 2(12 + 5)
= 2 × 17
= 34

So the perimeter of the rectangle is 34.

১২,০৮৭.

A ferry can travel twice as fast when empty as when it is full. It travels 20 miles with full load, spends 1 hour for unloading and returns to its original post empty. It took 11 hours to complete the journey. What is the speed of the ferry when it is empty?

ক
5
খ
6
গ
6.5
ঘ
8

ব্যাখ্যা

Question: A ferry can travel twice as fast when empty as when it is full. It travels 20 miles with full load, spends 1 hour for unloading and returns to its original post empty. It took 11 hours to complete the journey. What is the speed of the ferry when it is empty?

Solution:
ধরি,
ফেরিটির মাল বোঝাই অবস্থায় গতি বেগ x মাইল /ঘণ্টা
ফেরিটির খালি অবস্থায় গতি বেগ 2x মাইল/ঘণ্টা

মাল বোঝাই অবস্থায়
ফেরিটির 20 মাইল যেতে সময় লাগে = 20/x ঘণ্টা

খালি অবস্থায়
ফেরিটির 20 মাইল যেতে সময় লাগে =20/2x = 10/x ঘণ্টা

প্রশ্নমতে,
20/x + 10/x = 11 - 1
⇒ (20 + 10)/x = 10
⇒ 30/x = 10
⇒ 10x = 30
⇒ x = 3

∴ ফেরিটির খালি অবস্থায় গতি বেগ 2 × 3 = 6 মাইল/ঘণ্টা।

১২,০৮৮.

The sum of squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find their sum.

ক
35
খ
42
গ
20
ঘ
18

ব্যাখ্যা

Let the three numbers be x, y, and z.

Given:Sum of squares of three numbers is 138 and sum of their products taken two at a time is 131
Therefore,
x²+y²+z²=138
xy + yz + zx=131

Formula:
(a + b + c)²= a² + b² + c²+ 2 (ab + bc + ca)
This formula can be used to easily find the sum of three numbers.

Substituting the values, we get
(x + y + z)²= x²+ y²+ z²+ 2 (xy + yz + zx)
(x + y + z )²= 138 + 2(131)
(x + y + z )²= 400
Hence, (x + y + z) = 20.

১২,০৮৯.

A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

ক
3
খ
4
গ
15
ঘ
18

ব্যাখ্যা

Question: A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

Solution:
Let the number of correct answers be X
The number of incorrect answers will be 22 - X
For each correct answer the student got 3.5 points for a total of 3.5X
For each incorrect answer one point was taken out which is equivalent to - (22 - X)
The total he got for that was 63.5

So in short you have the following equation and solution.
3.5X - (22 - X) = 63.5
⇒ 3.5X - 22 + X = 63.5
⇒ 4.5X = 63.5 + 22
⇒ 4.5X = 85.5
⇒ 4.5X/4.5 = 85.5/4.5
∴ X = 19

So incorrect answers will be 22 - X = 22 - 19 = 3.

১২,০৯০.

A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

ক
ক) 40
খ
খ) 30
গ
গ) 50
ঘ
ঘ) 60
ঙ
ঙ) None of these

ব্যাখ্যা

Question: A Zoo keeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

Solution:
let, there are x horses and y pigeons.

x + y = 80
⇒ x = 80 - y

4x + 2y = 260
⇒ 4 (80 - y) + 2y = 260
⇒ 320 - 4y + 2y = 260
⇒ 2y = 320 - 260
⇒ 2y = 60
∴ y = 30

x = 80 - 30
= 50
∴ there are 50 horses.

১২,০৯১.

1/4 of Ram's money is equal to 1/6 of Shyam's money. If both together have Tk. 600 the difference between their amounts is-

ক
ক) 50
খ
খ) 120
গ
গ) 240
ঘ
ঘ) 360
ঙ
ঙ) None of these

ব্যাখ্যা

শ্যামের টাকা x হলে রামের টাকা (600 - x) টাকা।
প্রশ্নমতে, 1/4(600-x) = x/6
⇒6(600 - x) = 4x
⇒ 10x = 3600
⇒ x = 360
তাহলে রামের টাকা 600 - 360 = 240
সুতরাং তাদের টাকার পার্থক্য 360 - 240 = 120 টাকা।

১২,০৯২.

If the volume of a sphere is 36π cm³, what is the surface area of the sphere?

ক
100π cm²
খ
144π cm²
গ
124π cm²
ঘ
36π cm²

ব্যাখ্যা

Question: If the volume of a sphere is 36π cm³, what is the surface area of the sphere?

Solution:
Given that the volume, V = 36π cm³
or, (4/3)πr³ = 36π
or, r³ = 27
∴ r = 3 cm

Surface area of a sphere, A = 4πr²
= 4π(3)²
= 36π cm²

১২,০৯৩.

ক
x^abc
খ
x^{ab + bc + ca}
গ
x^{a + b + c}
ঘ
1

ব্যাখ্যা

Question:

Solution:

১২,০৯৪.

In a mixture 120 liters, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then estimate the quantity of water in liter to be further added in the mixture.

ক
60 liters
খ
80 liters
গ
120 liters
ঘ
160 liters

ব্যাখ্যা

Question: In a mixture 120 liters, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then estimate the quantity of water in liter to be further added in the mixture.

Solution:
Sum of the given ratio = 2 +1=3

Quantity of milk = 120 × (2/3) = 80 liters
Hence, quantity of water will be
= 120 - 80 = 40 liters

Assume,
x liters water needs to be added.
ATQ,
80/(x + 40) = 1/2
⇒ 160 = x + 40
∴ x = 120

∴ 120 liters water needs to be added.

