Bank Math

PrepBank · পাতা ১১২ / ১৬১ · ১১,১০১–১১,২০০ / ১৬,১২৪

১১,১০১.

If the price of an item is increased by 10% and then decreased by 10% , the net effect on the price of the item is -

ক
an increase of 9%
খ
a decrease of 1%
গ
an increase of 7%
ঘ
No Change

ব্যাখ্যা

Question: If the price of an item is increased by 10% and then decreased by 10% , the net effect on the price of the item is -

Solution:
Let,
The price of an item is 100 Tk.

If the price increased by 10%,
So, the new price will be after increased = 100 + {100 × (10/100)} Tk.
= 100 + 10 Tk.
= 110 Tk.

Then the new price decreased by 10%,
So, the new price will be after decreased = 110 - {110 × (10/100)} Tk.
= 110 - 11 Tk.
= 99 Tk.

∴ The net effect on the price of the item is = (100 - 99) Tk. decreased
= 1 Tk. decreased

১১,১০২.

The right circular cone of height 24 cm has a volume of 1232 cm³, then the area of its curved surface is?

ক
ক) 513 cm³
খ
খ) 530 cm³
গ
গ) 550 cm³
ঘ
ঘ) 570 cm³

ব্যাখ্যা

Question: The right circular cone of height 24 cm has a volume of 1232 cm³, then the area of its curved surface is?

Solution:
Volume of the cone = (1/3) × r² × h = 1232
⇒ (1/3) × (22/7) × r² × 24 = 1232
⇒ r² = (1232 × 7 × 3)/(22 × 24)
⇒ r² = 49
∴ r = 7

So, slant height l = √(7)² + (24)² = √625 = 25
So, curved surface area = πrl = (22/7) × 7 × 25 = 550 cm³

১১,১০৩.

On Dhaka- Sylhet highway 5% of the drivers are fined for exceeding the speed limit. However, 80% of the drivers who exceed the speed limit are not fined. What percentage of drivers on this highway exceed the speed limit?

ক
10
খ
15
গ
20
ঘ
25
ঙ
None of these

ব্যাখ্যা

প্রশ্ন: On Dhaka- Sylhet highway 5% of the drivers are fined for exceeding the speed limit. However, 80% of the drivers who exceed the speed limit are not fined. What percentage of drivers on this highway exceed the speed limit?

সমাধান:
ধরি,
হাইওয়েতে 100 জন চালক ছিল।

এখন,
গতিসীমা অতিক্রম করার জন্য 5% চালককে জরিমানা করা হয়।
∴ 100 জন চালকের 5% বা 5 জন চালককে জরিমানা করা হয়।

আবার,
চালকদের মধ্যে যারা গতিসীমা অতিক্রম করেছিল তাদের মধ্যে 80% চালককে জরিমানা করা হয়নি।
∴ চালকদের মধ্যে যারা গতিসীমা অতিক্রম করেছিল তাদের মধ্যে 20% চালককে জরিমানা করা হয়।

প্রশ্নমতে,
20% = 5
∴ 1% = 5/20
∴ 100% = (5 × 100)/20
= 25

১১,১০৪.

The midpoint of the line joining (10, 2) and (4, 8) is -

ক
(8, 4)
খ
(6, 6)
গ
(7, 5)
ঘ
(5, 7)

ব্যাখ্যা

Question: The midpoint of the line joining (10, 2) and (4, 8) is -

Solution:
The formula for the midpoint of (x₁, y₁) and (x₂, y₂) is
= ((x₁ + x₂)/2 , (y₁ + y₂)/2)

∴ The midpoint of the line joining (10, 2) and (4, 8) is
= (14/2 , 10/2)
= (7, 5)

১১,১০৫.

A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?

ক
ক) 72
খ
খ) 72.9
গ
গ) 73.8
ঘ
ঘ) 74.7

ব্যাখ্যা

Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n × T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.

১১,১০৬.

By what percentage above the cost price, a fan should be sold if a shopkeeper wants to make a profit of Tk. 500 and the marked price of the article is Tk 6000 which is 50% above the cost price?

ক
ক) 9.82%
খ
খ) 12.5%
গ
গ) 15.4%
ঘ
ঘ) 16.4%

ব্যাখ্যা

Question: By what percentage above the cost price, a fan should be sold if a shopkeeper wants to make a profit of Tk. 500 and the marked price of the article is Tk 6000 which is 50% above the cost price?

Solution:

Marked Price, MP = Tk. 6000, যা ক্রয়মূল্য (CP) এর ৫০ শতাংশ বেশি।
প্রশ্নমতে,

MP = CP + CP × 50%

=>MP = CP (1 + 50%)

=>MP = CP × 150/100

=>MP = CP × 1.5

=>6000 = CP × 1.5

=>CP= 6000 /1.5

=>CP= 4000

Cost price = Tk. 4000
Profit = Tk. 500

=> Profit%= 500 × 100%/4000 =12.5%

১১,১০৭.

The average temperature on Wednesday, Thursday and Friday was 25°. The average temperature on Thursday, Friday and Saturday was 24°. If the temperature on Saturday was 27°, what was the temperature on Wednesday?

ক
21°
খ
27°
গ
30°
ঘ
32°

ব্যাখ্যা

Question: The average temperature on Wednesday, Thursday and Friday was 25°. The average temperature on Thursday, Friday and Saturday was 24°. If the temperature on Saturday was 27°, what was the temperature on Wednesday?

Solution:

The total temperature on Wednesday, Thursday and Friday was 25° × 3 = 75°
The total temperature on Thursday, Friday and Saturday was 24° × 3 = 72°

Hence, the difference between the temperature on Wednesday and Saturday = 3°

If Saturday temperature =27°,
Then Wednesday's temperature = 27 + 3 = 30°

১১,১০৮.

An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If two marbles are drawn at random from the urn, what is the probability that both are red?

ক
ক) 1/6
খ
খ) 1/7
গ
গ) 2/15
ঘ
ঘ) 2/5

ব্যাখ্যা

Total number of balls = (6 + 4 + 2 + 3)
= 15.
Let,
E be the event of drawing 2 red balls.
Then,
n(E) = ⁶C₂
= (6 × 5)/(2 × 1)
= 15.
Also, n(S) = ¹⁵C₂
= (15 × 14)/(2 × 1)
= 105.
∴ P(E) = n(E)/n(S)
= 15/105
= 1/7.

১১,১০৯.

There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?

ক
364,500
খ
396,900
গ
45,000
ঘ
360,000

ব্যাখ্যা

Question: There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?

Solution:

From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold

Let,
x = number of hardback copies sold during this time

∴ 9x = number of paperback copies sold during this time

∴ x + 9x = total number of copies sold DURING THIS TIME PERIOD

A total of 441,000 copies of the novel were sold in all

36,000 hardback copies sold BEFORE the paperback version was issued.
So, we get:
36,000 + x + 9x = 441,000

⇒ 36,000 + 10x = 441,000

⇒ 10x = 405,000

∴ x = 40,500

∴ 9x = 9(40,500) = 364,500

∴ 364,500 paperback copies were sold

১১,১১০.

Titumir Express leave Rajshahi Central Station every day at 07.50 am and goes to Dinajpur Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio 1 : 4. The fare for this travel is in the ratio 3 : 1. The total fare collected was 224000 taka. What was the fare collected from I class passengers on that day?

ক
24000 taka
খ
48000 taka
গ
72000 taka
ঘ
96000 taka

ব্যাখ্যা

Let the number of passenger traveling by first class be x
Then, number of passenger traveling by second class will be 4x
But the fare is in the ratio 3 : 1
If 3y fare is collected per I class passenger, y would be collected per II class passenger
Fares of I class passengers : Fares of II class passengers
= x × 3y : 4x × y
= 3 : 4
If total fare is 3 + 4 = 7,
then I class passengers should pay 3 taka
Similarly,
we can calculate the fare of I class passengers when total was 224000 taka
Now, 7/3 = 224000/z(say)
or, z = 224000×3/7
or, z= 96000 taka

১১,১১১.

