Bank Math

PrepBank · পাতা ১০৯ / ১৬১ · ১০,৮০১–১০,৯০০ / ১৬,১২৪

১০,৮০১.

In a certain code, BRUSH = 49062 and FLAME = 75831. How is BLARE coded in the language?

ক
47384
খ
74318
গ
46318
ঘ
45891

ব্যাখ্যা

Question: In a certain code, BRUSH = 49062 and FLAME = 75831. How is BLARE coded in the language?

Solution:
Given,
B R U S H
↓ ↓ ↓ ↓ ↓
4 9 0 6 2

And,
F L A M E
↓ ↓ ↓ ↓ ↓
7 5 8 3 1

Therefore,
B L A R E
↓ ↓ ↓ ↓ ↓
4 5 8 9 1

∴ BLARE = 45891

১০,৮০২.

If 16th March, 2005 is Wednesday, what was the day of the week on 16th March, 2004?

ক
Tuesday
খ
Saturday
গ
Monday
ঘ
Friday

ব্যাখ্যা

Question: If 16th March, 2005 is Wednesday, what was the day of the week on 16th March, 2004?

Solution:
Since 16th March is coming after February leap year will not count in 2004.
Odd day is 1.

∴ 16th March, 2004 is Tuesday.

১০,৮০৩.

A person at 5km/h crosses a platform in 12 minutes. A train 1/4 length of the platform crosses the platform at 50km/h. How much time is required to cross the platform by the train?

ক
ক) 1.2 min
খ
খ) 1 min
গ
গ) 1.5 min
ঘ
ঘ) 2 min

ব্যাখ্যা

Question: A person at 5km/h crosses a platform in 12 minutes. A train 1/4 length of the platform crosses the platform at 50km/h. How much time is required to cross the platform by the train?

Solution:
The speed of the person is = 5km/h
time required to cross the platform is = 12min = 12/60 = 1/5 hour

so, the length of the platform is = 5 × 1/5 = 1km

the length of the train is = 1/4 = 0.25km

the speed of the train is = 50km/h

so, time required to cross the platform by the train is = {(1 + 0.25) km}/(50km/h)
= 1.25/50
= 0.025hour
= 0.025 × 60 min
= 1.5 min

১০,৮০৪.

In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 20° & ∠EOA = 80°, then find the value of ∠ECO.

ক
30°
খ
50°
গ
45°
ঘ
35°

ব্যাখ্যা

Question: In the given figure, AB is the diameter of the circle with center O. If ∠BOD = 20° & ∠EOA = 80°, then find the value of ∠ECO.

Solution:
∠EOA = 80°, ∠BOD = 20°
∠EOD = 180° - (80° + 20°) = 80°

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

In ΔOEC,
∠EOC = 80° + 20° = 100°, ∠OEC = 50°
∴ ∠ECO = 180°- (100° + 50°) = 30°

১০,৮০৫.

The price of a laptop is 50,000. How much do you need to pay if you get a 15% discount?

ক
Tk. 40000
খ
Tk. 42500
গ
Tk. 45000
ঘ
Tk. 41500

ব্যাখ্যা

Question: The price of a laptop is 50,000. How much do you need to pay if you get a 15% discount?

Solution:
For 15% discount,
Original price 100 paid price 85
∴ Original price 1 paid price 85/100
∴ Original price 50000 paid price (85 × 50000)/100
= 42500

১০,৮০৬.

Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The sum of two numbers is-

ক
ক) 56
খ
খ) 32
গ
গ) 88
ঘ
ঘ) 66

ব্যাখ্যা

Question: Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The sum of two numbers is-

Solution:
Let the numbers be 4x and 7x
Then,
⇒(4x + 4)/(7x + 4) = 3/5
⇒5(4x + 4) = 3(7x+4)
⇒20x + 20 = 21x + 12
⇒21x - 20x = 20 - 12
x = 8

∴ The sum of two numbers = 4x + 7x
= 11x
= 11 × 8
= 88

১০,৮০৭.

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

ক
173 m
খ
200 m
গ
273 m
ঘ
300 m

ব্যাখ্যা

Question: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Solution:

ধরি,
বাতিঘরের উচ্চতা AB = 100 মিটার
C ও D হলো জাহাজের অবস্থান

ΔABC এ
tan∠ACB = AB/BC
⇒ tan 30° = 100/BC
⇒ 1/√3 = 100/BC
∴ BC = 100√3

ΔABC এ
tan∠ADB = AB/BD
⇒ tan45° = 100/BD
⇒ 1 = 100/BD
∴ BD = 100

∴ CD = 100√3 + 100
= 173.205 + 100
= 273.205
≈ 273 m

১০,৮০৮.

In how many ways can 4 guests from a group of 7 guests be seated around a circular table?

ক
35
খ
340
গ
210
ঘ
810

ব্যাখ্যা

Question: In how many ways can 4 guests from a group of 7 guests be seated around a circular table?

Solution:
7 জন থেকে 4 জন নির্বাচন করার উপায়:
⁷C₄ = 7!/(4! × 3!)
= (7 × 6 × 5)/(3 × 2 × 1)
= 210/6 = 35

4 জন ব্যক্তিকে একটি গোলাকার টেবিলে সাজানোর উপায় = (4 -1)!
= 3!
= 6

∴ মোট উপায় = 35 × 6 = 210

১০,৮০৯.