১২,০৯৫.

Sunny and Rajib bought the same item. Sunny paid Tk 15,000. Rajib got discount and paid Tk. 3,000 less than Sunny. How much discount did Rajib get?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: Sunny and Rajib bought the same item. Sunny paid Tk 15,000. Rajib got discount and paid Tk. 3,000 less than Sunny. How much discount did Rajib get?

Solution:
In Tk. 15000 Rajib get discount Tk. 3000
In Tk. 1 Rajib get discount Tk. (3000/15000)
In Tk. 100 Rajib get discount Tk. (3000 × 100)/15000
= Tk. 20

∴ Rajib get 20% discount.

১২,০৯৬.

What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?

ক
ক) 668
খ
খ) 900
গ
গ) 980
ঘ
ঘ) 788

ব্যাখ্যা

Question: What is the least square number which is exactly divisible by 2, 3, 10, 18 and 20?
Solution:

The least or smallest number which is exactly divisible by 2, 3, 10, 18, and 20 is the LCM of 2, 3, 10, 18, and 20.

LCM (2, 3, 10, 18, 20) = 180

180 = 2² × 3² × 5

So, to become a perfect square 180 needs to be multiplied by 5.

Now, the least square number which is exactly divisible by 2, 3, 10, 18 and 20

⇒ 180 × 5 = 900

∴ The least-square number which is exactly divisible by 2, 3, 10, 18, and 20 is 900.

১২,০৯৭.

Four boys are standing in a line for a photograph. Rifat is to the right of Rafiq. Arif is to the right of Kamal. Kamal is between Rifat and Arif. Rafiq is at the extreme left end. Who is second from the right in the line?

ক
Kamal
খ
Rifat
গ
Arif
ঘ
Rafiq

ব্যাখ্যা

Question: Four boys are standing in a line for a photograph. Rifat is to the right of Rafiq. Arif is to the right of Kamal. Kamal is between Rifat and Arif. Rafiq is at the extreme left end. Who is second from the right in the line?

Solution:
রিফাত রফিকের ডানদিকে। রফিক ⇔ রিফাত
কামাল, রিফাত এবং আরিফের মাঝে। রিফাত ⇔ কামাল ⇔ আরিফ
রফিক একদম বামপ্রান্তে। রফিক ⇔ রিফাত ⇔ কামাল ⇔ আরিফ
∴ রফিক ⇔ রিফাত ⇔ কামাল ⇔ আরিফ।

∴ কামাল সারিটির ডানদিক থেকে দ্বিতীয় হবে।

১২,০৯৮.

A rectangular tank with a length of 8m and a width of 5m can store 60000 liters. What is the height of the tank?

ক
1.5 meters
খ
2 meters
গ
2.5 meters
ঘ
4 meters

ব্যাখ্যা

Question: A rectangular tank with a length of 8m and a width of 5m can store 60000 liters. What is the height of the tank?

Solution:
দেওয়া আছে, ট্যাংকের দৈর্ঘ্য (l) = 8m,
প্রস্থ (b) = 5 m, এবং
আয়তন (V) = 60000 লিটার।

ধরি, ট্যাংকটির উচ্চতা হল h মিটার।

আমরা জানি,
আয়তাকার ঘনবস্তুর আয়তন = দৈর্ঘ্য × প্রস্থ × উচ্চতা
= (8 × 5 × h) m³
= 40h m³

এখন, আমরা জানি, 1 m³ = 1000 লিটার।

প্রশ্নমতে,
40h × 1000 = 60000
⇒ 40h = 60000/1000
⇒ h = 60/40
∴ h = 1.5

সুতরাং, ট্যাংকটির উচ্চতা হলো 1.5 মিটার।

১২,০৯৯.

If 4(Nahid's Capital ) = 6(Safin's Capital ) = 10(Robin's Capital ), then out of the total profit of Tk. 4650 , Robin will receive-

ক
Tk. 900
খ
Tk. 1200
গ
Tk. 1450
ঘ
Tk. 1600

ব্যাখ্যা

Question: If 4(Nahid's Capital ) = 6(Safin's Capital ) = 10(Robin's Capital ), then out of the total profit of Tk. 4650 , Robin will receive-

Solution:
Let
Nahid's capital = a
Safin's capital = b
Robin's capital = c

ATQ,
4a = 6b = 10c
⇒ 2a = 3b = 5c
∴ b = 2a/3

∴ c = 2a/5

Nahid : Safin : Robin = a : 2a/3 : 2a/5
= 15 : 10 : 6 [Multiply by 15]

Robin's share = 4650 × (6/31)
= 150 × 6
= Tk. 900

১২,১০০.

What number will replace the '?' mark?
17, 24, 15, 22, 13, 20, 11, ?

ক
16
খ
18
গ
9
ঘ
13

ব্যাখ্যা

Question: What number will replace the '?' mark?
17, 24, 15, 22, 13, 20, 11, ?

Solution:
প্রদত্ত সিরিজে ২টি ধারা আছে,
১ম ধারা, 17, 15, 13, 11, ....... অর্থাৎ 2 করে কমছে।
২য় ধার, 24, 22, 20, 18, ....... অর্থাৎ ২ করে কমছে।

∴ সংখ্যা সিরিজের প্রশ্নবোধক চিহ্নের স্থানে 18 বসবে।