If sin A = 1/2 , then the value of cotA is -

ক
ক) 1/√3
খ
খ) √3
গ
গ) 1
ঘ
ঘ) √3/2

ব্যাখ্যা

Question: If sin A = 1/2 , then the value of cotA is -

Solution:
দেওয়া আছে,
sinA = 1/2

আমরা জানি,
cos²A = 1 - sin²A
= 1 - (1/2)²
= 1 - (1/4)
= (4 - 1)/4
= 3/4
∴ cosA = √(3/4)
= √3/2

এখন,
cotA = cosA/sinA
= (√3/2)/(1/2)
= √3

১১,১১২.

Between two consecutive years my incomes are in the ratio of 2 : 3 and expenses in the ratio 5 : 9. If my income in the second year is Tk. 45000 and my expenses in the first year is Tk. 25000 my total savings for the two years is -

ক
ক) Nil
খ
খ) Tk. 5000
গ
গ) Tk. 10000
ঘ
ঘ) Tk. 15000

ব্যাখ্যা

Let,
income in the first year be Tk. x and expenses in the second year be Tk. y
Then, x/45000 = 2/3 and 25000/y = 5/9
⇒ x = (2 × 45000)/3
= 30000
and y (25000 × 9)/5
= 45000.
∴ Total savings for 2 years
= Tk. [(30000 - 25000) + (45000 - 45000)]
= Tk. 5000.

১১,১১৩.

Twice the difference between two numbers is equal to their sum. If one number is 15, find the other number.

ক
5
খ
10
গ
15
ঘ
20

ব্যাখ্যা

Question: Twice the difference between two numbers is equal to their sum. If one number is 15, find the other number.

Solution:
Let,
Other number be x

ATQ,
x + 15 = 2(15 - x)
⇒ x + 15 = 30 - 2x
⇒ x + 2x = 30 - 15
⇒ 3x = 15
∴ x = 5

১১,১১৪.

What number divided by 50 gives 3.6%?

ক
ক) 1.8
খ
খ) 18
গ
গ) 180
ঘ
ঘ) None

ব্যাখ্যা

Question: What number divided by 50 gives 3.6%?

Solution:
3.6%
= 3.6/100
= 0.036

let, the number x

x / 50 = 0.036
⇒ x = 50 × 0.036
= 1.8

১১,১১৫.

A acquired an article at Tk. 200 and sold it to B with a 20% markup. B then sold it to C at a 10% markup. Find the amount C paid.

ক
Tk. 150
খ
Tk. 198
গ
Tk. 224
ঘ
Tk. 264

ব্যাখ্যা

Question: A acquired an article at Tk. 200 and sold it to B with a 20% markup. B then sold it to C at a 10% markup. Find the amount C paid.

Solution:
Price paid by B = 200 + (200/100 × 20) = 200 + 40 = 240

∴ Price paid by C = 240 + (240/100 × 10) = 240 + 24 = 264

Hence, Thus, the price at which C bought the article from B is: Tk. 264

১১,১১৬.

In a company of only 20 employees, 10 employees make Tk. 80,000/yr, 6 employees make Tk.150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is Tk. 175,000/yr, then what is the annual salary of each highest-paid employee?

ক
Tk. 350000
খ
Tk. 400000
গ
Tk. 450000
ঘ
Tk. 500000

ব্যাখ্যা

Question: In a company of only 20 employees, 10 employees make Tk. 80,000/yr, 6 employees make Tk.150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is Tk. 175,000/yr, then what is the annual salary of each highest-paid employee?

Solution:
Total salary = 20 × 175,000
= 3500000 taka

Salary of 4 highest-paid employees = 3500000 - 10 × 80000 - 6 × 150000
= 3500000 - 800000 - 900000
= 1800000

Each gets = 1800000/4
= Tk. 450000

১১,১১৭.

If a + b = 2, ab = 1 what is the value of (a, b)?

ক
ক) (1,1)
খ
খ) (2,1)
গ
গ) (1,3)
ঘ
ঘ) (2,2)

ব্যাখ্যা

Question: If a + b = 2, ab = 1 what is the value of (a, b)?

Solution:
Given that
a + b = 2...........(1)
ab = 1..................(2)

From (1)
b = 2 - a

Putting the value in (2), we get
a(2 - a) = 1
2a - a² = 1
2a = 1 + a²
a² - 2a + 1 = 0
(a - 1)²= 0
a - 1 = 0
a = 1

a = 1 Putting the value in (2), we get
1.b = 1
b = 1

(a, b) = (1,1)

১১,১১৮.

The price of a book is Tk. 200. Its price is increased by 15% and then decreased by 20%. What is the present price of the book?

ক
Tk. 184
খ
Tk. 154
গ
Tk. 164
ঘ
Tk. 170

ব্যাখ্যা

Question: The price of a book is Tk. 200. Its price is increased by 15% and then decreased by 20%. What is the present price of the book?

Solution:
Initial Cost = Tk. 200
After 15% increase in the cost, it becomes,
(200 + 15% of 200)
= 200 + 30
= Tk. 230

Now, Cost is decreased by 20%, So cost will become,
(230 - 20% of 230)
= 230 - 46
= Tk. 184

So, present cost is Tk. 184.

১১,১১৯.

If x = 2 + √5 and y = 2 - √5, find the value of x² + y².

ক
10
খ
15
গ
18
ঘ
8√5

ব্যাখ্যা

Question: If x = 2 + √5 and y = 2 - √5, find the value of x² + y².

Solution:
দেওয়া আছে,
x = 2 + √5
y = 2 - √5

∴ x + y = (2 + √5) + (2 - √5) = 4

এবং
xy = (2 + √5)(2 - √5)
= 2² - (√5)² = 4 - 5
= - 1

এখন,
x² + y²
= (x + y)² - 2xy
= (4)² - 2(- 1)
= 16 + 2
= 18

১১,১২০.

If log₃₂x = 0.8, then x is equal to -

ক
12
খ
10
গ
32
ঘ
16

ব্যাখ্যা

Question: If log₃₂x = 0.8, then x is equal to -

Solution:
log₃₂x = 0.8
⇒ 32^0.8 = x
⇒ (2⁵)^0.8 = x
⇒ (2⁵)^4/5 = x
⇒ 2⁴ = x
∴ x = 16

১১,১২১.

The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time do they meet?

ক
10 a.m.
খ
10:40 a.m.
গ
11 a.m.
ঘ
11: 20 a.m.

ব্যাখ্যা

Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time do they meet?

Solution:
Suppose they meet x hrs after = 8 a.m

Then,
[Distance moved by first in x hrs] + [Distance moved by second in (x - 1) hrs] = 330

Therefore, 60x + 75(x - 1) = 330
⇒ 60x + 75x - 75 = 330
⇒ 135x = 405
∴ x = 3

So,they meet at = (8 + 3)
= 11 a.m.

১১,১২২.

If the selling price is doubled, the profit triples. Find the profit percent.

ক
120%
খ
100 %
গ
130%
ঘ
140%

ব্যাখ্যা

Question: If the selling price is doubled, the profit triples. Find the profit percent.

Answer:
Let, Cost price = x taka
Selling price = y taka
Then, 3(y-x) = 2y-x
→ 3y- 2y = 3x- x
→ y = 2x
Then, Profit = (y- x) Taka = (2x- x) Taka
= x Taka
Profit percent =

= 100 %

১১,১২৩.

A family made a down payment of Tk. 7500 and borrowed the balance on a set of encyclopedias that cost Tk. 40000. The balance with interest was paid in 23 monthly payments of Tk. 1600 each and a final payment of Tk. 900. The amount of interest paid was what percent of the amount borrowed?

ক
16%
খ
14%
গ
12%
ঘ
6%

ব্যাখ্যা

Question: A family made a down payment of Tk. 7500 and borrowed the balance on a set of encyclopedias that cost Tk. 40000. The balance with interest was paid in 23 monthly payments of Tk. 1600 each and a final payment of Tk. 900. The amount of interest paid was what percent of the amount borrowed?

Solution:
Amount Borrowed = 40000 - 7500 = 32500

Total Balance with interest paid = 23 × 1600 + 900 = 37700
∴ Interest = 37700 - 32500 = 5200

∴ Percentage = (5200/32500) × 100 = 16%

১১,১২৪.