Compound interest on a certain sum at the rate of 12% per annum after 2 years is Tk. 1,42,464. Find the simple interest on that sum at the rate of 15% per annum for 7 years.

ক
ক) Tk. 5,68,000
খ
খ) Tk. 5,86,000
গ
গ) Tk. 5,88,000
ঘ
ঘ) Tk. 5,66,000

ব্যাখ্যা

Question: Compound interest on a certain sum at the rate of 12% per annum after 2 years is Tk. 1,42,464. Find the simple interest on that sum at the rate of 15% per annum for 7 years.

Solution:
Let the sum be, x.
Rate of interest = 12%
Period = 2 years

Hence, compound interest = x(1 + 12/100)² - x = 142464
x × 1.2544 - x = 142464

So, x = 142464/0.2544 = 560000

Hence, simple interest = 560000 × 15/100 × 7 = 588000

১০,৮১০.

A tap can fill a tank in 8 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

ক
ক) 6 hrs
খ
খ) 6 hrs 30 min
গ
গ) 4 hrs 30 min
ঘ
ঘ) 5 hrs

ব্যাখ্যা

Question: A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
Time taken by one tap to fill half the tank = 4 hrs
Remaining part after 4 hrs = (1 - 1/2) = 1/2
Part filled by the four taps in 1 hours = 4 × (1/8) = 1/2

Total time = 4 + 1 = 5 hrs

১০,৮১১.

(75% of 320) + (40% of 150) - ? = 170

ক
140
খ
130
গ
125
ঘ
120

ব্যাখ্যা

Question: (75% of 320) + (40% of 150) - ? = 170

Solution:
Let,
(75% of 320) + (40% of 150) - x = 170
⇒ {(75 × 320)/100} + {( 40 × 150)/100} - x = 170
⇒ 240 + 60 - x = 170
⇒ - x = 170 - 300
∴ x = 130

১০,৮১২.

Hamid, Jobayer and Sumon start a shop by investing Tk. 27,000. Tk. 72,000 and Tk. 81,000 respectively. At the end of the year, the profit was distributed among them and Sumon earned the share of Tk. 36,000. Find the total profit.

ক
Tk. 1,10,000
খ
Tk. 1,2,5000
গ
Tk. 98,000
ঘ
Tk. 80,000

ব্যাখ্যা

The ratio of shares of Hamid, Jobayer, and Sumon = Ratio of their investments
Hamid : Jobayer : Sumon = 27000 : 72000 : 81000 = 3 : 8 : 9

Given share of profit earned by Smith =Tk. 36,000
Total no. of shares = 3 + 8 + 9 = 20 shares
Sumon's share = 9/20
Let total profit = Tk. X
36000/X = 9/20
X = (36000 × 20)/9 = 80,000.

১০,৮১৩.

A son's present age is three-sevenths of his father’s age. After 7 years, he will be half of his father’s age. Find the present age of the father.

ক
39 years
খ
49 years
গ
47 years
ঘ
59 years
ঙ
56 years

ব্যাখ্যা

Question: A son's present age is three-sevenths of his father’s age. After 7 years, he will be half of his father’s age. Find the present age of the father.

Solution:
Let, the father's present age be x years

Then, the son's present age (3x/7) years

∴ (3x/7) + 7 = (1/2) × (x + 7)
⇒ (3x + 49)/7 = (1/2) × (x + 7)
⇒ 7x + 49 = 6x + 98
⇒ x = 49

∴ the present age of the father is 49 years.

১০,৮১৪.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

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

ব্যাখ্যা

Let man's rate upstream be x kmph
Then, his rate downstream = 2x kmph
∴ (speed in still water) : (Speed of stream)
=(2x+x)/2 : (2x−x)/2
= 3x/2 : x/2 = 3 : 1

১০,৮১৫.

Out of 7,500 applications for a recruitment test, 1,500 failed to appear for the test. What percent of the total applicants did appear for the test?

ক
ক) 25
খ
খ) 50
গ
গ) 75
ঘ
ঘ) 80

ব্যাখ্যা

Question: Out of 7,500 applications for a recruitment test, 1,500 failed to appear for the test. What percent of the total applicants did appear for the test?

Solution:
পরীক্ষার্থী = ৭৫০০ জন
অনুপস্থিত = ১৫০০ জন
উপস্থিত = ৭৫০০ - ১৫০০ জন
= ৬০০০ জন

শতকরা উপস্থিত = ৬০০০ ×১০০%/৭৫০০
= ৮০%

১০,৮১৬.

The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

ক
ক) 0
খ
খ) 1
গ
গ) 10
ঘ
ঘ) 19
ঙ
ঙ) None of these

ব্যাখ্যা

Average of 20 numbers = 0
∴ Sum of 20 numbers (0 × 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20^th number is (-a)

১০,৮১৭.

