Bank Math

PrepBank · পাতা ১৩ / ১৬১ · ১,২০১–১,৩০০ / ১৬,১২৪

১,২০১.

The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?

ক
30
খ
48
গ
60
ঘ
96

ব্যাখ্যা

Question:

The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?

Solution:
From the figure it follows that,
2x - 2 = 3x - 8
∴ x = 6.

The area = (1/2) × (base) × (height)
= (1/2) × (3x - 2) × x
= (1/2) × 16 × 6
= 48.

১,২০২.

The LCM and HCF of two numbers is 1820 and 26. If one number is 130 then the other number is?

ক
ক) 364
খ
খ) 1690
গ
গ) 70
ঘ
ঘ) 1264

ব্যাখ্যা

প্রশ্ন: দুটি সংখ্যার ল.সা.গু এবং গ.সা.গু যথাক্রমে 1820 এবং 26 । একটি সংখ্যা 130 হলে অপর সংখ্যাটি কত?

সমাধান:
ধরি,
অপর সংখ্যাটি = p
আমরা জানি,
দুটি সংখ্যার গুণফল = ল.সা.গু × গ.সা.গু
130p = 1820 × 26
p = (1820 × 26)/130
= 364

১,২০৩.

Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

ক
6 hours
খ
8 hours
গ
9 hours
ঘ
10 hours

ব্যাখ্যা

Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Solution:
Let,
the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours

ATQ,
{1/x + 1/(x + 6)} = 1/4
⇒ (x + 6 + x)/{x(x + 6)} = 1/4
⇒ (2x + 6)/(x² + 6x) = 1/4
⇒ (x² + 6x) = 8x + 24
⇒ x² + 6x - 8x - 24 = 0
⇒ x² - 2x - 24 = 0
⇒ x² - 6x + 4x - 24 = 0
⇒ x(x - 6) + 4(x - 6) = 0
⇒ (x - 6)(x + 4) = 0
⇒ x = 6 or - 4
∴ x = 6 [neglecting the negative value of x]

∴ the cistern be filled by pipe A alone in 6 hours

১,২০৪.

A sum of money amounts to Tk 9800 after 5 years and Tk. 12005. after 8 years at the same rate of simple interest. The rate of interest per annum is -

ক
15%
খ
12%
গ
8%
ঘ
5%

ব্যাখ্যা

Question: A sum of money amounts to Tk 9800 after 5 years and Tk. 12005. after 8 years at the same rate of simple interest. The rate of interest per annum is -

Solution:
Simple interest for 3 years
= 12005 - 9800 = 2205
Simple interest for 5 years
= (2205/3) × 5 = 3675

Some of money = 9800 - 3675 = 6125

∴ Rate of interest = (100 × 2205)/(6125 × 3)
= 12%

১,২০৫.

The number of terms between 11 and 200 which are divisible by 7 but not by 3 is -

ক
ক) 18
খ
খ) 19
গ
গ) 27
ঘ
ঘ) 28

ব্যাখ্যা

Multiple of 7 between 11 and 200 are 14, 21, 28, 35, 42,....., 189, 196
T_m = 196 ⇒ 14 + (m - 1) × 7 = 196
⇒ (m - 1) × 7 = 182
⇒ (m - 1) = 26
⇒ m = 27.
Multiples of 7 and 3 both i.e. that of 21 are 21, 42, 63,......., 189
T_n = 189
⇒ 21 + (n - 1) × 21 = 189
⇒ (n - 1) × 21 = 168
⇒ (n - 1) = 8
⇒ n = 9.
Required number of terms = (27 - 9) = 18
Answer : 18

১,২০৬.

The area of the largest triangle that can be inscribed in a semi-circle of radius r, is-

ক
2r²
খ
r³
গ
2r³
ঘ
r²

ব্যাখ্যা

Question: The area of the largest triangle that can be inscribed in a semi-circle of radius r, is-

Solution:
Largest triangle inscribed in a semicircle has,
Base = diameter of semicircle = 2r
Height = radius = r (vertex at the top of the semicircle)

We know,
Area of triangle = (1/2) × base × height
= (1/2) × 2r × r
= r²

১,২০৭.

The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

ক
23 years
খ
22 years
গ
20 years
ঘ
21 years

ব্যাখ্যা

Question: The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

Solution:
Let the present age of the son = x
Then, the present age of the mother = (60 - x)

As per question:
Six years ago mother's age was 5 times the age of her son:
So, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 84 = 6x
⇒ x = 84/6
∴ x = 14 Years

Age of son after 6 years
= x + 6
= 14 + 6
= 20 Years

১,২০৮.

Find the value of

ক
9
খ
6
গ
12
ঘ
7

ব্যাখ্যা

Question: Find the value of .

Solution:

১,২০৯.

ক
ক) 17
খ
খ) 19
গ
গ) 361
ঘ
ঘ) 21

ব্যাখ্যা

Question:

Solution:
এখানে,
√27225 = 165
√38416 = 196

এখন,

= √(165 + 196)
= √361
= 19

১,২১০.

The sum of ages of Jamal, Kamal and Rashed is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is present of Rashed?

ক
ক) 34 years
খ
খ) 36 years
গ
গ) 38 years
ঘ
ঘ) 40 years

ব্যাখ্যা

10 years ago age of Jamal = 2x
10 years ago age of Kamal= 3x
10 years ago age of Rashed= 4x

Now
2x + 10 + 3x + 10 + 4x + 10 = 93
9x + 30 = 93
9x = 93 - 30
9x = 63
x = 7

∴present age of Rashed = (4 × 7) + 10
= 28 + 10
=38 years

১,২১১.

Probability of 3 students solving a question are 1/2, 1/3, and 1/4. Probability to solve the question is:

ক
1/4
খ
3/4
গ
1/2
ঘ
7/12

ব্যাখ্যা

Question: Probability of 3 students solving a question are 1/2, 1/3, and 1/4. Probability to solve the question is:

Solution:
Probability of 3 students,
P(A) = 1/2, ∴ P(A′) = 1/2
P(B) = 1/3, ∴ P(B′) = 2/3
P(C) = 1/4, ∴ P(C′) = 3/4

So, Probability of no one solve the question is = (1/2) × (2/3) × (3/4)
= 1/4
∴ P(None) = 1/4

Then, The probability to solve the question is = 1 - 1/4
= 3/4
Hence, the correct answer is 3/4.

১,২১২.

If tan(θ + 30°) = √3, what is the value of sinθ?

ক
1
খ
1/√2
গ
1/2
ঘ
0

ব্যাখ্যা

Question: If tan(θ + 30°) = √3, what is the value of sinθ?

Solution:
Given that,
tan(θ + 30°) = √3
⇒ tan(θ + 30°) = tan 60°
⇒ θ + 30° = 60°
⇒ θ = 60° - 30°
⇒ θ = 30°

Now,
sinθ
= sin 30°
= 1/2

১,২১৩.

A ferry can carry 24 buses or 36 cars at a time. If there are 18 buses on the ferry, how many cars can be loaded onto it?

ক
6
খ
8
গ
9
ঘ
12

ব্যাখ্যা

Question: A ferry can carry 24 buses or 36 cars at a time. If there are 18 buses on the ferry, how many cars can be loaded onto it?

Solution:
Here,
24 buses = 36 cars
∴ 1 bus = 36/24 cars
∴ 18 buses = (36 × 18)/24 cars
= 27 cars

∴ Required number of cars = 36 - 27 = 9 cars

১,২১৪.

How many degrees are between the hands of a clock at 4 : 26?

ক
23°
খ
29°
গ
35°
ঘ
55°

ব্যাখ্যা

Question: How many degrees are between the hands of a clock at 4 : 26?

Solution:
Value of angle = {(11 × 26) - (60 × 4)}/2
= (286 - 240)/2
= 46/2
= 23°

১,২১৫.

Five years ago, Kalam’s age was twice that of his daughter's age and the present age of Kalam and his daughter is in the ratio of 11:6 respectively. What is Kalam's age?