A certain factory employed 600 men and 400 women and the average wage was TK. 25.50 per day, If a woman got TK. 5 less than a man, then what are their daily wages?

ক
ক) m:25.50 w:27.50
খ
খ) m:27.50 w:22.50
গ
গ) m:26.50 w:27.50
ঘ
ঘ) m: 24.50 w:26.50
ঙ
ঙ) m:26.00 w:27.00

ব্যাখ্যা

Then, daily wage of a woman = TK. (x - 5).
Now,
600x + 400 (x - 5) = 25.50 × (600 + 400)
=> 1000x = 27500
=> x = 27.50.
Man's daily wages = TK. 27.50;
Woman's daily wages = (x - 5)
= TK. 22.50.

১১,১২৫.

a² - √5a + 1= 0 হলে, a² + (1/a²) এর মান কত?

ক
1
খ
2
গ
1/2
ঘ
2/3
ঙ
None

ব্যাখ্যা

প্রশ্ন: a² - √5a + 1= 0 হলে, a² + (1/a²) এর মান কত?

সমাধান:
a² - √5a + 1= 0
⇒ a² + 1 = √5a
⇒ (a²/a) + (1/a) = √5a/a
⇒ a + (1/a) = √5

এখন,
a² + (1/a²) = {a + (1/a)}²- 2 ⋅ a ⋅ (1/a)
= (√5)² - 2
= 5 - 2
= 3

১১,১২৬.

What least number must be added to 1056, So that the sum is completely divisible by 23?

ক
ক) 2
খ
খ) 3
গ
গ) 18
ঘ
ঘ) 21

ব্যাখ্যা

1056 ÷ 23, quotient = 45, remainder = 21
Since the remainder is not zero.
So, 1056 is not exactly divisible by 23
So, we take the next multiple of 23. Next multiple = 46
So, 23 X 46 = 1058
So, 1058 is exactly divisible by 23.
1958 - 1056 = 2
Hence, 2 is the least number to be added to 1056.

১১,১২৭.

A, B and C enter into a partnership investing Tk. 35000, Tk. 45000 and Tk. 55000 respectively. The share of A in an annual profit of Tk. 81,000 is

ক
ক) Tk. 21,000
খ
খ) Tk. 27,000
গ
গ) Tk. 33,000
ঘ
ঘ) Tk. 41,000

ব্যাখ্যা

A : B : C = 35000 : 45000 : 55000 = 7 : 9 : 11
sum of ratio = 7 + 9 + 11 = 27
A's share = 81,000 × 7/27 = 21,000

১১,১২৮.

A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -

ক
12 days
খ
14 days
গ
16 days
ঘ
18 days

ব্যাখ্যা

Question: A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -

Solution:
Let, A, B, and C take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively

Now,
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, A takes = 6 × 3 = 18 days

১১,১২৯.

The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is-

ক
ক) 4
খ
খ) 8
গ
গ) 16
ঘ
ঘ) Data inadequate

ব্যাখ্যা

The average of the remaining two numbers is = (8×14 - 6×16)/2 = 8

১১,১৩০.

If a : b = 4 : 3 then what is the value of (3a + 2b)/(3a - 2b).

ক
1
খ
6
গ
3
ঘ
2

ব্যাখ্যা

Question: If a : b = 4 : 3 then what is the value of (3a + 2b)/(3a - 2b).

Solution:
a : b = 4 : 3
a/b = 4/3
a = 4b/3

given,
(3a + 2b)/(3a - 2b)
= (4b + 2b)/(4b - 2b)
= 6b/2b
= 3

১১,১৩১.

and

, then what is the value of

ক
2
খ
4
গ
8
ঘ
6

ব্যাখ্যা

Question: If

and

, then what is the value of

?

Solution:
Given that,

⇒

১১,১৩২.

If log_x4 = 0.4, then the value of x is-

ক
ক) 4
খ
খ) 8
গ
গ) 16
ঘ
ঘ) 32

ব্যাখ্যা

Question: If log_x4 = 0.4, then the value of x is-

Solution:
Given that
log_x4 = 0.4
log_x4 = 4/10
log_x4 = 2/5
x^2/5 = 4
x = 4^5/2
x = (2²)^5/2
x = 2⁵
x = 32

১১,১৩৩.

A 9 cm × 8 cm × 15 cm block of ice is being melted to make identical ice cubes. If surface area any two sides of the cubes has to be 72cm² how many ice cubes can be made?

ক
3
খ
5
গ
7
ঘ
9
ঙ
11

ব্যাখ্যা

Question: A 9 cm × 8 cm × 15 cm block of ice is being melted to make identical ice cubes. If surface area any two sides of the cubes has to be 72cm² how many ice cubes can be made?

Solution:
বড় ব্লকের আয়তন = 9 × 8 × 15 = 1080 cm³

একটি ঘন আইস কিউবের সব পাশ সমান ⇒ প্রতিটি পাশে ক্ষেত্রফল হবে a²

তাহলে দুই পাশের মোট পৃষ্ঠের ক্ষেত্রফল,
2a² = 72
⇒ a² = 72/2 = 36
⇒ a² = 6²
∴ a = 6 cm

এবং প্রতিটি আইস কিউবের আয়তন = a³ = 6³ = 216 cm³

∴ মোট আইস কিউবের সংখ্যা = 1080/216 = 5টি

১১,১৩৪.

There is 90% increase in an amount in 9 years at simple interest. What will be the compound interest of Tk.1200 after 2 years at the same rate?

ক
ক) Tk. 696
খ
খ) Tk. 252
গ
গ) Tk. 196
ঘ
ঘ) Tk. 793

ব্যাখ্যা

If principal is Tk. 100
∴ Interest = 90% of Tk. 100 = Tk. 90
We know, interest, I = Pnr
Therefore, rate of interest, r = I/(Pn)
∴ Rate of Interest = 90 / (100 × 9) = 1/10 = (1/10) × 100% = 10%
Compound interest = 1200 × (1 + 10/100)² - 1200
= 1200 × 11/10 × 11/10 -1200
= 1452 -1200
= 252

১১,১৩৫.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

ক
11 days
খ
13 days
গ
20 (3/17) days
ঘ
25 days
ঙ
None of these

ব্যাখ্যা

Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.

Then,
10 : 13 :: 23 : x
=> x = (23 x 13)/10
=> x = 299.
A's 1 day's work = 1/23
B's 1 day's work = 10/299.

(A + B)'s 1 day's work = (1/23 + 10/299)
= 23/299
= 13.
Therefore, A and B together can complete the work in 13 days.

১১,১৩৬.

Find the rate of discount being given on a shirt whose selling price is Tk.546 after deducting a discount of Tk.104 on its marked price.

ক
18%
খ
10%
গ
16%
ঘ
20%
ঙ
None

ব্যাখ্যা

Question: Find the rate of discount being given on a shirt whose selling price is Tk.546 after deducting a discount of Tk.104 on its marked price.

Solution:
The price written on the item = 546 + 104 Tk.
= 650 Tk.

On 650 Taka, the commission is 104 Taka.
∴ Therefore, the commission on 100 Taka is (104 × 100)/650 Tk.
= 16 Tk.

১১,১৩৭.

In an acute angled triangle ABC, if cos 2(A + B - C) = 0 and cot (B + C - A) = √3,then the value of angle ∠B is-

ক
ক) 105°/2
খ
খ) 75°/2
গ
গ) 45°/2
ঘ
ঘ) 55°/2

ব্যাখ্যা

দেয়া আছে,
cos 2(A + B - C) = 0
cos 2(A + B - C) = cos 90°
2(A + B - C) = 90°
A + B - C = 45°................. (1)

cot (B + C - A) = √3
B + C - A = cot 30°
B + C - A = 30°....................(2)

(1) + (2) ⇒
A + B - C + B + C - A = 45° + 30°
2B = 75°
B = 75°/2

১১,১৩৮.

In your wallet, there are Tk 1000, Tk 500, and Tk 100 notes in the ratio 3 : 5 : 2, amounting to Tk 22,800. Find the number of each note respectively.