A sum of Tk. 1600 gives a simple interest of Tk. 252 in 2 years and 4 months. The rate of interest per annum is:

ক
3.45%
খ
4%
গ
5.25%
ঘ
6.75%

ব্যাখ্যা

Question: A sum of Tk. 1600 gives a simple interest of Tk 252 in 2 years and 4 months. The rate of interest per annum is:

Solution:
2 years and 4 months = 2 + (1/3) years
= 7/3 hours

let, rate of interest is r%

252 = 1600 × (7/3) × (r/100)
⇒ 252 = 112r/3
⇒ r = 6.75

১০,৮১৮.

If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?

ক
ক) 50% increase
খ
খ) 25% increase
গ
গ) 25% decrease
ঘ
ঘ) 50% decrease

ব্যাখ্যা

Let original length = 10
original breadth = 10
Then, original area = 10 × 10 = 100
Length is halved
⇒ New length = 10/2
= 5
breadth is tripled.
⇒ New breadth = 10 × 3
= 30
New area = 5 × 30
= 150
Increase in area
= new area - original area
= 150 - 100
= 50
Percentage increase in area
= {(increase in area/original area) × 100}%
= {(50/100) × 100}%
= 50%.

১০,৮১৯.

L can finish a work in 16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.

ক
48/5 days
খ
48/7 days
গ
48/11 days
ঘ
10 days

ব্যাখ্যা

Question: L can finish a work in 16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.

Solution:
(L + M + N)’s 1 day’s work =1/4
L’s 1 day’s work = 1/16
M’s 1 day’s work = 1/12

Therefore, N’s 1 day’s work
= 1/4 - (1/16 + 1/12)
= 1/4 - 7/48 = 5/48

So, N alone can do the work in 48/5 days.

১০,৮২০.

If (x + 3)² = 225 then what is the value of x - 1?

ক
ক) 12
খ
খ) 15
গ
গ) - 13
ঘ
ঘ) - 19

ব্যাখ্যা

Question: If (x + 3)² = 225 then what is the value of x - 1?

Solution:
(x + 3)² = 225
⇒ x + 3 = ± 15
Take the negative value wet get,
x + 3 = - 15
⇒ x = - 15 - 3
∴ x = - 18

∴ x - 1 = - 18 - 1 = - 19

১০,৮২১.

In how many ways can 5 balls can be chosen from 9 different balls?

ক
102
খ
110
গ
118
ঘ
126

ব্যাখ্যা

Question: In how many ways can 5 balls can be chosen from 9 different balls?

Solution:
Here,
Total number of different balls, n = 9
Chosen balls from different balls, r = 5

The number of ways 5 balls can be chosen is
= ⁿC_r
= n!/{r!(n - r)!}
= 9!/{5!(9 - 5)!}
= 9!/(5! × 4!)
= (9 × 8 × 7 × 6 × 5!)/(5! × 4!)
= (9 × 8 × 7 × 6)/4!
= 3024/(4 × 3 × 2 × 1)
= 3024/24
= 126

∴ 5 balls can be chosen from 9 different balls in 126 ways.

১০,৮২২.

If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average (arithmetic mean) annual increase in the index over this period?

ক
(x + 100)/18
খ
x/18
গ
(100 - x)/18
ঘ
(x - 100)/18
ঙ
(100x)/18

ব্যাখ্যা

Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average (arithmetic mean) annual increase in the index over this period?

Solution:
consumer price index at End Of 1967 = 100
consumer price index at End Of 1985 = x
It says that CPI rose which means x > 100

Total Number of Years = 1985 - 1967 = 18 Years

Average = Total Gain/No. Of Years
Average = (x - 100)/18

১০,৮২৩.

If x + 1/x = 1 then, find the value of x² + (1/x²) + 2 is -

ক
ক) 2
খ
খ) 1
গ
গ) -1
ঘ
ঘ) 0

ব্যাখ্যা

Question: If x + 1/x = 1 then, find the value of x² + (1/x²) + 2 is -

Solution:
Given that
x + 1/x = 1

Now,
x² + 1/x² + 2
= x² + (1/x)² + 2
= (x + 1/x)² - 2 . x .1/x + 2
= 1² - 2 + 2
= 1

১০,৮২৪.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

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

ব্যাখ্যা

Let speed upstream = x
Then, speed downstream = 2x
Speed in still water
= (2x+x)/2
= 3x/2
Speed of the stream
= (2x−x)/2
= x/2
Speed in still water : Speed of the stream
= 3x/2 : x/2
= 3:1

১০,৮২৫.

If a + (1/a) = 4, then the value of a³ + (1/a³) is:

ক
56
খ
54
গ
52
ঘ
50

ব্যাখ্যা

Question: If a + (1/a) = 4, then the value of a³ + (1/a³) is:

Solution:
a³ + (1/a³)
= {a + (1/a)}³ - 3 · a · (1/a){a + (1/a)}
= 4³ - 3 · 4
= 64 - 12
= 52

১০,৮২৬.

(10)² is how many times of (0.01)³?

ক
ক) 10⁵
খ
খ) 10⁶
গ
গ) 10⁷
ঘ
ঘ) 10⁸

ব্যাখ্যা

Question: (10)² is how many times of (0.01)³?