ক
55
খ
53
গ
57
ঘ
54

ব্যাখ্যা

Let K be Kalam's age and D be his daughter's age
Five years ago, K-5 = 2(D-5)
K - 2D = -5 ....(1)
and their ages are in the ratio 11:6.
i.e., K/D = 11/6
6K = 11D
⇒ K = 11D/6 ....(2)
Sub. K = 11D/6 in (2)
⇒ (11D/6) - 2D = -5
⇒ 11D - 12D = -30
⇒ -D = -30
⇒ D=30
Thus, the age of his daughter is 30 years.
Now, K = 11 x 30/6 = 55 years
Hence the age of Kalam is 55 years.

১,২১৬.

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

ক
1/3
খ
2/5
গ
3/5
ঘ
3/7

ব্যাখ্যা

Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

Solution:
Total number of balls
= (8 + 7 + 6)
= 21

Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue
= 7/21
= 1/3

১,২১৭.

The fourth proportional of the values 2.1, 3.5, 5.4 is

ক
ক) 7.5
খ
খ) 8.6
গ
গ) 9.0
ঘ
ঘ) 6.0

ব্যাখ্যা

Given:
2.1, 3.5, 5.4

Formula Used:
If a : b :: c : d
then a × d = b × c

a : b :: c : d,
⇒ 2.1 : 3.5 :: 5.4 : d
⇒ 2.1 × d = 3.5 × 5.4
⇒ d = 9.0

∴ The required answer is 9.0

১,২১৮.

P and Q are two positive integers such that PQ = 60. Which of the following cannot be the value of P + Q?

ক
16
খ
19
গ
20
ঘ
23

ব্যাখ্যা

Question: P and Q are two positive integers such that PQ = 60. Which of the following cannot be the value of P + Q?

Solution:
60-এর উৎপাদক জোড়াগুলো হল:
1 × 60 = 60 ⇒ P + Q = 1 + 60 = 61
2 × 30 = 60 ⇒ P + Q = 2 + 30 = 32
3 × 20 = 60 ⇒ P + Q = 3 + 20 = 23
4 × 15 = 60 ⇒ P + Q = 4 + 15 = 19
5 × 12 = 60 ⇒ P + Q = 5 + 12 = 17
6 × 10 = 60 ⇒ P + Q = 6 + 10 = 16

সুতরাং, P + Q এর সম্ভাব্য মানগুলো: 16, 17, 19, 23, 32, 61.

তাই, P + Q = 20 হতে পারে না।

১,২১৯.

At simple interest of 5%, 6% and 8% for three consecutive years, the interest earned is Tk. 760. Find The principle?

ক
ক) Tk. 4,000
খ
খ) Tk. 4,600
গ
গ) Tk. 3,200
ঘ
ঘ) Tk. 3,600

ব্যাখ্যা

ধরি,
আসল x টাকা

প্রশ্নমতে,
{( x×1×5) +(x×1×6 )+(x×1×8)} /100 = 760
(5x +6x +8x) /100 = 760
19x/100 = 760
x = (760 × 100)/19
= 4000

১,২২০.

3²⁰ + 3²⁰ + 3²⁰ = ?

ক
3²¹
খ
3²³
গ
3⁶⁰
ঘ
9²⁰

ব্যাখ্যা

Question: 3²⁰ + 3²⁰ + 3²⁰ = ?

Solution:
3²⁰ + 3²⁰ + 3²⁰
= 3 × 3²⁰
= 3¹^{+ 20}
= 3²¹

১,২২১.

A manufacturer sells three products i.e. A, B and C. Product A costs 200 and sells for 250. Product B costs 150 and sells for 180. Product C costs 100 and sells for 115. On which product, he has maximum percentage of profit?

ক
ক) A only
খ
খ) C only
গ
গ) A and C both
ঘ
ঘ) B only

ব্যাখ্যা

Question: A manufacturer sells three products i.e. A, B and C. Product A costs 200 and sells for 250. Product B costs 150 and sells for 180. Product C costs 100 and sells for 115. On which product, he has maximum percentage of profit?

Solution:
Product A’s percentage of profit = {(250 - 200)/200} × 100 = 25%
Product B’s percentage of profit = {(180 - 150)/150} × 100 = 20%
Product C’s percentage of profit = {(115 - 100)/100} × 100 = 15%

So, only product A has the highest profit margin.

১,২২২.

A specific bank branch serves 256 clients on average every day. The ratio between tellers and clients is 1 : 32, so that every teller serves 32 people on average every day. The management wishes to change this ratio to 1 : 20. How many new tellers should be hired?

ক
4
খ
5
গ
9
ঘ
12

ব্যাখ্যা

Question: A specific bank branch serves 256 clients on average every day. The ratio between tellers and clients is 1 : 32, so that every teller serves 32 people on average every day. The management wishes to change this ratio to 1 : 20. How many new tellers should be hired?

Question:

First, let's determine the approximate number of tellers in the branch. We will term this number X

Clients/tellers = 256/X = 32/1

⇒ 256 = 32X

∴ X = 8

There are currently 8 tellers working in the branch.

Let,
needed teller number be Y

Clients/tellers = 256/Y = 20/1

⇒ 256 = 20Y

∴ Y = 12.8

Since we cannot have a fraction as the number of tellers, we will round this number down to 13.

∴ New tellers should be hired 13 - 8 = 5

১,২২৩.

An amount of Tk 10000 becomes Tk 11025 in 1 year if the interest is compounded half-yearly. What is the rate of compound interest per annum?

ক
7%
খ
8%
গ
9%
ঘ
10%

ব্যাখ্যা

Question: An amount of Tk 10000 becomes Tk 11025 in 1 year if the interest is compounded half-yearly. What is the rate of compound interest per annum?

Solution:
Let the compound interest be r

ATQ,
10000 × {1 + (r/2)}² = 11025
⇒ {(2 + r)/2}² = 11025/10000
⇒ (2 + r)/2 = 105/100 [applying square root]
⇒ 2 + r = 210/100
⇒ 200 + 100r = 210
⇒ 100r = 10
⇒ r = 10/100
⇒ r = (10/100) × 100%
⇒ r = 10%

১,২২৪.

The length of the bridge, which a train 130 meters long and travelling at 46.8 km/hr can cross in 30 seconds, is:

ক
ক) 260 m
খ
খ) 250 m
গ
গ) 245 m
ঘ
ঘ) 265 m

ব্যাখ্যা

Question: The length of the bridge, which a train 130 meters long and travelling at 46.8 km/hr can cross in 30 seconds, is:

Solution:
Let,
The length of the bridge is x meter

∴ The train has to travel 130 + x meter to cross the bridge.

The velocity of the train 46.8 km/hr
= (46.8 × 1000)/3600 m/s
= 13 m/s

The train travels in 1 second 13 meters
∴ The train travels in 30 seconds (13 × 30) meters
= 390 meters

Now,
130 + x = 390
⇒ x = 390 - 130
∴ x = 260

∴The length of the bridge is 260 meters

১,২২৫.

If 4 years ago the ratio between the ages of Nuha and Naba was 5 : 6 and the sum of their ages at present is 52. What is the ratio of their present ages ?

ক
3 : 8
খ
4 : 7
গ
6 : 7
ঘ
5 : 9

ব্যাখ্যা

Question : If 4 years ago the ratio between the ages of Nuha and Naba was 5 : 6 and the sum of their ages at present is 52. What is the ratio of their present ages ?

Solution :
Let
Four years ago, Nuha's age was = 5x
and Naba's age was = 6x

According to the question,
(5x + 4) + (6x + 4) = 52
⇒ 11x + 8 = 52
⇒ 11x = 52 - 8
⇒11x = 44
∴ x = 4

∴ Present age of Nuha = 5x + 4
= 5 × 4 + 4
= 24

∴ Present age of Naba = 6x + 4
= 6 × 4 + 4
= 28

So the ratio of their present ages = 24 : 28
= 6 : 7

১,২২৬.