ক
12, 20, 10
খ
22, 10, 17
গ
12, 20, 8
ঘ
10, 18, 27

ব্যাখ্যা

Question: In your wallet, there are Tk 1000, Tk 500, and Tk 100 notes in the ratio 3 : 5 : 2, amounting to Tk 22,800. Find the number of each note respectively.

Solution:
Let,
The number of Tk 1000 notes is 3x
The number of Tk 500 notes is 5x
The number of Tk 100 notes is 2x

ATQ,
1000 × 3x + 500 × 5x + 100 × 2x = 22800
⇒ 3000x + 2500x + 200x = 22800
⇒ 5700x = 22800
⇒ x = 22800 / 5700
⇒ x = 4

Number of Tk 1000 note = 3x = 3 × 4 = 12
Number of Tk 500 note = 5x = 5 × 4 = 20
Number of Tk 100 note = 2x = 2 × 4 = 8

Therefore, the number of Tk 1000, Tk 500, and Tk 100 notes are respectively 12, 20, and 8.

১১,১৩৯.

The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is :

ক
ক) 35
খ
খ) 45
গ
গ) 55
ঘ
ঘ) 120

ব্যাখ্যা

Question: The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is :

Solution:
The average of five numbers is 27
The sum of five numbers is (27 × 5)
= 135

let, the excluded number is x

so,
(135 - x)/4 = 20
⇒ 135 - x = 80
⇒ x = 135 - 80
∴ x = 55

১১,১৪০.

Which number will complete the series:
6, 13, 25, 51, 101, ?

ক
50
খ
201
গ
202
ঘ
203

ব্যাখ্যা

Question: Which number will complete the series:
6, 13, 25, 51, 101, ?

Solution:
The pattern is 2n + 1, 2n - 1, 2n + 1, 2n - 1, ... ... ; [n = 6, 13, 25, 51, 101, ... ...]

Here,
(2 × 6) + 1 = 12 + 1 = 13
(2 × 13) - 1 = 26 - 1 = 25
.
.
.
So, missing term = (2 × 101) + 1 = 202 + 1 = 203

১১,১৪১.

If 8 workers can finish a job in 24 days, how many days will it take 12 workers to complete the same job, assuming they all work at the same rate?

ক
12 days
খ
16 days
গ
21 days
ঘ
18 days

ব্যাখ্যা

Question: If 8 workers can finish a job in 24 days, how many days will it take 12 workers to complete the same job, assuming they all work at the same rate?

Solution:
8 workers can complete the work in 24 days
∴ 1 worker can complete the work in = 8 × 24 days = 192 days

∴ 12 workers can complete the work in = 192/12 days
= 16 days

∴ It will take 12 workers 16 days to complete the same job.

১১,১৪২.

Two pipes A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are open together to fill the tank in 15 minutes, find the capacity of the tank?

ক
ক) 160 gallons
খ
খ) 150 gallons
গ
গ) 120 gallons
ঘ
ঘ) 60 gallons

ব্যাখ্যা

Work done by the C pipe in 1 minute
= 1/15 − (1/20 + 1/24)
= (1/15 − 11/120)
= −1/40 [−ve means emptying]
∴ Volume of 1/ 40 part = 3 gallons.
Volume of whole = (3 × 40) gallons = 120 gallons.

১১,১৪৩.

The distance between two points (- 6, y) and (18, 6) is 26 units. Find the value of y.

ক
4
খ
- 10
গ
3
ঘ
- 4

ব্যাখ্যা

Question: The distance between two points (- 6, y) and (18, 6) is 26 units. Find the value of y.

Solution:
Given that,
The distance between two point = 26 units
The value of the first co-ordinate = (x₁, y₁) = (- 6, y)
The value of the second co-ordinate = (x₂, y₂) = (18, 6)

We know,
Distance = √{(x₂ - x₁)²+ (y₂ - y₁)²}

According to the question,
26 = √{(18 - (- 6))² + (6 - y)²
⇒ 24² + (6 - y)² = 26² ;[Squaring on both sides of the equation.]
⇒ 576 + (6 - y)² = 676
⇒ (6 - y)² = 100 = 10²
⇒ 6 - y = 10
⇒ y = 6 - 10
∴ y = - 4

∴ The required answer is - 4.

১১,১৪৪.

P is 25% more efficient than Q. How much time will they, working together, take to complete a job which Q alone could have done in 27 days?

ক
8 days
খ
15 days
গ
18 days
ঘ
12 days

ব্যাখ্যা

Question: P is 25% more efficient than Q. How much time will they, working together, take to complete a job which Q alone could have done in 27 days?

Solution:
P, Q এর থেকে 25% বেশি দক্ষ।
⇒ P : Q = 125 : 100 = 5 : 4

Q এক দিনে কাজ করে = 4 ইউনিট
P এক দিনে কাজ করে = 5 ইউনিট

মোট কাজ = Q এর দৈনিক কাজ × Q এর দিন
= 4 × 27 = 108 ইউনিট

একসাথে এক দিনে কাজ করে = 5 + 4 = 9 ইউনিট

তাহলে কাজ শেষ করতে সময় লাগবে = 108 ÷ 9 দিন
= 12 দিন

সুতরাং, P এবং Q একত্রে কাজটি শেষ করতে 12 দিন সময় নেবে।

১১,১৪৫.

একটি কোম্পানি 'ক' মোট p টাকা লাভ করেছিল। লাভের অর্ধেক কোম্পানির প্রতিষ্ঠাতা পাওয়ার পর বাকি অর্ধেক সমানভাবে তাঁর চারজন অংশীদারের মধ্যে ভাগ করে দেয়া হয়। p-এর হিসেবে, প্রতিটি অংশীদার কত টাকা পেয়েছিলো?

ক
p/2
খ
p/6
গ
2p
ঘ
3p
ঙ
p/8

ব্যাখ্যা

প্রশ্ন: একটি কোম্পানি 'ক' মোট p টাকা লাভ করেছিল। লাভের অর্ধেক কোম্পানির প্রতিষ্ঠাতা পাওয়ার পর বাকি অর্ধেক সমানভাবে তাঁর চারজন অংশীদারের মধ্যে ভাগ করে দেয়া হয়। p-এর হিসেবে, প্রতিটি অংশীদার কত টাকা পেয়েছিলো?

সমাধান:
এখানে, কোম্পানি 'ক' এর মোট লাভ = p টাকা

প্রতিষ্ঠাতা পায় লাভের অর্ধেক = p/2

∴ বাকি লাভ = (p − p/2) টাকা
= p/2 টাকা

বাকি অংশ 4 জন অংশীদারের মধ্যে সমানভাবে ভাগ করা হয়,
∴ প্রতিজন অংশীদার পায় = (p/2)/4
= (p/2) × (1/4)
= p/8

১১,১৪৬.

If A : B = 3 : 4, C : B = 5 : 4, C : D = 10 : 9, then A : B : C : D = ?

ক
6 : 8 : 12 : 9
খ
6 : 8 : 10 : 9
গ
11 : 8 : 10 : 9
ঘ
6 : 8 : 10 : 15

ব্যাখ্যা

A : B = 3 : 4 = 6 : 8
B : C = 4 : 5 = 8 : 10
C : D = 10 : 9
A : B : C : D = 6 : 8 : 10 : 9

১১,১৪৭.

Maruf was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know one third of my age". What is the age of maruf?

ক
48 years
খ
54 years
গ
56 years
ঘ
None of the above

ব্যাখ্যা

প্রশ্ন: Maruf was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know one third of my age". What is the age of maruf?

সমাধান:

Let the age of maruf = x years

Then,

⇒ 3(x + 3) - 3(x - 3) = x

⇒ 3x + 9 - 3x + 9 = x

⇒ x = 18

ATQ,
x/3 = 18
∴ x = 18 × 3 = 54 years

∴ The age of maruf is 54 years.

১১,১৪৮.

Find the single discount equivalent to a series discount of 30%, 20% and 10%.