Solution:
(10)²/(0.01)³
= (10)²/(1/100)³
= 10²/(1/10²)³
= 10²/(1/10⁶)
= 10² × 10⁶
= 10^{2 + 6}
= 10⁸

১০,৮২৭.

Rahim invested in all Tk. 2,600 in three different schemes at 8%, 4% and 6% per annum simple interest. At the end of the year, he received the same interest in all the three schemes. What is the money invested in scheme having 4% rate of interest?

ক
ক) Tk. 700
খ
খ) Tk. 800
গ
গ) Tk. 750
ঘ
ঘ) Tk. 1,200

ব্যাখ্যা

Question: Rahim invested in all Tk. 2,600 in three different schemes at 8%, 4% and 6% per annum simple interest. At the end of the year, he received the same interest in all the three schemes. What is the money invested in scheme having 4% rate of interest?

Solution:
Rahim invested Tk. 2600 at 4%, 6% and 8% respectively.
Let the three parts be x, y and z.

(x × 4 × 1)/100 = (y × 6 × 1)/100 = (z × 8 × 1)/100
4x =6y = 8z
2x = 3y = 4z

Now
2x = 3y
x/y = 3/2
x : y = 3 : 2

3y = 4z
y/z = 4/3
y : z = 4 : 3

x : y : Z = 6 : 4 : 3

Sum invested at 4%= Tk. (6 × 2600)/13
= Tk .1200

১০,৮২৮.

If the average of 6, 15, 22, and 'x' is 15, what is the value of 'x'?

ক
ক) 24
খ
খ) 17
গ
গ) 23
ঘ
ঘ) 19

ব্যাখ্যা

Question: If the average of 6, 15, 22, and 'x' is 15, what is the value of 'x'?

Solution:
According to the question,
(6 + 15 + 22 + x) / 4 = 15
⇒ 43 + x = 60
⇒ x = 17

১০,৮২৯.

Mitu is 60 years old and Ritu is 80 years old. How many years ago their age ratio was 4 : 6?

ক
20 years
খ
22 years
গ
25 years
ঘ
18 years

ব্যাখ্যা

Question: Mitu is 60 years old and Ritu is 80 years old. How many years ago their age ratio was 4 : 6?

Solution:
Let us assume x years ago.
At present, Mitu is 60 years old
and Ritu is 80 years old.
X years ago, Mitu’s age = (60 - x) and Ritu’s age (80 - x)

ATQ,
(60 - x)/(80-x) = 4/6
⇒ 6(60 - x) = 4(80 - x)
⇒ 360 - 6x = 320 - 4x
⇒ 6x - 4x = 360 - 320
⇒ 2x = 40
∴ x = 20

Therefore, 20 years ago their age ratio was 4 : 6.

১০,৮৩০.

Motin bought two varieties of rice, costing Tk. 50 kg and Tk. 60 kg each, and mixed them in some ratio. Then he sold the mixture at Tk. 70 kg making a profit of 20%, what was the ratio of the mixture?

ক
2 : 3
খ
1 : 10
গ
1 : 5
ঘ
2 : 7
ঙ
None

ব্যাখ্যা

Question: Motin bought two varieties of rice, costing Tk. 50 kg and Tk. 60 kg each, and mixed them in some ratio. Then he sold the mixture at Tk. 70 kg making a profit of 20%, what was the ratio of the mixture?

Solution:
মনে করি,
প্রথম পদের চাল কিনলো x কেজি
দ্বিতীয় পদের চাল কিনলো y কেজি

মোট খরচ = (50x + 60y) টাকা
মোট চালের পরিমাণ = (x + y) কেজি
মোট বিক্রয়মূল্য = 70 (x + y) = 70x + 70y

লাভ = 70x + 70y - 50x - 60y
= 20x + 10y টাকা

প্রশ্নমতে,
20x + 10y = (50x + 60y) 20%
বা, 20x + 10y = (50x + 60y) 20/100
বা, 10(2x + y) = 10(5x + 6y) 1/5
বা, 2x + y = (5x + 6y) 1/5
বা, 10x + 5y = 5x + 6y
বা, 5x = y
বা, x/y = 1/5
∴ x : y = 1 : 5

১০,৮৩১.

7 is added to a certain number; the sum is multiplied by 5, the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is:

ক
20
খ
30
গ
40
ঘ
60

ব্যাখ্যা

Question: 7 is added to a certain number; the sum is multiplied by 5, the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is:

Solution:
Let the original number be x

Now
{5(x + 7)/9} - 3 = 12
⇒ {5(x + 7) - 27}/9 = 12
⇒ 5(x + 7) - 27 = 108
⇒ 5x + 35 - 27 = 108
⇒ 5x + 8 = 108
⇒ 5x = 100
∴ x = 20

১০,৮৩২.

What is the slope of a line perpendicular to the line whose equation is 2x + 5y = 10?

ক
5/2
খ
- 2/5
গ
4/3
ঘ
3/8

ব্যাখ্যা

Question: What is the slope of a line perpendicular to the line whose equation is 2x + 5y = 10?