How many shares of market value Tk. 25 each can be purchased for Tk.15300, brokerage being 2% ?

ক
ক) 450
খ
খ) 400
গ
গ) 550
ঘ
ঘ) 600

ব্যাখ্যা

CP of each share = Tk. (25 + 2% of 25) = Tk. 25.50.

Number of shares= 15300/25.50
= 600

১,২২৭.

Tickets numbered 1 to 25 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a prime number or a multiple of 5?

ক
11/20
খ
13/20
গ
17/25
ঘ
13/25

ব্যাখ্যা

Question: Tickets numbered 1 to 25 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a prime number or a multiple of 5?

Solution:
Given,
Total number = 25
Prime number between 1 to 25 = {2, 3, 5, 7, 11, 13, 17, 19, 23}
A multiple of 5 between 1 to 25 = {5,10, 15, 20, 25}

∴ Prime number or a multiple of 5 between 1 to 25 = {2, 3, 5, 7, 10, 11, 13, 15, 17, 19, 23, 20, 25} = 13 numbers

So, Probability = 13/25

১,২২৮.

Two numbers are in the ratio 5:4 and their difference is 10. What is the smallest number?

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

ব্যাখ্যা

Given ratio = 5 : 4
Let the numbers are 5x and 4x
ATQ, 5x - 4x = 10
So, x = 10
∴ Smallest number = 4×10 = 40

১,২২৯.

40 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture. Find how many litres water will be added?

ক
ক) 3 litres
খ
খ) 5 litres
গ
গ) 6 litres
ঘ
ঘ) 8 litres

ব্যাখ্যা

Water in the mixture = 40×(10/100) = 4 litres
And, Milk in the mixture = 40 − 4 = 36 litres
Let x litres of water is mixed
⇒ (4 + x)/(40 + x) = 20/100
⇒ x = 5 litres

১,২৩০.

In a throw of a coin, find the probability of getting a head?

ক
ক) 1/3
খ
খ) 1/6
গ
গ) 1/2
ঘ
ঘ) 1/4
ঙ
ঙ) None of the above

ব্যাখ্যা

No explanation added.

১,২৩১.

In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by b -

ক
21 m
খ
26 m
গ
28 m
ঘ
29 m

ব্যাখ্যা

A : B = 100 : 75
B : C = 100 : 96

∴ A : C = A/B × B/C
= (100/75) × (100/96)
= 100/72
100 : 72

∴ A beats C by
100 - 72 = 28 m.

১,২৩২.

Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

ক
ক) 1/4
খ
খ) 1/2
গ
গ) 1/3
ঘ
ঘ) 1/8

ব্যাখ্যা

Here S = {TTT, TTH,THT, HTT, THH, HTH, HHT, HHH}.
Let,
E = event of getting at least two heads
= {THH, HTH, HHT, HHH}.
∴ P(E) = n(E)/n(S)
= 4/8
= 1/2.

১,২৩৩.

What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years?

ক
Tk. 2325
খ
Tk. 1825
গ
Tk. 3225
ঘ
Tk. 4225

ব্যাখ্যা

Question: What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years?

Solution:
Compound Principal = 10000(1 + 15/100)²
= 10000 × (115/100)²
= (10000 × 115 × 115)/(100 × 100)
= 13225

∴ Compound interest = 13225 - 10000 = 3225

১,২৩৪.

A building contractor undertook to finish a certain work in 162 days and employed 150 men. After 72 days, he found that he already done 2/3 of the work. How many men can be discharged now, so that the work finish in time?

ক
ক) 70
খ
খ) 75
গ
গ) 80
ঘ
ঘ) 90

ব্যাখ্যা

Question: A building contractor undertook to finish a certain work in 162 days and employed 150 men. After 72 days, he found that he already done 2/3 of the work. How many men can be discharged now, so that the work finish in time?

Solution:
2/3 of the work done in 72 days by 150 men
∴ Day remaining = 162 - 72 = 90 days

Work remaining = 1- (2/3) = 1/3

In 72 days 2/3 of the work can be done by 150 men
In 1 day 1 of the work can be done by (150 × 3 × 72)/2 men
In 90 days 1/3 of the work can be done by = (150 × 3 × 72)/(2 × 3 × 90) men
= 60 men

∴ The number of men can be discharged = 150 - 60 = 90 men

১,২৩৫.

The present age of Mr. Sanyal is three times the age of his son. After six years, the ratio of their ages will be 5 : 2. What is the present age of Mr. Sanyal?

ক
45
খ
48
গ
50
ঘ
54
ঙ
59

ব্যাখ্যা

Let the son's age be x years ,
Therefore, Mr. Sanyal's age = 3x years
According to the question,
(3x + 6)/(x + 6) = 5/2 or, x = 18
∴ Present age of Mr. Sanyal = 3x years = (3 × 18) years = 54 years

১,২৩৬.

36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]. Simplify the expression.

ক
20
খ
21
গ
22
ঘ
23

ব্যাখ্যা

Question: 36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]. Simplify the expression.

Solution:
36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]
= 36 - [18 - {14 - (15 - 2 × 2)}]
= 36 - [18 - {14 - (15 - 4)}]
= 36 - [18 - {14 - 11}]
= 36 - [18 - 3]
= 36 - 15
= 21

১,২৩৭.

A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.

ক
0 kmph , 5 kmph
খ
5 kmph , 5 kmph
গ
15 kmph , 5 kmph
ঘ
10 kmph , 5 kmph
ঙ
None of these

ব্যাখ্যা

Question: A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.

Solution:
If a is rate downstream and b is rate upstream
Rate in still water = (a + b)/2
Rate of current = (a - b)/2

Rate in still water = (20 + 10)/2 = 15 kmph
Rate of current = (20 - 10)/2 = 5 kmph

১,২৩৮.

(21 - 30) : Read the following questions carefully and choose the right answer.
21. The diameters of two circles are the side of a square and the diagonal of the square. The ratio of the area of the smaller circle and the larger circle is-

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

ব্যাখ্যা

ABCD বর্গের বাহুর দৈর্ঘ্য a
ABCD বর্গের কর্ণের দৈর্ঘ্য = a√2

P বৃত্তের ব্যাস = a
P বৃত্তের ব্যাসার্ধ = a/2

Q বৃত্তের ব্যাস = a√2
Q বৃত্তের ব্যাসার্ধ = a√2/2 = a/√2

P এবং Q বৃত্তের ক্ষেত্রফলের অনুপাত = π(a/2)² : π(a/√2)²
= 1/4 : 1/2
= 1 : 2

১,২৩৯.

A and B invest in a business in the ratio 7 : 3. If 20% of the total profit goes to charity and B's share is TK 12000, the total profit is-

ক
30,000 taka
খ
40,000 taka
গ
50,000 taka
ঘ
60,000 taka

ব্যাখ্যা

Question: A and B invest in a business in the ratio 7 : 3. If 20% of the total profit goes to charity and B's share is TK 12000, the total profit is-

Solution:
মনে করি,
মোট লাভ 100 টাকা
20% দান করার পর থাকে = (100 - 100 এর 20%) = 80 টাকা

80 টাকার মধ্যে B পাবে = 80 × (3/10) = 24 টাকা

24 টাকা পায় যখন মোট লাভ 100 টাকা
∴ 12000 টাকা পায় যখন মোট লাভ = (12000 × 100)/24 = 50,000 টাকা

১,২৪০.

ক
0
খ
12
গ
112
ঘ
None of these

ব্যাখ্যা

Question:

Solution:
Here,
Mean = 20
Number of observation = 10

১,২৪১.

A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?

ক
ক) 96.66 mph
খ
খ) 100 mph
গ
গ) 106.66 mph
ঘ
ঘ) 160 mph

ব্যাখ্যা

প্রশ্ন: A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?

সমাধান:
Distance covered in 4 hours = 4 × 40 miles
= 160 miles

Speed required to cover the same distance in 1.5 hours = 160/1.5 mph
= 106.66 mph

১,২৪২.