ক
46.9%
খ
51.07%
গ
56.49%
ঘ
50%
ঙ
49.6%

ব্যাখ্যা

Let marked price be Tk. 100

Therefore, selling price = 90%, 80% and 70% of Tk. 100

Selling price = (90/100) × (80/100) × (70/100) × 100 = 50.4

Selling Price = Tk. 50.4

Required discount = Marked Price – Selling Price

= 100 – 50.4

= 49.6%

১১,১৪৯.

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

ক
Tk. 15
খ
Tk. 21
গ
Tk. 18
ঘ
Tk. 12

ব্যাখ্যা

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

Solution:
Dividend on Tk. 20 = Tk. (9/100) × 20 = Tk. 9/5

Tk. 12 is an income on Tk. 100.
∴ Tk. 9/5 is an income on = Tk. (100 × 9)/(12 × 5)
= Tk.15

১১,১৫০.

Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?

ক
ক) 6.52
খ
খ) 8.14
গ
গ) 4.18
ঘ
ঘ) 5.02

ব্যাখ্যা

Distance to be covered = πD = 40π km
Relative speed of bikers = 16 + 14 = 30 kmph.
Now, time = distance/speed = 40π/30
= 4.18 hrs.

১১,১৫১.

The ratio of length and breadth of a rectangular park is 4 : 2. If a cat running along the boundary of the park at the speed of 18 km/hr completes one round in 10 minutes, find the area of the park in square meters.

ক
50000 sq. m.
খ
45000 sq. m.
গ
68000 sq. m.
ঘ
55000 sq. m.
ঙ
None of these

ব্যাখ্যা

Question: The ratio of length and breadth of a rectangular park is 4 : 2. If a cat running along the boundary of the park at the speed of 18 km/hr completes one round in 10 minutes, find the area of the park in square meters.

Solution:
One round of the park is equal to the perimeter of the park.
So, by completing one round, the cat covers a distance equal to the perimeter of the park.
Now,
Distance or perimeter = speed × time
= 18 × (10/60)
= 3 km
= 3000 meters

Let Length = 4x and breadth = 2x
So, Perimeter:
2(4x + 2x) = 3000
⇒ 8x + 4x = 3000
⇒ 12x = 3000
∴ x = 3000/12 = 250 meters

So, Length = 4 × 250 = 1000 meters
And, Breadth = 2 × 250 = 500 meters

Area = Length × Breadth
= 1000 × 500
= 500000 sq. m.

১১,১৫২.

A train 150m long passes a pole in 15 seconds and crosses another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train in (km/h) is -

ক
ক) 60 km/hr
খ
খ) 66 km/hr
গ
গ) 72 km/hr
ঘ
ঘ) 99 km/hr

ব্যাখ্যা

Speed of the first train :
= 150/15 = 10 m/s
Time taken by trains to cross each other = 8 s
And, relative speed of two trains :
= (150+150)/8 = 37.5
∴ Speed of the second train :
= (37.5 - 10) × 18/5
= 99 km/h

১১,১৫৩.

A town's population increased by 1200 people, and then this new population decreased 11%. The town now had 32 less people than it did before the 1200 increase. Find the original population.

ক
10000
খ
11000
গ
12000
ঘ
13000

ব্যাখ্যা

Question: A town's population increased by 1200 people, and then this new population decreased 11%. The town now had 32 less people than it did before the 1200 increase. Find the original population.

Solution:
Let,
the population = P
So, the increased population will be = P + 1200
The population after 11% decrease in population becomes = P − 32

Therefore,
P − 32 = (P + 1200) − (11/100)(P + 1200)
⇒ p - 32 = (100p + 120000 - 11p - 13200)/100
⇒ 89p + 106800 = 100p - 3200
⇒ 89p - 100p = - 3200 - 106800
⇒ - 11p = - 110000
∴ p = 10000

So, the total population is 10000.

১১,১৫৪.

Insert the missing number in the given series: 8, 7, 11, 12, 14, 17, 17, 22,....

ক
20
খ
22
গ
18
ঘ
19

ব্যাখ্যা

Qyestion: Insert the missing number in the given series: 8, 7, 11, 12, 14, 17, 17, 22, ....

Solution:
These are two series
1^st series odd positions terms = 8, 11, 14, 17, 20 increasing by 3.

and
2^nd even positions terms = 7, 12, 17, 22 increasing by 5.

The 9th term is in an odd position, so it follows the first pattern = 17 + 3 = 20

১১,১৫৫.

The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?

ক
ক) 29
খ
খ) 70
গ
গ) 92
ঘ
ঘ) Can not be determined

ব্যাখ্যা

Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 63
⇔ 9 (x - y) = 63
x - y = 7.
There are several numbers like this, e.g. 70-07, 81-18 and 92-29. Thus, the correct answer is - ঘ) Can not be determined

তবে, ঘ) Can not be determined এই অপশন না থাকলে 29 কে উত্তর হিসেবে নেয়া যেত।

১১,১৫৬.

The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?

ক
7 : 3
খ
1 : 5
গ
7 : 9
ঘ
9 : 2
ঙ
3 : 2

ব্যাখ্যা

Question: The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?

Solution:
Let,
son's age 10 years ago be x years.
Then, father’s age 10 years ago = 3x years.

Son's present age = (x + 10) years
Father's present age = (3x + 10) years.

according to the question,
(3x + 10) + 10 = 2 (x + 10 + 10)
⇒ 3x + 20 = 2 (x + 20)
⇒ 3x + 20 = 2x + 40
∴ x = 20

Ratio of present ages of father and the son
= (3x + 10)/(x + 10)
= {(3 × 20) + 10}/(20 + 10)
= 70/30
= 7 : 3

১১,১৫৭.

A committee of 5 members is to be formed by selecting out of 6 men and 7 women. What is the probability that the committee has exactly 2 men and 3 women?

ক
ক) 175/429
খ
খ) 140/429
গ
গ) 315/429
ঘ
ঘ) 1/2

ব্যাখ্যা

Question: A committee of 5 members is to be formed by selecting out of 6 men and 7 women. What is the probability that the committee has exactly 2 men and 3 women?

Solution:
Total member = 6 + 7 = 13
2 men can be selected out of 6 men in ⁶C₂ ways
3 women can be selected out of 7 women in ⁷C₃ ways
Required number of ways = ⁶C₂ × ⁷C₃ = 15 × 35 = 525

The total number of ways to make committee with all members = ¹³C₅ = 1287

∴ The probability that the committee has exactly 2 men and 3 women = 525/1287
= 175/429

১১,১৫৮.

A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35,000, A receives-

ক
Tk. 8400
খ
Tk. 12500
গ
Tk. 14700
ঘ
Tk. 15000

ব্যাখ্যা

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

Solution:
let, C subscribes x taka
B subscribes x + 5000 taka
A subscribes x + 5000 + 4000
= x + 9000 taka

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

A receives = {(x + 9000)/50000} × 35000
= (21000/50000) × 35000
= 14700 taka

১১,১৫৯.

A train, having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train -

ক
ক) 8 seconds
খ
খ) 4 seconds
গ
গ) 10 seconds
ঘ
ঘ) 6 seconds

ব্যাখ্যা

Distance = 110 meter.
Since the train and man move in opposite directions, the relative speed
= (60 + 6) km/hr.
= 66 km/hr.
= 66 × (5/18) m/s.
= 110/6 m/s.
Time = 110/(110/6)
= 6 seconds.

১১,১৬০.

If m² - 2m = 1, then m³ - 1/m³ =?

ক
2
খ
8
গ
10
ঘ
14

ব্যাখ্যা

Question: If m² - 2m = 1, then m³ - 1/m³ =?

Solution:
Given that,
m² - 2m = 1
⇒ m² - 1 = 2m
∴ m - 1/m = 2

Now,
m³ - 1/m³
= (m - 1/m)³+ 3.m.(1/m)(m - 1/m)
= (2)³ + 3 × 2
= 8 + 6
= 14

১১,১৬১.

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?

ক
4/13
খ
2/13
গ
1/2
ঘ
3/13

ব্যাখ্যা

Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?

Solution:
Total card = 52
Total face card = (4 + 4 + 4) = 12

∴ Probability = Number of face cards/Total number of cards = 12/52 = 3/13

১১,১৬২.