Solution:
প্রদত্ত সরল রেখার সমীকরণ: 2x + 5y = 10

y = mx + c আকারে লিখি, যেখানে m হলো রেখার ঢাল।
5y = - 2x + 10
⇒ y = (- 2/5)x + 2

অতএব, মূল রেখার ঢাল (m) = - 2/5

আমরা জানি, কোনো রেখার উপর লম্ব রেখার ঢাল m = - 1/m
= - 1/(- 2/5)
= 5/2

∴ লম্ব রেখার ঢাল = 5/2

১০,৮৩৩.

If a square mirror has a 20 inch diagonal, what is the approximate perimeter of the mirror, in inches?

ক
ক) 40
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 80

ব্যাখ্যা

Let, Side of square = x
Here, √2x = 20
Or, 2x² = 400
⇒ x²= 200
⇒ x = 14.14
So, perimeter = 4 × 14.14 = 56.56 ≅ 60 [As the approximate value was asked]

১০,৮৩৪.

During an election, the victorious candidate received 70% of the votes and won with a margin of 60,000 votes. How many total votes were cast?

ক
170,000
খ
250,000
গ
130,000
ঘ
150,000

ব্যাখ্যা

Question: During an election, the victorious candidate received 70% of the votes and won with a margin of 60,000 votes. How many total votes were cast?

Solution:
Let, The victorious candidate secured 0.70x votes,
and the losing candidate secured 0.30x votes.

ATQ,
0.70x - 0.30x = 60,000
⇒ 0.40x = 60,000
⇒ x = 60,000 / 0.40
= 150,000

Thus, the total number of votes cast was 150,000.

১০,৮৩৫.

The difference between the two numbers is 11 and one-fifth of their sum is 9. Find the numbers.

ক
ক) 28 and 16
খ
খ) 28 and 17
গ
গ) 28 and 18
ঘ
ঘ) 28 and 19

ব্যাখ্যা

Let, The numbers are x & y,
therefore,
x - y = 11 ------ (1) and
1/5(x + y) = 9 or, x + y = 45 ------ (2)
adding two equation we got,
2x = 56 or, x = 28,
putting the value of x in equation 1,
we get, y = 17

১০,৮৩৬.

ক
1/2
খ
2/3
গ
1/4
ঘ
3/4

ব্যাখ্যা

Question:

Solution:

১০,৮৩৭.

If (4P + 1)² = 441, then P³/3P = ?

ক
3/25
খ
25/3
গ
20/3
ঘ
18/5

ব্যাখ্যা

Question: If (4P + 1)² = 441, then P³/3P = ?

Solution:
(4P + 1)² = 441
or, (4P + 1) = √441
or, 4P + 1 = 21
or, 4P = 21 - 1
or, 4P = 20
or, P = 20/4
∴ P = 5

∴ P³/3P = 5³/(3 × 5)
= 125/15
= 25/3

১০,৮৩৮.

Rafi is as much younger than Sagar as he is older than Piyal. If the sum of the ages of Piyal and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Rafi and Piyal's age?

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

ব্যাখ্যা

Question: Rafi is as much younger than Sagar as he is older than Piyal. If the sum of the ages of Piyal and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Rafi and Piyal's age?

Solution:
Sagar's age is 48 years
the sum of the ages of Piyal and Sagar is 66 years
∴ The age of Piyal is = 66 - 48 year
= 18 year

let, age of rafi is x

48 - x = x - 18
⇒ 2x = 66
∴ x = 33
the difference between Rafi and Piyal's age is = 33 - 18
= 15 years

১০,৮৩৯.

A train, 800 metre long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in metres)?

ক
ক) 430 metre
খ
খ) 440 metre
গ
গ) 260 metre
ঘ
ঘ) 450 metre
ঙ
ঙ) 500 metre

ব্যাখ্যা

Let length of the tunnel = x metre
Then, distance = (800 + x) metre
Time = 1 minute = 60 seconds
Speed = 78 km/hr
= 78 × 5 /18 m/s
= 65/3 m/s

800 + x = 60 × 65/3
⇒ 800 + x = 1300
⇒ x = 500

১০,৮৪০.

A takes twice as much times as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in.

ক
ক) 4 days
খ
খ) 8 days
গ
গ) 6 days
ঘ
ঘ) 12 days

ব্যাখ্যা

ধরি A, B, C কাজটি করতে সময় নেয় x , x/2 , x/3 দিন
তারা 1 দিনে করে যথাক্রমে 1/x , 2/x , 3/x অংশ কাজ

প্রশ্নমতে ,
1/x + 2/x + 3/x = 1/2
(1 + 2 + 3)/x = 1/2
6/x = 1/2
x = 12
B কাজটি করতে সময় নেয় = 12/2= 6 দিন

১০,৮৪১.

If |2x - 3| ≤ 9, then which of the following intervals represents all possible values of the expression 5x + 7?

ক
[ - 8, 32]
খ
[ - 10, 35]
গ
[ - 11, 33]
ঘ
[ - 8, 37]

ব্যাখ্যা

Question: If |2x - 3| ≤ 9, then which of the following intervals represents all possible values of the expression 5x + 7?