If dividing P(x) = 4x³ - 7x² + bx - 5 by (x - 3) results the remainder 10, then find the value of b.

ক
5
খ
6
গ
-10
ঘ
-12

ব্যাখ্যা

Question: If dividing P(x) = 4x³- 7x² + bx - 5 by (x - 3) results the remainder 10, then find the value of b.

Solution:
According to the Remainder Theorem, if a polynomial P(x) is divided by (x - c), then the remainder = P(c).
Here divisor is (x - 3).
So remainder = P(3).

Now,
P(3) = 4(3)³ - 7(3)² + b(3) - 5

= 4 × 27 - 7 × 9 + 3b - 5

= 108 - 63 + 3b - 5

= 40 + 3b

According to the question, the remainder is 10.
So, 40 + 3b = 10

⇒ 3b = 10 - 40
⇒ 3b = - 30
⇒ b = - 10

১,২৪৩.

If A's salary is 30% more than B's, then how much percent is B's salary less than A's?

ক
ক) 30
খ
খ) 25
গ
গ) 300/13
ঘ
ঘ) 100/3

ব্যাখ্যা

Question: If A's salary is 30% more than B's, then how much percent is B's salary less than A's?

Solution:
ধরি, B এর বেতন ১০০ টাকা
A এর বেতন = ১০০ + ৩০
= ১৩০ টাকা

b এর বেতন কম = ১৩০ - ১০০
= ৩০ টাকা

B এর বেতন A থেকে শতকরা কম = (৩০/১৩০)× ১০০%
= (৩০০/১৩)%

১,২৪৪.

A person who has an income of Tk. 10,000 pays what percent of his or her income in taxes?

ক
ক) 2%
খ
খ) 2.2%
গ
গ) 2.5%
ঘ
ঘ) 3%

ব্যাখ্যা

Question: A person who has an income of Tk. 10,000 pays what percent of his or her income in taxes?

Solution:
১০০০০ টাকা ইনকাম থাকলে কর দিতে হবে = ১৪০ + (৮০০০ টাকার বেশি ইনকামের ৪%)
= ১৪০ + (১০০০০ - ৮০০০) এর ৪%
= ১৪০ + ৮০
= ২২০ টাকা

২২০ টাকা ১০০০০ টাকার = (২২০/১০০০০) × ১০০%
= ২.২%

১,২৪৫.

If 4x - y = 6 and 2x + 3y = 10 find the value of 2x + 5y.

ক
14
খ
12
গ
10
ঘ
8

ব্যাখ্যা

Question: If 4x - y = 6 and 2x + 3y = 10 find the value of 2x + 5y.

Solution:
4x - y = 6 ------------ (1)
2x + 3y = 10 ---------- (2)

Multiplying equ (1) by 2
8x - 2y = 12 --------- (3)

(2) + (3) ⇒
2x + 3y = 10
8x - 2y = 12
10x + y = 22
y = 22 - 10x --------- (4)

Putting the value of y in (2)
2x + 3(22 - 10x) = 10
⇒ 2x + 66 - 30x = 10
⇒ - 28x = 10 - 66
⇒ - 28x = - 56
∴ x = 2

Putting x = 2 in (4),
y = 22 - 10 × 2
⇒ y = 22 - 20
∴ y = 2

Now, 2x + 5y = 2 . 2 + 5 . 2 = 4 + 10 = 14

১,২৪৬.

The average of 5 consecutive number integers starting with m as the first integer is n. Then n =?

ক
2m + 2
খ
5m
গ
m + 2
ঘ
mn + 2

ব্যাখ্যা

Question: The average of 5 consecutive number integers starting with m as the first integer is n. Then n =?

Solution:
দেয়া আছে,
প্রথম সংখ্যাটি = m

প্রশ্নমতে
{m + (m +1) + (m + 2) + (m + 3) + (m + 4)}/5 = n
⇒ m + m + 1 + m + 2 + m + 3 + m + 4 = 5n
⇒ 5m + 10 = 5n
⇒ 5n = 5(m + 2)
⇒ n = m + 2

১,২৪৭.

The ratio between the speeds of two trains is 7 : 8 . If the second train runs 400 km in 4 hours, What is the speed of the first train?

ক
86.5
খ
87.5
গ
88.5
ঘ
89.5
ঙ
90.5

ব্যাখ্যা

Let the speed of the trains be 7 x and 8 x respectively.
Speed of second train = 400 /4 = 100 km/hr
⇒ 8 x = 100
⇒ x = 100/8 = 12.5
Speed of the first train = 7x = 7 × 12.5
= 87.5 km/hr

১,২৪৮.

Which of the following fractions is greater than 3/4 and less than 5/6?

ক
ক) 2/3
খ
খ) 4/5
গ
গ) 9/10
ঘ
ঘ) 1/2

ব্যাখ্যা

3/4 = 0.75
5/6 = 0.83
2/3 = 0.667
4/5 = 0.80
9/10 = 0.9
1/2 = 0.50

So, the fraction 4/5 is greater than 3/4 and less than 5/6

১,২৪৯.

একজন ব্যক্তি স্থির পানিতে ঘণ্টায় ৫ কি.মি. যেতে পারে। যদি স্রোতের বেগ ১ কি.মি/ঘণ্টা হয় তাহলে একটি নির্দিষ্ট স্থানে গিয়ে ফিরে আসতে ২ ঘণ্টা সময় লাগে। স্থানটির দূরত্ব কত?

ক
ক) ৪.৮ কি.মি
খ
খ) ৩.৬ কি.মি
গ
গ) ২.৪ কি.মি
ঘ
ঘ) ৬.১২ কি.মি

ব্যাখ্যা

প্রশ্ন: একজন ব্যক্তি স্থির পানিতে ঘণ্টায় ৫ কি.মি. যেতে পারে। যদি স্রোতের বেগ ১ কি.মি/ঘণ্টা হয় তাহলে একটি নির্দিষ্ট স্থানে গিয়ে ফিরে আসতে ২ ঘণ্টা সময় লাগে। স্থানটির দূরত্ব কত?

সমাধান:
ধরি ,
স্থানটির দূরত্ব x কি.মি.

স্রোতের অনুকূলে গতিবেগ = ৫ + ১ = ৬ কি.মি./ঘণ্টা
স্রোতের প্রতিকূলে গতিবেগ = ৫ - ১ = ৪ কি.মি./ঘণ্টা

প্রশ্নমতে,
(x /৪) + (x /৬) = ২
(৩x + ২x)/১২ = ২
৫x /১২ = ২
৫x = ২৪
x = ২৪ /৫
x = ৪.৮ কি.মি।

১,২৫০.

The average of 6 numbers is 25. If 3 more numbers, with an average of 22 are added to these numbers, what will be the average of the combined 9 numbers?

ক
ক) 24
খ
খ) 25
গ
গ) 26
ঘ
ঘ) 28

ব্যাখ্যা

Sum of 6 numbers = (6 × 25) = 150.
Sum of 3 additional numbers = (3 × 22) = 66.
Sum of (6 + 3) =9 numbers = (150 + 66) = 216
∴ average of the combined 9 numbers = 216/9 = 24

১,২৫১.

If a= √3/2, then √(1 + a) + √(1 - a)= ?

ক
ক) √3
খ
খ) 2 - √3
গ
গ) 2 + √3
ঘ
ঘ) √3/2

ব্যাখ্যা

let
√(1 +a) + √(1 - a) = x
{√(1 +a) + √(1 - a)}² = x²(1 +a) + (1 - a) + 2 {√(1 +a) × √(1 - a)} =x²2 + 2 {√(1 +a) × √(1 - a)} = x²
2 + 2 √(1 - a²) = x²2 + 2√{1- (√3/2)²} = x²2 + 2 √{ 1- 3/4} = x²2 + 2 √{( 4- 3)/4}= x²
2 + 2 × 1/2 = x²2 + 1 = x²
x² = 3
∴ x = √3

১,২৫২.