A collection of books went on sale and 2/3 of them was sold for Tk 2.30 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?

ক
ক) 165.6
খ
খ) 180
গ
গ) 135.6
ঘ
ঘ) 90

ব্যাখ্যা

Remaining books = 1 - 2/3 = 1/3
1/3 of the books = 36 books
So, 2/3 of the books = 36×(2/3) / (1/3) = 72

∴ Total amount received for the sold books = 72 x 2.30 = 165.6 TK

১১,১৬৩.

Rajan got married 10 years ago. His present age is (6/5) times of his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marrige. The present age of Rajan's sister is = ?

ক
ক) 40 year
খ
খ) 50 year
গ
গ) 60 year
ঘ
ঘ) 70 year

ব্যাখ্যা

Question: Rajan got married 10 years ago. His present age is (6/5) times of his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marrige. The present age of Rajan's sister is = ?

Solution:
Present age of Rajan is = x year

x = (6/5) (x - 10)
⇒ 5x = 6x - 60
⇒ 6x - 5x = 60
⇒ x = 60 years

at time of marriage, rajan's age is 60 - 10 = 50 years
at time of marriage, rajan's sister age is = 50 - 10 years = 40 years

∴ The present age of rajan's sister age is = 40 + 10 = 50 year

১১,১৬৪.

Which of the following numbers is a divisor of (49¹⁵ - 1)?

ক
8
খ
14
গ
48
ঘ
50

ব্যাখ্যা

Question: Which of the following numbers is a divisor of (49¹⁵ - 1)?

Solution:
aⁿ - bⁿ is divisible by (a + b) when n is an even positive integer.
Here, a & b should be prime number.

(49¹⁵ - 1)
⇒ {(7²)¹⁵ - 1)
⇒ (7³⁰ - 1)
Here, 30 is a positive integer.
According to the concept, (7³⁰ - 1) is divisible by (7 + 1) i.e., 8.
∴ 8 is a divisor of (49¹⁵ - 1).

১১,১৬৫.

Sarah sold her bicycle for Taka. 5000 while making a profit of Taka. 570. Then what is the price at which she bought that cycle?

ক
3330 Taka
খ
3430 Taka
গ
4000 Taka
ঘ
4430 Taka

ব্যাখ্যা

Question: Sarah sold her bicycle for Taka. 5000 while making a profit of Taka. 570. Then what is the price at which she bought that cycle?

Solution:
Given,
Selling Price (SP) = Taka. 5000
Profit = 570 Taka
Thus, Cost Price = Selling Price - Profit
⇒ Cost Price = 5000 - 570
⇒ Cost Price = 4430 Taka
Thus, cost price of the bicycle is Taka 4430

১১,১৬৬.

A box contains 10 balls, of which 3 are red and the rest are blue. How many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all 6 balls of the same color?

ক
168
খ
124
গ
268
ঘ
328

ব্যাখ্যা

Question: A box contains 10 balls, of which 3 are red and the rest are blue. How many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all 6 balls of the same color?

Solution:
Six balls can be selected in the following ways,
One red ball and 5 blue balls
Or Two red balls and 4 blue balls.
Total number of ways,
= (³C₁ × ⁷C₅) + (³C₂ × ⁴C₇)
= 63 + 105
= 168

১১,১৬৭.

Which is the smallest fraction?

ক
ক) 5/13
খ
খ) 18/36
গ
গ) 16/31
ঘ
ঘ) 4/12

ব্যাখ্যা

Question: Which is the smallest fraction?

Solution:
5/13 = 0.385

18/36
= 1/2
= 0.5

16/31
= 0.516

4/12
= 1/3
= 0.33

So, 4/12 is the smallest fraction.

১১,১৬৮.

A man travels a certain distance at a rate of 20 miles an hour and returns at the rate of 30 miles an hour. What is his average speed?

ক
ক) 24
খ
খ) 25.5
গ
গ) 25
ঘ
ঘ) None

ব্যাখ্যা

Question: A man travels a certain distance at a rate of 20 miles an hour and returns at the rate of 30 miles an hour. What is his average speed?

Solution:
ধরি, x মিটার দূরত্ব অতিক্রম করে।
x মিটার যেতে সময় লাগে x/20 ঘণ্টা
x মিটার ফিরে আসতে সময় লাগে x/30 ঘণ্টা

∴ গড় গতিবেগ = মোট দূরত্ব / মোট সময়
= x + x / (x/20) + (x/30)
= 2x/(3x + 2x)/60
= 2x/5x/60
= 24 km/hr

১১,১৬৯.

In a mixture of 35 liters, milk and water are in the ratio of 3:4. How much milk would be added to the mixture to make the ratio equal?

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

ব্যাখ্যা

Question: In a mixture of 35 liters, milk and water are in the ratio of 3:4. How much milk would be added to the mixture to make the ratio equal?

Solution:
amount of milk
= (3/7)*35
= 15 litres
amount of water
= (4/7)*35
= 20 litres

the amount of milk to be added is
= (20-15)
= 5 litres.

১১,১৭০.

If the second term in an arithmetic sequence is 4 and the tenth term is 15, what is the first term in the sequence?

ক
ক) 1.18
খ
খ) 1.27
গ
গ) 1.38
ঘ
ঘ) 2.63

ব্যাখ্যা

Here, Second term is = a + (2 - 1)d = 4
∴ a + d = 4 ...... (i)
and, Tenth term is = a + (10 - 1) = 15
∴ a + 9d = 15 ...... (ii)
Now, (i)×9 - (ii),
8a = 21
∴ a = 2.625 ≅ 2.63

১১,১৭১.

If n/23 is 2 more than m/23, then n = ?

ক
m + 23
খ
m - 41
গ
m + 46
ঘ
m + 42

ব্যাখ্যা

Question: If n/23 is 2 more than m/23, then n = ?

Solution:
n/23 = (m/23) + 2
⇒ n/23 = (m + 46)/23
∴ n = m + 46

১১,১৭২.

Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

ক
1000
খ
850
গ
972
ঘ
1260

ব্যাখ্যা

Question: Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
72% of x = (3/4) of x - 30
⇒ 72x/100 = (3x/4) - 30
⇒ 18x/25 = (3x/4) - 30
⇒ (3x/4) - (18x/25) = 30
⇒ (75x - 72x)/100 = 30
⇒ 3x/100 = 30
⇒ 3x = 3000
⇒ x = 3000/3
∴ x = 1000

So, the number is 1000

১১,১৭৩.

Junayed purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

ক
5000
খ
6000
গ
4000
ঘ
7000

ব্যাখ্যা

Question: Junayed purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

Solution:
Let the cost price of each of the articles = 100.
The selling price of the first articles = 120
and the selling price of the second articles = 122.5
The difference in the selling price = 122.5 - 120 = 2.5

The difference in the selling price = 2.5 if the cost price = 100
If the difference in selling price = 150, then the cost price = (150 × 100)/2.5 = 6000

১১,১৭৪.

A, B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000 resp. The respective share of A, B and C in an annual profit of Tk 40500 are.

ক
Tk. 10500, Tk. 12500, Tk. 16500
খ
Tk. 10500, Tk. 13500, Tk. 15500
গ
Tk. 10500, Tk. 13500, Tk. 16500
ঘ
Tk. 11500, Tk. 13500, Tk. 16500

ব্যাখ্যা

Question: A, B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000 resp. The respective share of A, B and C in an annual profit of Tk 40500 are.

Solution:
A : B : C = 35000 : 45000 : 55000
= 7 : 9 : 11
Now, we are having the ratio. to get the share, first make total of above ratio. then get each share.

A's Share = 40500 × (7/27) = Tk. 10500
B's Share = 40500 × (9/27) = Tk. 13500
C's Share = 40500 × (11/27) = Tk. 16500

১১,১৭৫.

Kawser travelled 4/7 as many miles on foot as by water and 2/5 as many miles on horseback as by water. If he covered total of 3036 miles, how many miles did he travel on foot?

ক
860 miles
খ
880 miles
গ
840 miles
ঘ
820 miles

ব্যাখ্যা

Question: Kawser travelled 4/7 as many miles on foot as by water and 2/5 as many miles on horseback as by water. If he covered total of 3036 miles, how many miles did he travel on foot?