Solution:
Start with the given inequality:
|2x - 3| ≤ 9

Rewrite as a compound inequality:
- 9 ≤ 2x - 3 ≤ 9
⇒ - 9 + 3 ≤ 2x - 3 + 3 ≤ 9 + 3
⇒ - 6 ≤ 2x ≤ 12
⇒ - 3 ≤ x ≤ 6

Now, find the range of 5x + 7:
Multiply the interval by 5:
5(- 3) ≤ 5x ≤ 5(6)
⇒ - 15 ≤ 5x ≤ 30
⇒ - 15 + 7 ≤ 5x + 7 ≤ 30 + 7
⇒ - 8 ≤ 5x + 7 ≤ 37

So, all possible values of 5x + 7 lie in the interval: [ - 8, 37 ]

১০,৮৪২.

The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is -

ক
40 years
খ
35 years
গ
50 years
ঘ
55 years

ব্যাখ্যা

Sum of the present ages of husband, wife and child = {(27 × 3) + (3 × 3)} years = 90 years.

Sum of the present ages of wife and child = {(20 × 2) + (5 × 2)} years = 50 years.

Husband's present age = (90 - 50) years = 40 years

১০,৮৪৩.

Shuvo is 60 years old and Rubel is 80 years old. How many years ago their age ratio was 4 : 6?

ক
10 years
খ
20 years
গ
15 years
ঘ
25 years

ব্যাখ্যা

প্রশ্ন: Shuvo is 60 years old and Rubel is 80 years old. How many years ago their age ratio was 4 : 6?

সমাধান:

Let x years ago their age ratio was 4 : 6

ATQ,

(60 - x)/(80 - x) = 4/6

⇒ 6 × (60 - x) = 4 × (80 - x)

⇒ 360 - 6x = 320 - 4x

⇒ 6x – 4x = 360 – 320

⇒ 2x = 40

∴ x = 20

Therefore, 20 years ago their age ratio was 4 : 6

১০,৮৪৪.

A manufacturer sells three products i.e. X, Y and Z. Product X costs 250 and sells for 330, Product Y costs 150 and sells for 210. Product Z costs 100 and sells 120. On which product, he has maximum percentage of profit?

ক
X only
খ
Y only
গ
X and Y both
ঘ
Z only

ব্যাখ্যা

Question: A manufacturer sells three products i.e. X, Y and Z. Product X costs 250 and sells for 330, Product Y costs 150 and sells for 210. Product Z costs 100 and sells 120. On which product, he has maximum percentage of profit?

Solution:
We know that,
Profit Percentage = {(Selling Price − Cost Price)/Cost Price } × 100

Product X,
Profit = 330 − 250 = 80
Profit Percentage = (80/250) × 100 = 32%

Product Y,
Profit = 210 − 150 = 60
Profit Percentage = (60/150) × 100 = 40%

Product Z,
Profit = 120 − 100 =20
Profit Percentage = (20/100) × 100 = 20%

∴ Product Y has the highest profit percentage of 40%.

১০,৮৪৫.

A bank offers 10% compound interest calculated half-yearly. A customer deposits Tk. 2000 on 1st January and another Tk. 2000 on 1st July of the same year. How much interest will he earn at the end of the year?

ক
Tk. 295
খ
Tk. 305
গ
Tk. 315
ঘ
Tk. 330

ব্যাখ্যা

Question: A bank offers 10% compound interest calculated half-yearly. A customer deposits Tk. 2000 on 1st January and another Tk. 2000 on 1st July of the same year. How much interest will he earn at the end of the year?

Solution:
Here,
Half-yearly interest rate = 10% ÷ 2 = 5%
Now,
The first deposit of Tk. 2000 was made on 1st January.
It stays for 12 months, so it earns interest twice (i.e., 2 half-years).
∴ A₁ = P(1 + r/100)ⁿ
= 2000 × {1 + 5/100}²
= 2000 × (1.05)²
= 2000 × 1.1025
= 2205

Now,
The second deposit of Tk. 2000 was made on 1st July.
It stays for 6 months, so it earns interest only once (1 half-year).
∴ A₂ = P(1 + r/100)ⁿ
= 2000 × (1 + 5/100)¹
= 2000 × 1.05
= 2100

Total amount = 2205 + 2100 = 4305
Total money deposited = 2000 + 2000 = 4000

∴ Interest earned = 4305 - 4000 = Tk. 305

∴ The customer would have gained Tk. 305 by way of interest.

১০,৮৪৬.

A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Tk. 240. What is original price per kg of sugar?

ক
Tk. 10
খ
Tk. 18
গ
Tk. 25
ঘ
Tk. 22

ব্যাখ্যা

Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Tk. 240. What is original price per kg of sugar?

Solution:
Given that,
Price of sugar reduced by 20%.
With Rs. 240, she can buy 6 kg more sugar than before.
Let the original price per kg of sugar be x Rs.

Now,
Original quantity she could buy for Tk. 240,
∴ Quantity = 240/x kg

After 20% reduction, new price per kg = Tk. 0.8x
∴ Quantity = 240/0.8x = 240/(4x/5) = 1200/4x = 300/x kg

ATQ,
⇒ (300/x) - (240/x) = 6
⇒ (300 - 240)/x = 6
⇒ 60/x = 6
⇒ x = 60/6
∴ x = 10

So the original price per kg of sugar = Tk. 10

১০,৮৪৭.