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that the selected students are 2 boys and 1 girl, is -

ক
ক) 21/46
খ
খ) 25/117
গ
গ) 1/50
ঘ
ঘ) 3/25

ব্যাখ্যা

Let,
S be the sample space and
E be the event of select.
Then,
n(S) = number of ways of selecting 3 students out of 25
= ²⁵C₃
= (25 × 24 × 23)/(3 × 2 × 1)
= 2300.
And,
n(E) = (¹⁵C₂ × ¹⁰C₁)
= {(15 × 14)/(2 × 1)} × 10
= 1050.
∴ P(E) = n(E)/n(S)
= 1050/2300
= 21/46.

১,২৫৩.

A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is =?

ক
40%
খ
45%
গ
50%
ঘ
54%

ব্যাখ্যা

Question: A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/3 selling price of 33 m of cloth

Let selling price of 33 meters of cloth = 3x
∴ profit = 1/3 (3x) = x

So, cost price = selling price - profit = 3x - x = 2x

% Profit = (x/2x) × 100% = 50%

১,২৫৪.

What should come in place of both x in the equation x /√128 = √162/x.

ক
12
খ
14
গ
144
ঘ
196

ব্যাখ্যা

Question: What should come in place of both x in the equation x /√128 = √162/x.

Solution:
x /√128 = √162/x
⇒ x² = √(128 × 162)
⇒ x² = √(64 × 2 × 18 × 9)
⇒ x² = √(8² × 6² × 3²)
⇒ x² = 8 × 6 × 3
⇒ x² = 144
∴ x = 12

১,২৫৫.

A motorboat takes 3 hour to travel 12 km upstream and 12 km downstream in a river with a current of 3 km/hr. What is the boat’s speed in still water?

ক
8 km/hr
খ
9 km/hr
গ
12 km/hr
ঘ
1 km/hr
ঙ
None of these

ব্যাখ্যা

Question: A motorboat takes 3 hour to travel 12 km upstream and 12 km downstream in a river with a current of 3 km/hr. What is the boat’s speed in still water?

Solution:
Let, still water speed = x
Then,
Upstream speed = x - 3
Downstream speed = x + 3

ATQ,
⇒ {12/(x - 3)} + {12/ (x + 3)} = 3
⇒ 12(x - 3 + x + 3)/(x² - 9) = 3
⇒ 24x = 3x² - 27
⇒ x² - 8x - 9 = 0
⇒ x² - 9x + x - 9 = 0
⇒ x(x - 9) + 1(x - 9) = 0
⇒ (x - 9)(x + 1) = 0
⇒ x = 9, - 1
∴ x = 9 (positive value only valid)

So the speed of the motorboat in still water is 9 km/hr.

১,২৫৬.

The average of 50 numbers is 20. If two numbers 37 and 43 are discarded, find the average of the remaining numbers.

ক
17.19
খ
19.17
গ
23.17
ঘ
21.17
ঙ
None of these

ব্যাখ্যা

Question: The average of 50 numbers is 20. If two numbers 37 and 43 are discarded, find the average of the remaining numbers.

Solution:
Given,

Average of 50 numbers = 20

Sum of 50 numbers = 20 × 50 = 1000

Sum of discarded numbers = 37 + 43 = 80

Sum of remaining numbers = 1000 - 80 = 920

Now, total remaining numbers = 50 - 2 = 48

Average of remaining numbers = 920/48 = 19.17

১,২৫৭.

There are 3 circles A, B and C (C > B > A). Area of the circle A is 100 Square Inch and B is 50% of C and 200% of A. What is the area of C?

ক
ক) 200 Sq Inch
খ
খ) 300 Sq Inch
গ
গ) 400 Sq Inch
ঘ
ঘ) 800 Sq Inch

ব্যাখ্যা

Question: There are 3 circles A, B and C (C > B > A). Area of the circle A is 100 Square Inch and B is 50% of C and 200% of A. What is the area of C?

Solution:
Area of the circle A is 100 Square Inch

Area of B = 200% of A.
= (200/100) × 100
= 200 square inch

Area of B = 50% of C
⇒ Area of B = area of C/2
⇒ area of C = 2 × Area of B
= 2 × 200
= 400 square inch

১,২৫৮.

Mina lives 3 km west of Lina's house. Rina lives 8 km north of Lina's house and 3 km west of Tina's house. What is the minimum distance from Mina's house to Tina's house?

ক
8 km
খ
12 km
গ
15 km
ঘ
10 km

ব্যাখ্যা

Question: Mina lives 3 km west of Lina's house. Rina lives 8 km north of Lina's house and 3 km west of Tina's house. What is the minimum distance from Mina's house to Tina's house?

Solution:

So, distance,
(ad)² = (cd + ce)² + (ae)²
⇒ (ad)² = (3 + 3)² + (8)²
⇒ (ad)² = 36 + 64
⇒ (ad)² = 100
∴ ad = 10

So the minimum distance from Mina's house to Tina's house = 10 km

১,২৫৯.

If a² + (2a/3) + 1/9 = 0, then (a - 2/3)² = ?

ক
ক) 1
খ
খ) 1/3
গ
গ) 9
ঘ
ঘ) 27

ব্যাখ্যা

Question: If a² + (2a/3) + 1/9 = 0, then (a - 2/3)² = ?

Solution:
a² + 2a/3 + 1/9 = 0
⇒ a² + (1/3)² + 2 × a × (1/3) = 0
⇒ (a + 1/3)² = 0
⇒ a + 1/3 = 0
⇒ a = - 1/3

Now,
{(- 1/3) - (2/3)}²
= {(- 1 - 2)/3}²
= {(- 3)/3}²
= (- 1)²
= 1

১,২৬০.

A team played 40 games in a season and won in 24 of them. What percent of games played did the team win?

ক
ক) 70%
খ
খ) 40%
গ
গ) 60%
ঘ
ঘ) 35%

ব্যাখ্যা

Number of games played = 40
Number of won games = 24
Percentage of games played = (24/40)× 100
= 60%

১,২৬১.

At a stationary shop, it costs Tk. 185 for 4 gel-pens, 8ball-point pens and 1 marker pen and Tk. 315 for 7 gel-pens, 15 ball-point pens and 1 marker pen. What would be the cost of 3 gel-pen, 3 ball-point pen and 3 marker pen?

ক
Tk. 55
খ
Tk. 120
গ
Tk. 155
ঘ
Tk. 165

ব্যাখ্যা

Question: At a stationary shop, it costs Tk. 185 for 4 gel-pens, 8 ball-point pens and 1 marker pen and Tk. 315 for 7 gel-pens, 15 ball-point pens and 1 marker pen. What would be the cost of 3 gel-pen, 3 ball-point pen and 3 marker pen?

Solution:
Let,
the cost of 1 gel-pen, 1 ball-point pen and 1 marker pen respectively x, y, z.

ATQ,
7x + 15y + z = 315 .............. (1)
4x + 8y + z = 185 ............... (2)

From (1) - (2) we get,
3x + 7y = 130 ............ (3)
⇒ 6x + 14y = 260 .............. (4) [multiplied with 2]

From (1) - (4) we get,
x + y + z = 55
⇒ 3x + 3y + 3z = 55 × 3 = 165.

∴ The cost of 3 gel-pen, 3 ball-point pen and 3 marker pen is 165 taka

১,২৬২.

What is the 10th term of the geometric sequence: 4 + 8 +16 + ........?

ক
2048
খ
1080
গ
1640
ঘ
1264
ঙ
None

ব্যাখ্যা

Question: What is the 10th term of the geometric sequence: 4 + 8 +16 + ........?

Solution:
দেওয়া আছে,
প্রদত্ত ধারাটির প্রথম পদ, a = 4,
সাধারণ অনুপাত, r = 8/4 = 2

আমরা জানি,
গুণোত্তর ধারার n তম পদ = ar^{n - 1}
∴ ধারাটির 10 তম পদ = 4 × 2^{10 - 1}
= 4 × 2⁹
= 4 × 512
= 2048

১,২৬৩.