Solution:
Suppose Kawser travelled x miles by water, 4x/7 miles on foot and 2x/5 miles on horseback.

ATQ,
x + 4x/7 + 2x/5 = 3036
⇒ 69x/35 = 3036
⇒ x = (3036 × 35)/69
∴ x = 1540

∴ Distance travelled on foot :
=(4 ×1540)/7 miles
= 880 miles

১১,১৭৬.

A 180 metre long train crosses a platform thrice its length in 40 seconds. What is the speed of the train in km/hr?

ক
ক) 54.8 km/hr
খ
খ) 58.8 km/hr
গ
গ) 62.8 km/hr
ঘ
ঘ) 64.8 km/hr

ব্যাখ্যা

Length of train = 180 m
Length of platform = (3 ×180)m = 540m

∴Speed of train (180 + 540)/40 m/sec
= 720/40 m/sec
= 18 × (18/5) km/hr
= 64.8 km/hr

১১,১৭৭.

A train running at the speed of 60 kmph crosses a 200m long platform in 27 seconds. What is the length of the train?

ক
ক) 220 metres
খ
খ) 250 metres
গ
গ) 180 metres
ঘ
ঘ) 350 metres

ব্যাখ্যা

Speed = 60 × (1000/3600)m/sec
= 50/3m/sec

Time = 27 sec

Let the length of the train be x metres
Now
(x + 200)/27 = 50/3
3(x + 200) = (27 × 50)
3x + 600 = 1350
3x = 1350 - 600
3x = 750
x = 250

১১,১৭৮.

A rectangular water tank is 8 m high, 6 m long and 2.5m wide. How many liters of water can it hold?

ক
1,30,000 litre
খ
1,10,000 litre
গ
1,25,000 litre
ঘ
1,20,000 litre

ব্যাখ্যা

Question: A rectangular water tank is 8 m high, 6 m long and 2.5m wide. How many liters of water can it hold?

Solution:
Volume = length × width × height
= (6 × 2.5 × 8) m³
= 120 m³

1 m³ = 1000 litre
120 m³ = 120 × 1000 litre
= 1,20,000 litre

১১,১৭৯.

Quantity A = (- 6)⁴and Quantity B = (- 6)⁵

ক
ক) Quantity A is greater
খ
খ) Quantity B is greater
গ
গ) Two quantities are equal
ঘ
ঘ) The relationship indeterminate
ঙ
ঙ) None of these

ব্যাখ্যা

Question: Quantity A = (- 6)⁴and Quantity B = (- 6)⁵Solution:
Quantity A = (- 6)⁴= 1296

Quantity B = (- 6)⁵
= - 7776

∴ Quantity A is greater.

১১,১৮০.

Rina and Trina walk from same point in opposite directions at the rate 3 km/hr and 2 km/hr respectively. How far will they be from each other after 3 hrs?

ক
ক) 9 km
খ
খ) 12 km
গ
গ) 15 km
ঘ
ঘ) 18 km

ব্যাখ্যা

Question: Rina and Trina walk from same point in opposite directions at the rate 3 km/hr and 2 km/hr respectively. How far will they be from each other after 3 hrs?

Solution:
Since Rina and Trina walk in opposite directions.
Distance covered per hour = Relative speed × Time
= (3 + 2) × 1 = 5 km [opposite direction]

∴ Distance covered in 3 hours = 5 × 3 = 15 km.

১১,১৮১.

What will be the water image of the word “CONFIDENT”?

ব্যাখ্যা

Question: What will be the water image of the word “CONFIDENT”?

Solution:
CONFIDENT শব্দটির পানিতে প্রতিবিম্ব হবে:

সঠিক উত্তর: ঘ

১১,১৮২.

Present population of a city is 90 lac. What will be the population of the city after 3 years if the growth rate of population of that city is 40 per thousand?

ক
1,00,94,665
খ
1,01,23,776
গ
1,03,83,568
ঘ
1,04,93,306

ব্যাখ্যা

Question: Present population of a city is 90 lac. What will be the population of the city after 3 years if the growth rate of population of that city is 40 per thousand?

Solution:
Given,
Present population of the city is P = 90,00,000
growth rate of population, r = (40/1000) × 100%
= 4%
time n = 3 years

Here, in the case of growth of population, formula for compound principal is applicable
∴ C = P(1 + r)ⁿ
= 90,00,000(1 + 4/100)³
= 90,00,000(104/100)³
= 90,00,000 × (104/100) × (104/100) × (104/100)
= 9 x 104 x 104 x 104
= 1,01,23,776

১১,১৮৩.

The solutions of 2x² + 3x - 2 = 0 are

ক
ক) x = -3 and x = 2
খ
খ) x = 1/2 and x = -2
গ
গ) x = -1 and x = 2
ঘ
ঘ) x = 1 and x = - 2

ব্যাখ্যা

2x² + 3x - 2 = 0
Or, 2x² + 4x - x - 2 = 0
Or, 2x(x+2) - 1(x+2) = 0
Or, (2x - 1)(x + 2) = 0
Either, (2x - 1) = 0 Or, (x + 2) = 0
x = 1/2, -2

১১,১৮৪.

A and B undertook to do a piece of work for Tk. 4,500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of money is -

ক
ক) Tk. 950
খ
খ) Tk. 850
গ
গ) Tk. 750
ঘ
ঘ) Tk. 650

ব্যাখ্যা

Time taken by A to do the work = 8 days
Time taken by B to do the work = 12 days
Time taken by A, B and C together to do the work = 4 days

Calculation:
Let the total work be LCM (8, 12, 4).

LCM (8, 12, 4) = 24 unit

In one day A do = 24/8 unit
⇒ 3 unit

In one day B do = 24/12 unit
⇒ 2 unit

In one day A, B and C do = 24/4 unit
⇒ 6 unit

In one day only C do = 6 - (3 + 2)
⇒ 1 unit

The proportion of their shares = A's 1-day work : B's 1-day work : C's 1-day work
⇒ 3 : 2 : 1

According to the question,
Total share = 4500
⇒ 6 unit = 4500
⇒ 1 unit = 750

So, C's share = Tk. 750

∴ The C’s share of the money is Tk. 750.

১১,১৮৫.

A student has 7 pants and 8 shirts. The number of ways in which he can wear the dress in different combinations is -

ক
ক) 52
খ
খ) 56
গ
গ) 54
ঘ
ঘ) 58

ব্যাখ্যা

প্রশ্ন : A student has 7 pants and 8 shirts. The number of ways in which he can wear the dress in different combinations is -

সমাধান:

No. of shirts =8
No. of pants =7
No. of ways he can wear his clothes = No. of ways he can wear a shirt AND No. of ways to wear pant =8×7= 56

১১,১৮৬.

If the sum of two numbers is 36, and their HCF and LCM are 3 and 105 respectively, what is the sum of the reciprocals of the two numbers?

ক
3/35
খ
4/35
গ
6/37
ঘ
2/33

ব্যাখ্যা

Question: If the sum of two numbers is 36, and their HCF and LCM are 3 and 105 respectively, what is the sum of the reciprocals of the two numbers?

Solution:
Let, the numbers be a and b.

Then, a + b = 36 and ab = 3 × 105 = 315 [∵ Product of the numbers = HCF×LCM]

∴ sum of their reciprocals
= (1/a) + (1/b)
= (a + b)/ab
= 36/315
= 4/35

১১,১৮৭.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

ক
Tk. 3972
খ
Tk. 3980
গ
Tk. 3575
ঘ
Tk. 3950

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

Solution:
Given that,
Increase in amount after 6 years = 60%

We know,
A = P(1 + r/100)ⁿsimple Interest = (principal × rate × time)/100

Now,
Let the amount at 1^st year be 100x
∴ Increased in amount = 60% of 100x = 60x
⇒ 60x = (100x × 6 × r)/100
⇒ 6r = 60
⇒ r = 60/6 = 10
∴ r = 10%

∴ Compound Interest after 3 years = P(1 + r/100)ⁿ- P
= 12000(1 + 10/100)³ - 12000
= 12000 × (11/10)³ - 12000
= 12000 × (11/10) × (11/10) × (11/10) - 12000
= 15972 - 12000
= Tk. 3972

∴ The required answer is Tk. 3972

১১,১৮৮.