What is the H.C.F. of 9/14, 12/21 and 15/28?

ক
1/28
খ
2/21
গ
4/9
ঘ
1/5

ব্যাখ্যা

Question: What is the H.C.F. of 9/14, 12/21 and 15/28?

Solution:
We know,
H.C.F. of fractions = (H.C.F. of numerators)/(L.C.M of denominators)

H.C.F of numerators = H.C.F. of 9, 12 and 15 = 3
& L.C.M of denominators = L.C.M. of 14, 21 and 28 = 84

∴ Required H.C.F. = 3/84 = 1/28

১০,৮৪৮.

Robi is 10 years older than Kazi. However, 5 years ago Robi was twice as old as Kazi. How old is Kazi now?

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

ব্যাখ্যা

Question: Robi is 10 years older than Kazi. However, 5 years ago Robi was twice as old as Kazi. How old is Kazi now?

Solution:
Let,
The age of Kazi is x years
∴ The age of Robi is x + 10 years
5 years ago the age of Kazi was x - 5 years
5 years ago the age of Robi was x +10 - 5 years = x + 5 years

ATQ,
2(x - 5) = x + 5
⇒ 2x - 10 = x + 5
⇒ x = 15

∴ The age of Kazi is 15 years

১০,৮৪৯.

In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, then the present age of A is-

ক
ক) 39 years
খ
খ) 41 years
গ
গ) 48 years
ঘ
ঘ) 52 years

ব্যাখ্যা

Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, then the present age of A is-

Solution:
Let the present age of B be x years.
Then, the present age of A would be (x + 9) years.
After 10 years, the age of A would be (x + 9 + 10) = (x + 19) years and before then years, the age of B was (x - 10) years.

Now,
(x + 19) = 2(x - 10)
x + 19 = 2x - 20
x = 19 + 20 = 39 years

The present age of B is 39 years

The present age of A is 39 + 9 = 48 years

১০,৮৫০.

5 - [4 - {3 - (3 - 3 - 6)}] is equal to:

ক
ক) 10
খ
খ) 20
গ
গ) 15
ঘ
ঘ) 5

ব্যাখ্যা

Given,
5 - [4 - {3 - (3 - 3 - 6)}]
= 5 - [4 - {3 - (-6)}]
= 5 - [4 - {3 +6}]
= 5 - [4 - {9}]
= 5 - [4 - 9]
= 5 - [-5]
= 5 + 5
= 10

১০,৮৫১.

Four bells ring at intervals of 6, 8, 12 and 18 minutes respectively. If they all ring together at 2 : 00 noon, when will they ring together again?

ক
2 : 24 PM
খ
3 : 10 AM
গ
2 : 20 PM
ঘ
3 : 12 PM

ব্যাখ্যা

Question: Four bells ring at intervals of 6, 8, 12 and 18 minutes respectively. If they all ring together at 2 : 00 noon, when will they ring together again?

Solution:
চারটি ঘণ্টা দুপুর 2 টায় একত্রে বাজলে 6, 8, 12, 18 এর ল.সা.গুর সমান সময়ের পর ঘণ্টাগুলো পুনরায় একত্রে বাজবে।

সংখ্যা গুলোর মৌলিক উৎপাদক
6 = 2 × 3
8 = 2 × 2 × 2
12 = 2 × 2× 3
18 = 2 × 3 × 3

6, 8, 12, 18 এর ল.সা.গু. = 2 × 2 × 2 × 3 × 3 = 72
অর্থাৎ 72 মিনিট

সুতরাং, ঘণ্টা গুলো একবার দুপুর 2 টায় বাজার পর পুনরায় বাজবে = 2 টা + 72 মিনিটে
= 2 টা + (60 + 12) মিনিটে
= 2 টা + 1 ঘণ্টা 12 মিনিটে
= 3 টা 12 মিনিটে

১০,৮৫২.

If one-fifth of one-sixth of a number is 10, then what is 2/3 of that number?

ক
200
খ
180
গ
150
ঘ
220

ব্যাখ্যা

Question: If one-fifth of one-sixth of a number is 10, then what is 2/3 of that number?

Solution:
Let the number be x.
So one-sixth of the number = x/6

Now, one-fifth of one-sixth of the number = (1/5) × (x/6) = x/30

According to the question:
⇒ x/30 = 10
⇒ x = 10 × 30
∴ x = 300

∴ Now calculate 2/3 of the number = (2/3) × 300
= 2 × 100
= 200

১০,৮৫৩.

The compound interest on Taka 12,000 for 2 years at 10% per annum compounded half-yearly is -

ক
2,422 Taka
খ
2,444 Taka
গ
2,586 Taka
ঘ
2,678 Taka

ব্যাখ্যা

Question: The compound interest on Taka 12,000 for 2 years at 10% per annum compounded half-yearly is -

Solution:
Given,
P = 12,000 (Principal)
r = 10% = 0.1
Compounded half-yearly means, n = 2
Time, t = 2 years

Compound Interest = A - P
= 14586 - 12000
= 2586 Taka

১০,৮৫৪.