If A = 2, B = 4, C = 6, D = 8, E = 10 and so on, what is the meaning of following number 40, 18, 14, 10, 36

ক
RIVER
খ
TIGER
গ
FIGHT
ঘ
RIGHT

ব্যাখ্যা

Question: If A = 2, B = 4, C = 6, D = 8, E = 10 and so on, what is the meaning of following number 40, 18, 14, 10, 36

Solution:
Given,
A = 2, B = 4, C = 6, D = 8, E = 10.......

∴ Each code = Letter position × 2

So
40 ÷ 2 = 20 → T
18 ÷ 2 = 9 → I
14 ÷ 2 = 7 → G
10 ÷ 2 = 5 → E
36 ÷ 2 = 18 → R

the meaning of following number = TIGER

১,২৬৪.

The speed of three cars is in the ratio of 3 : 4 : 5. The ratio of the times taken by these cars to travel the same distance is-

ক
20 : 15 : 12
খ
15 : 20 : 12
গ
12 : 15 : 20
ঘ
20 : 12 : 15

ব্যাখ্যা

Question: The speed of three cars is in the ratio of 3 : 4 : 5. The ratio of the times taken by these cars to travel the same distance is-

Solution:
যেহেতু দূরত্ব একই থাকে, তাই গতিবেগ সময়ের সাথে ব্যস্তানুপাতিক হয়।
⇒ গতিবেগ ∝ (1/সময়)
⇒ s ∝ (1/t)

∴ সময়ের অনুপাত = 1/3 : 1/4 : 1/5
= (1/3 × 60) : (1/4 × 60) : (1/5 × 60)
= 20 : 15 : 12

১,২৬৫.

Which number will complete the series 4, 25, 151, _ , 5443.

ক
1007
খ
807
গ
907
ঘ
707

ব্যাখ্যা

Question: Which number will complete the series 4, 25, 151, —, 5443.

Solution:
Given,
4
(4 × 6 + 1) = 25
(25 × 6 + 1) = 151
(151 × 6 + 1) = 907
(907 × 6 + 1) = 5443

১,২৬৬.

০.৩৫ কে ভগ্নাংশে প্রকাশ করলে কত হবে?

ক
ক) ৭/২০
খ
খ) ৭/২৫
গ
গ) ৫/২০
ঘ
ঘ) ৫/২৫

ব্যাখ্যা

প্রশ্ন: ০.৩৫ কে ভগ্নাংশে প্রকাশ করলে কত হবে?

সমাধান:
০.৩৫
= ৩৫/১০০
= ৭/২০

১,২৬৭.

The length of the one side of a square is 4√2 cm. What is the length of the diagonal of the square?

ক
4 cm
খ
8 cm
গ
32 cm
ঘ
16√2 cm

ব্যাখ্যা

Question: The length of the one side of a square is 4√2 cm. What is the length of the diagonal of the square?

Solution:
Given that,
The length of the one side of a square is a = 4√2 cm.

∴ The length of diagonal of the square is a√2 = (4√2) × √2 cm
= 4 × 2 cm
= 8 cm

১,২৬৮.

In a boat there are 6 men whose average weight is increased by 1.5 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?

ক
65 kg
খ
66 kg
গ
68 kg
ঘ
69 kg

ব্যাখ্যা

Question: In a boat there are 6 men whose average weight is increased by 1.5 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?

Solution:
Total weight increased = (6 × 1.5) kg
= 9 kg

So the weight of new person = (60 + 9) kg
= 69 kg

১,২৬৯.

Two numbers are in the ratio 3 : 5. If 8 is added to both the numbers, their ratio becomes 2 : 3. The greater number is

ক
ক) 24
খ
খ) 36
গ
গ) 40
ঘ
ঘ) 45

ব্যাখ্যা

Two numbers are 3y and 5y
(3y + 8)/(5y + 8) = 2/3
10y + 16 = 9y + 24
y = 8
The greater number is 5 × 8 = 40

১,২৭০.

The average age of a group of 20 employees is 26 years. When 4 more employees join the group, the average age increases by 4 years. The average age of the new employees is?

ক
30 years
খ
38 years
গ
45 years
ঘ
48 years
ঙ
50 years

ব্যাখ্যা

Question: The average age of a group of 20 employees is 26 years. When 4 more employees join the group, the average age increases by 4 years. What is the average age of the new employees?

Solution:
Average age of 20 employees = 26 years
∴ Total age of 20 employees = 20 × 26 = 520 years

After 4 more employees join:
Total number of employees = 20 + 4 = 24 employees
New average age = 26 + 4 = 30 years
Total age of 24 employees = 24 × 30 = 720 years

∴ Total age of 4 new employees = 720 - 520 = 200 years

∴ Average age of 4 new employees = 200 ÷ 4 = 50 years

১,২৭১.

Rahim's regular pay is Tk 40 per hour up to 40 hours. Overtime is paid at twice the regular rate. If he was paid Tk 2400 in total, how many hours of overtime did he work?

ক
5 hours
খ
10 hours
গ
7 hours
ঘ
9 hours
ঙ
11 hours

ব্যাখ্যা

Question: Rahim's regular pay is Tk 40 per hour up to 40 hours. Overtime is paid at twice the regular rate. If he was paid Tk 2400 in total, how many hours of overtime did he work?

Solution:
Rahim’s regular wage for 40 hours = (40 × 40) = 1600 Taka.
Amount earned from overtime = (2400 - 1600) Taka = 800 Taka.
Since the overtime rate is twice the regular hourly wage,
Total overtime hours worked = 800 ÷ (40 × 2) hours
= 800 ÷ 80
= 10 hours

১,২৭২.

A hall is 30m long and 10m broad. If the sum of the areas of the floor and the ceiling is equal to of the areas of four walls, the volume of the hall is-

ক
2250 m³
খ
2480 m³
গ
2050 m³
ঘ
1875 m³

ব্যাখ্যা

Question: A hall is 30m long and 10m broad. If the sum of the areas of the floor and the ceiling is equal to of the areas of four walls, the volume of the hall is-

Solution:
Let,
The height of the hall = h

Given that,
Length of the room = 30 m
Breadth of the room = 10 m

According to the question,
2 × (30 × 10) = 2 × (30 + 10) × h
⇒ 2 × 40 × h = 2 × (30 × 10)
⇒ 40h = 300
⇒ h = 300/40
⇒ h = 30/4
∴ h = 15/2

We know,
Volume = 30 × 10 × (15/2)
= 2250 m³

১,২৭৩.

Find the average of all prime numbers between 20 and 50?

ক
ক) 35.86
খ
খ) 42.75
গ
গ) 32.66
ঘ
ঘ) None of these

ব্যাখ্যা

Question: Find the average of all prime numbers between 20 and 50?

Solution:
Prime number between 20 and 50 = 23, 29, 31, 37, 41, 43, 47

∴ average = (23 + 29 + 31 + 37 + 41 + 43 + 47) / 7 = 35.86

১,২৭৪.

Two small circular shape objects of diameter 16 meter and 12 meter are to be replaced by a bigger circular shape object. What would be the radius of this new circular shape object, if the new circular shape object has to occupy the same space as the two small circular shape objects?

ক
10 meter
খ
14 meter
গ
18 meter
ঘ
20 meter

ব্যাখ্যা

Question: Two small circular shape objects of diameter 16 meter and 12 meter are to be replaced by a bigger circular shape object. What would be the radius of this new circular shape object, if the new circular shape object has to occupy the same space as the two small circular shape objects?

Solution:
Let,
the radius of the new circular shape object be = R m
Then,
πR² = (π × 8²) + (π×6²)
⇒ πR² = 64π + 36π
⇒ πR² = 100π
⇒ R² = 100
⇒ R² =10²
∴ R =10

১,২৭৫.