Salma's average in four tests is 80%. What mark does she need to score in her fifth test to make her average 84%?

ক
100%
খ
94%
গ
84%
ঘ
96%
ঙ
None of these

ব্যাখ্যা

Question: Salma's average in four tests is 80%. What mark does she need to score in her fifth test to make her average 84%?

Solution:
Total score on 4 tests = 80 × 4 = 320
Total score on 5 tests = 84 × 5 = 420

The score in the fifth test is = 420 - 320
= 100 or 100%

১১,১৮৯.

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

ক
ক) 1/13
খ
খ) 2/13
গ
গ) 4/13
ঘ
ঘ) 1/26

ব্যাখ্যা

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

১১,১৯০.

Solve the inequality (3x - 8)/(x + 7) > 8

ক
(- 64/5, - 7)
খ
(- 7, 0)
গ
(- 7, 7)
ঘ
(- 5, 7)
ঙ
None of these

ব্যাখ্যা

Question: Solve the inequality (3x - 8)/(x + 7) > 8

Solution:

The solution is x ∈ (- 64/5, - 7)

১১,১৯১.

A batsman scores 72 runs in the 18th innings and increases his average by 2. What is his average after the 18th innings?

ক
38
খ
35
গ
40
ঘ
32

ব্যাখ্যা

Question: A batsman scores 72 runs in the 18th innings and increases his average by 2. What is his average after the 18th innings?

Solution:
ধরি,
17 তম ইনিংসে তার গড় রান = x
∴ মোট রান = 17x

18 তম ইনিংসে 72 রান করায় তার গড় 2 রান বৃদ্ধি পায়।
∴ নতুন গড় = x + 2
∴ মোট রান = 18(x + 2)

প্রশ্নমতে,
17x + 72 = 18(x + 2)
⇒ 17x + 72 = 18x + 36
⇒ 18x - 17x = 72 - 36
⇒ x = 36

∴ 18 তম ইনিংস পর নতুন গড় = x + 2
= 36 + 2 = 38 রান

১১,১৯২.

Johny's Tennis Camp is open only to teenagers- all campers must be between 13 and 19 years old, inclusive. Which of the following inequalities can be used to determine if a person who is y years old is eligible to attend the camp?

ক
।y - 13। ≤ 6
খ
।y । ≤ 3
গ
।y - 19। ≤ 13
ঘ
।y - 16। ≤ 3

ব্যাখ্যা

Question: Johny's Tennis Camp is open only to teenagers- all campers must be between 13 and 19 years old, inclusive. Which of the following inequalities can be used to determine if a person who is y years old is eligible to attend the camp?

Solution:
13 ≤ y ≤ 19
⇒ 13 - 16 ≤ y - 16 ≤ 19 - 16
⇒ - 3 ≤ y - 16 ≤ 3
⇒ ।y - 16। ≤ 3

১১,১৯৩.

The smallest number added to 680621 to make the sum a perfect square is:

ক
4
খ
5
গ
6
ঘ
8

ব্যাখ্যা

Question: The smallest number added to 680621 to make the sum a perfect square is:

Solution:
এখানে
(825)² = 825 × 825
= 680625

প্রদত্ত সংখ্যা = 680621
নির্ণেয় ক্ষুদ্রতম সংখ্যা = (680625 - 680621) = 4

১১,১৯৪.

A mixture of 30litre of sprit and water contains 20% water. How much water must be added to the mixture to raise the percentage of water to 25%

ক
2 litre
খ
3 litre
গ
8 litre
ঘ
None

ব্যাখ্যা

Question: A mixture of 30 litre of sprit and water contains 20% water. How much water must be added to the mixture to raise the percentage of water to 25%

Solution:
20 লিটার মিশ্রণে পানি আছে = (30 এর 20/100) = 6 লিটার

∴ স্পিরিট আছে = 30 - 6 = 24 লিটার

এখন নতুন মিশ্রণে পানি থাকবে 25 ভাগ এবং স্পিরিট থাকবে 75 ভাগ ।

প্রশ্নমতে,
⇒ 24/(6 + x) = 75/25
⇒ 24/(6 + x) = 3
⇒ 18 + 3x = 24
⇒ 3x = 24 - 18
⇒ 3x = 6
⇒ x = 6/3
∴ x = 2

∴ ২ লিটার পানি মিশ্রণে যোগ করতে হবে।

১১,১৯৫.

An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If three marbles are picked up at random, what is the probability that 2 are blue and 1 is yellow ?

ক
ক) 18/455
খ
খ) 13/411
গ
গ) 17/423
ঘ
ঘ) 23/117

ব্যাখ্যা

Total number of marbles = (6 + 4 + 2 + 3) = 15
Let E be the event of drawing 2 blue and 1 yellow marble.
Then, n(E) = ⁴C₂× ³C₁
=(4 × 3)/(2 × 1) × 3
= 18
Also, n(S) = ¹⁵C₃ = 15 × 14 × 13/(3 × 2 × 1)
= 455
∴P(E) = n(E)/n(S) = 18/455

১১,১৯৬.

Find the polynomial equation of the lowest degree in terms of a whose roots are -3 and 8.

ক
a² + 9a - 24 = 0
খ
a² - 6a - 18 = 0
গ
a² - 12a + 24 = 0
ঘ
a² - 5a - 24 = 0

ব্যাখ্যা

Question: Find the polynomial equation of the lowest degree in terms of a whose roots are -3 and 8.

Solution:
Let,
The roots are α = - 3 and β = 8 .
Thus, the corresponding polynomial equation is,
⇒ a² - (α + β)a + αβ = 0
⇒ a² - (- 3 + 8)a + (- 3)8 = 0
⇒ a² - 5a - 24 = 0

১১,১৯৭.

The monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves BDT 30 per month, what would be the total amount of their monthly income?

ক
240
খ
300
গ
540
ঘ
600

ব্যাখ্যা

Question: The monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves BDT 30 per month, what would be the total amount of their monthly income?

Solution:
Let,
Their monthly income = 4a and 5a
Their monthly expenses = 7b and 9b

According to the conditions,
4a - 7b = 30 . . . . . (1)
5a - 9b = 30 . . . . . (2)

Multiply equation (1) and (2) by 9 and 7 respectively,
36a - 63b = 270 . . . . (3)
35a - 63b = 210 . . . . (4)

(3) - (2) ⇒
36a - 63b -35a + 63b = 270 - 210
⇒ a = 60

Hence, their total income = 4 × 60 + 5 × 60 tk
= 540

So, the total amount of their monthly income is 540 tk.

১১,১৯৮.

A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train?

ক
300 meters
খ
400 meters
গ
375 meters
ঘ
425 meters

ব্যাখ্যা

Question: A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train?

Solution:
Speed = 90 km/h = (90 × 1000)/3600 = 25 m/s

We know,
Length = speed × time = 25 × 15 = 375 meters

So the length of the train is 375 meters.

১১,১৯৯.

What percentage of the whole week does Rakibul spend in office, if his office hours are 9 am to 5 pm from Sunday to Thursday?

ক
23.81%
খ
33.33%
গ
42.23%
ঘ
25.5%

ব্যাখ্যা

Question: What percentage of the whole week does Rakibul spend in office, if his office hours are 9 am to 5 pm from Sunday to Thursday?

Solution:
Percentage = {(5 × 8)/(7 × 24)} × 100%
= (5/21) × 100%
= 23.81%

১১,২০০.

Three numbers are in the ratio 1 : 2 : 3 and their H.C.F 14. The smallest number is-

ক
ক) 14
খ
খ) 28
গ
গ) 42
ঘ
ঘ) 84

ব্যাখ্যা

Given that
The ratio of three numbers 1 : 2 : 3
Let the numbers be x, 2x and 3x.
The HCF in x, 2x and 3x is x

Hence,
x = 14;

The smallest number is 14