A's salary is 50% more than that of B. Then B's salary is less than that of A by:

ক
50%
খ
(100/3)%
গ
(111/5)%
ঘ
67%

ব্যাখ্যা

Question: A's salary is 50% more than that of B. Then B's salary is less than that of A by:

Solution:
Let salary of B = 100
∴ Salary of A = 100 + 50% of 100 = 150

B salary is lesser then A = 150 - 100 = 50
Required % (50/150) × 100 = (100/3)%

Hence, B's salary is less than that of A by: (100/3)%

১,২৭৬.

There are eight teachers and four administrators in a school. A task force of 5 people needs to be formed. How many different ways can a task force be formed that contains three teachers and two administrators?

ক
286
খ
242
গ
336
ঘ
384
ঙ
None

ব্যাখ্যা

Question: There are eight teachers and four administrators in a school. A task force of 5 people needs to be formed. How many different ways can a task force be formed that contains three teachers and two administrators?

Solution:
Have: 8 teachers, 4 administrators
Want: 3 teachers AND 2 administrators

Total ways = ⁸C₃ × ⁴C₂
= 56 × 6
= 336
Therefore, there are 336 different ways to form a task force that contains three teachers and two administrators.

১,২৭৭.

A cake is divided into 18 pieces. If Niloy takes 1/3^rd of the cake and Nihal takes 1/3^rd of the cake left, how many pieces are left?

ক
4
খ
6
গ
8
ঘ
10

ব্যাখ্যা

Question: A cake is divided into 18 pieces. If Niloy takes 1/3^rd of the cake and Nihal takes 1/3^rd of the cake left, how many pieces are left?

Solution:
Niloy কেক নেয় = 18 × (1/3) = 6 টুকরা
বাকি রইল = 18 - 6 = 12 টুকরা
Nihal কেক নেয় = 12 × (1/3) = 4 টুকরা

অবশিষ্ট রইল = 12 - 4 = 8 টুকরা

১,২৭৮.

The average of 7 consecutive numbers is 21. The largest of these numbers is-

ক
22
খ
23
গ
24
ঘ
25

ব্যাখ্যা

Question: The average of 7 consecutive numbers is 21. The largest of these numbers is-

Solution:
Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then,
(x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6)/7 = 21
⇒ 7x + 21 = 147
⇒ 7x = 126
∴ x = 18

∴ Largest number = x + 6 = 18 + 6 = 24

১,২৭৯.

A certain sum of money consists of 30 coins some of which are 10 paisa coins and the rest are 5 paisa coins. If the total value of the coins is Tk. 2, what is the number of 10 paisa coins?

ক
10
খ
8
গ
15
ঘ
12
ঙ
None of these

ব্যাখ্যা

Question: A certain sum of money consists of 30 coins some of which are 10 paisa coins and the rest are 5 paisa coins. If the total value of the coins is Tk. 2, what is the number of 10 paisa coins?

Solution:
Let,
Number of 10 paisa coins be x
Number of 5 paisa coins 30 - x

ATQ,
x × 10 + (30 - x)5 = 200
⇒ 10x + 150 - 5x = 200
⇒ 5x = 50
∴ x = 10

১,২৮০.

In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together?

ক
4320
খ
1440
গ
13440
ঘ
360

ব্যাখ্যা

Question: In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels always come together?

Solution:
The given word contains 8 different letters.
We keep the vowels (OAE) together and treat them as 1 letter.
Thus, we have to arrange the 6 letters SFTWR(OAE)
These can be arranged in 6! = 6 5 × 4 × 3 × 2 × 1 = 720 ways

And,
The vowels (OAE) can be arranged among themselves in 3! = 3 × 2 × 1 = 6 ways.

∴ Required number of ways = (720 × 6) = 4320

১,২৮১.

If 21215120 represents 'bloat' then 6121135 represents -

ক
ক) voice
খ
খ) bald
গ
গ) flame
ঘ
ঘ) castle

ব্যাখ্যা

Bloat এরঃ
B হলো 2^nd Alphabet.
L হলো 12^th Alphabet.
O হলো 15^th Alphabet.
A হলো 1^st Alphabet.
T হলো 20^th Alphabet.
Flame এরঃ
F হলো 6^th Alphabet.
L হলো 12^th Alphabet.
A হলো 1^st Alphabet.
M হলো 13^th Alphabet.
E হলো 5^th Alphabet.

১,২৮২.

How many years will it take for an investment of Tk. 10000 to earn Tk. 3000 in simple interest at a rate of 6%?

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

ব্যাখ্যা

Question: How many years will it take for an investment of Tk. 10000 to earn Tk. 3000 in simple interest at a rate of 6%?

Solution:
Given that,
Principal, P = 10000
Simple Interest, I = 3000
Rate of interest, r = 6%
Time, n = ?

We know,
I = Pnr/100
⇒ 3000 = (10000 × n × 6)/100
⇒ 3000 = 100 × n × 6
⇒ 3000 = 600n
⇒ n = 3000/600
⇒ n = 5

So, it will take 5 years for the investment to earn Tk. 3000 at 6% simple interest.

১,২৮৩.

A boat takes 30 minutes less to travel 12 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is-

ক
7 mph
খ
5 mph
গ
3 mph
ঘ
2 mph

ব্যাখ্যা

Question: A boat takes 30 minutes less to travel 12 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is-

Solution:
Let,
The speed of the stream = x mph

Then,
Speed downstream = (10 + x) mph
Speed upstream = (10 - x) mph

ATQ,
{12/(10 - x) - 12/(10 + x)} = 30/60
⇒ (24x × 60) = 30(100 - x²)
⇒ x² + 48x - 100 = 0
⇒ (x + 50)(x - 2) = 0
∴ x = 2 mph

১,২৮৪.

A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

ক
4 days
খ
5 days
গ
3 days
ঘ
6 days
ঙ
7 days

ব্যাখ্যা

Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

Solution:
Remaining days = 40 - 35 = 5 days
After engaging 100 men total men = 100 + 100 = 200

200 men can finish the work in = 5 days
1 men can finish the work in = 5 × 200 days
So, 100 men can do it in (5 × 200)/100 days
=10 days.

Now, he will be behind schedule by = 10 - 5 days
= 5 days

১,২৮৫.

A, B, C hired a car for Tk. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were:

ক
ক) 150
খ
খ) 160
গ
গ) 170
ঘ
ঘ) 180
ঙ
ঙ) 200

ব্যাখ্যা

A : B : C = 7 : 8 : 11.
Hire charges paid by B = Tk. (520 × 8/26)
= Tk. 160.

১,২৮৬.

If θ = 30° then the value of cosθ - sin2θ is -

ক
ক) 0
খ
খ) 1
গ
গ) 2
ঘ
ঘ) 1/2

ব্যাখ্যা

Question: If θ = 30° then the value of cosθ - sin2θ is -

Solution:
দেওয়া আছে,
θ = 30°

∴ cos30° - sin(2 ×30°)
= cos30° - sin60°
= (√3/2) - (√3/2)
= (√3 - √3)/2
= 0/2
= 0

১,২৮৭.

An investment becomes Tk. 6,720 in 2 years and Tk. 7,392 in 3 years at compound interest. Find the rate of interest per annum.

ক
8%
খ
9%
গ
10%
ঘ
11%

ব্যাখ্যা

Question: An investment becomes Tk. 6,720 in 2 years and Tk. 7,392 in 3 years at compound interest. Find the rate of interest per annum.

Solution:
Let the principal = P, rate = R%.

Compound Interest:
A = P[1 + 100/R]^T

Amount after 2 years = 6,720
6,720 = P[1 + 100/R]²

Amount after 3 years = 7,392
7,392 = P[1 + 100/R]³

Divide the 3rd year amount by 2nd year amount:
7,392/6,720 = P(1 + R/100)³/ P(1 + R/100)²
⇒ 1.1 = 1 + R/100 [7,392/6,720 = 1.1]
⇒ 1.1 - 1 = R/100
⇒ 0.1 = R/100
⇒ R = 0.1 × 100
⇒ R = 10%

∴ R = 10%

১,২৮৮.

In a proportion the product of 1^st and 4^th terms is 40 and that of 2^nd and 3^rd terms is 2.5x. Then the value of x is-

ক
ক) 16
খ
খ) 26
গ
গ) 56
ঘ
ঘ) 76
ঙ
ঙ) 96

ব্যাখ্যা

Product of 1^st and 4^th terms (extremes) = product of 2^nd and 3^rd terms (means)
⇒ 2.5x = 40
⇒ x = 40/2.5 = 16

১,২৮৯.

In a room of 36 people, 20 players play chase while 28 players play poker. How many players play both?

ক
ক) 45
খ
খ) 20
গ
গ) 12
ঘ
ঘ) 28

ব্যাখ্যা

We know,
Total = n(A) + n(B) - both + none
⇒ 36 = 20 + 28 - both + 0
⇒ 36 = 48 - both
⇒ both = 48 - 36
⇒ both = 12

১,২৯০.

In how many ways can a person invite his 4 friends?

ক
ক) 4
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 15

ব্যাখ্যা

Question: In how many ways can a person invite his 4 friends?

Solution:
Number of ways = ⁴C₁ +⁴C₂ +⁴C₃ + ⁴C₄
= 4 + 6 + 4 + 1
= 15

১,২৯১.

Murad bought equal number of 20-paisa and 30-paisa stamps. If the total cost of the stamps was tk 10, what was the total number of stamps that Murad bought?

ক
25
খ
34
গ
40
ঘ
46
ঙ
None of these

ব্যাখ্যা

Question: Murad bought equal number of 20-paisa and 30-paisa stamps. If the total cost of the stamps was tk 10, what was the total number of stamps that Murad bought?

Solution:
Let's represent the number of 20-paisa stamps as 'x' and the number of 30-paisa stamps as 'y'.
Since Murad bought an equal number of 20-paisa and 30-paisa stamps, we know that x = y.

ATQ,
20x + 30y = 1000 [10 tk = 1000 paisa]
⇒ 50x = 1000
⇒ x = 20

∴ Total stamps = x + y = 20 + 20 = 40
Therefore, the total number of stamps Murad bought is 40.

১,২৯২.

In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by -

ক
ক) 18m
খ
খ) 20m
গ
গ) 25m
ঘ
ঘ) 27m

ব্যাখ্যা

Question: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by -

Solution:
A : B = 200 : 169
A : C = 200 : 182

B/C = (B/A) × (A/C)
= 169/182

So, in a 350 race B will pass = (169/182) × 350
= 325m

hence, C will beat B by (350 - 325) or, 25 metres

১,২৯৩.

The respective ratio between the speed of a car, a train, and a bus is 5 : 9 : 4. The average speed of the car, bus and train is 72 km/hr together. What is the average speed of the car and the train together?

ক
ক) 82 km/hr
খ
খ) 72 km/hr
গ
গ) 67kms/er
ঘ
ঘ) 84 km/hr

ব্যাখ্যা

Question: The respective ratio between the speed of a car, a train, and a bus is 5 : 9 : 4. The average speed of the car, bus and train is 72 km/hr together. What is the average speed of the car and the train together?

Solution:
Let the common ratio be x
Car speed= 5x
Train speed = 9x
Bus speed is 4x

∴ Average speed of Car, Train, Bus = (5x + 9x + 4x)/3 = 6x

ATQ,
6x = 72
x = 12

Car speed is = (5 × 12) km/hr = 60 km/hr
Train speed is = (9 × 12) km/hr = 108 km/hr

∴ Average speed of Car& train together is = (60 + 108)/2km/hr = 84 km/hr

১,২৯৪.

In the series 3, 9, 15, ….. what will be the 21^st term?

ক
117
খ
121
গ
123
ঘ
129

ব্যাখ্যা

Question: In the series 3, 9, 15, ….. what will be the 21^st term?

Solution:
Here,
9 - 3 = 6
15 - 9 = 6
So, the series is an A.P. in which a = 3 and d = 6.

∴ 21^st term = a + (21 - 1) d
= a + 20d
= 3 + 20 × 6
= 123

১,২৯৫.

In a certain code language, 'APPLE' is coded as '50', and 'BANANA' is coded as '33'. How will 'ORANGE' be coded in that code language?

ক
60
খ
74
গ
86
ঘ
54

ব্যাখ্যা

Question: In a certain code language, 'APPLE' is coded as '50', and 'BANANA' is coded as '33'. How will 'ORANGE' be coded in that code language?

Solution:

এখানে প্রতিটি অক্ষরের Alphabetical Position (A = 1, B = 2, …, Z = 26) যোগ করা হয়েছে।

APPLE = A(1) + P(16) + P(16) + L(12) + E(5)
= 1 + 16 + 16 + 12 + 5
= 50

BANANA = B(2) + A(1) + N(14) + A(1) + N(14) + A(1)
= 2 + 1 + 14 + 1 + 14 + 1
= 33

অতএব,
ORANGE = O(15) + R(18) + A(1) + N(14) + G(7) + E(5)
= 15 + 18 + 1 + 14 + 7 + 5
= 60

১,২৯৬.

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

ক
22 Years
খ
23 Years
গ
24 Years
ঘ
25 Years

ব্যাখ্যা

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

Solution:
Let the average age of the whole team by x years.
Total age of the whole team 11x years
Age of the captain 26 years
Age of the wiket-keeper 26 + 3 = 29 years

The average age of the remaining players after excluding the ages of captain and wicketkeeper = x - 1
∴ Total age of the players without the ages of captain and wicketkeeper = 9(x - 1)

We can say,
11x - (26 + 29) = 9(x - 1)
⇒ 11x - 55 = 9x - 9
⇒ 11x - 9x = - 9 + 55
⇒ 2x = 46
∴ x = 23 Years.

১,২৯৭.

If kamal travels 20 km/hr, he reaches the office 10 minutes late and if he travels at 25 km/hr, he reaches the office 5 minutes earlier. The office is at a distance of.

ক
ক) 25 km.
খ
খ) 35 km.
গ
গ) 45 km.
ঘ
ঘ) 30 km.

ব্যাখ্যা

Question: If kamal travels 20 km/hr, he reaches the office 10 minutes late and if he travels at 25 km/hr, he reaches the office 5 minutes earlier. The office is at a distance of.

Solution:
অফিসের দূরত্ব x হলে,
কামাল x দূরত্ব যায় (x/20) এবং (x/25) সময়ে।
The difference between the time = {5 - (-10)} ⇒ 15 minutes

ATQ,
Or, (x/20) - (x/25) = 15/60
Or, (5x - 4x)/100 = 1/4
Or, x/100 = 1/4
Or, 4x = 100
Or, x = 25

১,২৯৮.

Which number is 40% less than 90?

ক
39
খ
51
গ
46
ঘ
54

ব্যাখ্যা

Question: Which number is 40% less than 90?

Solution:
Required number = 60% of 90
= (90 × 60)/100
= 54

১,২৯৯.

The average weight of 12 students is 52 kg. If a new student joins, the average becomes 53 kg. What is the weight of the new student?

ক
62 kg
খ
63 kg
গ
64 kg
ঘ
65 kg

ব্যাখ্যা

Question: The average weight of 12 students is 52 kg. If a new student joins, the average becomes 53 kg. What is the weight of the new student?

Solution:
Average weight of 12 students = 52
Total weight = 12 × 52
= 624 kg.

Let the weight of the new student = x kg.
New total number of students = 13

New average = 53
Total weight = 13 × 53
= 689 kg.

Weight of new student = new total - original total
= 689 - 624
= 65 kg

∴ The weight of the new student is 65 kg.

১,৩০০.

If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is -

ক
ক) 38
খ
খ) 39
গ
গ) 40
ঘ
ঘ) 41

ব্যাখ্যা

Let daughter’s age be = A
and mother’s age be = B

ATQ, 2A + B = 70 ..... (i)
and, A + 2B = 95 ..... (ii)
(ii)×2 - (i) ⇒ 3B = 120
⇒ B = 40