Simplify the expression using BODMAS rule (105 + 206) - 550 ÷ 5² + 10

ক
399
খ
289
গ
298
ঘ
299

ব্যাখ্যা

Question: Simplify the expression using BODMAS rule (105 + 206) - 550 ÷ 5² + 10

Solution:
(105 + 206) - 550 ÷ 5² + 10
= 311 - 550 ÷ 25 + 10
= 311 - 22 + 10
= 289 + 10
= 299

১০,৮৫৫.

How much sugar at Tk. 95 a kg should be added to 17 kg of tea at Tk. 200 a kg so that the mixture be worth Tk. 130 a kg.?

ক
11 kg
খ
17 kg
গ
21 kg
ঘ
34 kg

ব্যাখ্যা

Question: How much sugar at Tk. 95 a kg should be added to 17 kg of tea at Tk. 200 a kg so that the mixture be worth Tk. 130 a kg.?

Solution:
Ratio in which tea and sugar should be mixed
= 200 - 130 : 130 - 95 = 70 : 35 = 10 : 5 = 2 : 1
Let x be quantity at 95/kg.

∴ 2 : 1 = x : 17
⇒ 2/1 = x/17
⇒ x = 34
hence x = 34 kg.

১০,৮৫৬.

If 2^{x - 1} + 2^{x + 1} = 320, then x is equal to-

ক
ক) 6
খ
খ) 7
গ
গ) 8
ঘ
ঘ) 9

ব্যাখ্যা

2^{x - 1} + 2^{x + 1} = 320
2^x.2^-1 + 2^x.2¹ = 320
2^x(2 + 1/2) = 320
2^x(5/2) = 320
2^x = 320 × (2/5)
2^x = 128
2^x = 2⁷
x = 7

১০,৮৫৭.

Shorna's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

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

ব্যাখ্যা

প্রশ্ন: Shorna's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

সমাধান:
স্বর্ণার ভাই তার থেকে ৪ বছরের ছোট।

স্বর্ণার ভাইয়ের জন্মের সময় তার মায়ের বয়স ছিল ৩৬ বছর
তাহলে স্বর্ণার জন্মের সময় তার মায়ের বয়স ছিল ৩৬ - ৪ বছর = ৩২ বছর

এবং স্বর্ণার জন্মের সময় তার বাবার বয়স ছিল ৩৮ বছর

তার বাবা মায়ের বয়সের পার্থক্য = ৩৮ - ৩২ বছর
= ৬ বছর

১০,৮৫৮.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

ক
9 hours
খ
10 hours
গ
12 hours
ঘ
14 hours

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

Solution:
Let, the leak can drain the full water in X hours
in one hour,
the leak drains 1/X
the pump pores 1/2

so, in one hour the tank fills = 1/2 - 1/X
= (X - 2)/2X

Atq,
2x/(X - 2) = 7/3
6X = 7X - 14
X = 14

So, the leak will drain the whole water in just 14 hours.

১০,৮৫৯.

A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is :

ক
4 : 1
খ
3 : 1
গ
2 : 1
ঘ
4 : 3

ব্যাখ্যা

Question: A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is :

Solution:
Let the original speed be S₁ and time t₁ and distance be D.
Now,
(D/2)/2t₁=S₂
S₂ = D/4t₁ and, S₁ = D/t₁

Thus,
S1_/S₂ = 4/1
= 4 : 1

১০,৮৬০.

Find out the missing number on the series:

ক
1/√2
খ
√2
গ
2
ঘ
1

ব্যাখ্যা

Question:
Find out the missing number on the series:

Solution:
এখানে ধারাটির প্রতিটি পদ √2 গুণ আকারে বাড়ছে।
তাই ধারাটি হবে, 1/(2√2), 1/2, 1/√2, 1, √2, 2, 2√2

∴ মিসিং পদটি হবে = 1

১০,৮৬১.

If a pen cost Tk. 50 after 10% discount, then what is the actual price or marked price (MP) of the pen?

ক
Tk. 50.55
খ
Tk. 60.66
গ
Tk. 55.55
ঘ
Tk. 50

ব্যাখ্যা

Question: If a pen cost Tk.50 after 10% discount, then what is the actual price or marked price (MP) of the pen?

Solution:

Since, we know;

MP - D = SP ........(1)

where MP is marked price, D is discount, SP is selling price.

Percentage discount, D% = D/MP × 100

⇒ D = (D% × MP)/100 ........(2)

Substitute value of D in (1).

MP - (D% × MP)/100 = SP

⇒ MP × (100 - D%)/100 = SP

Putting the given values in formula

MP × (100 - 10)/100 = 50

⇒ MP × (90/100) = 50

⇒ MP = (50 × 100)/90

∴ MP = 55.55

১০,৮৬২.

A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak with empty the cistern in

ক
24 hours
খ
30 hours
গ
40 hours
ঘ
50 hours

ব্যাখ্যা

Filled in 1 hour 1/10 portion of cistern
Because of a leak in its bottom, filled 1/15 portion of cistern
In 1 hour, empty = (1/10 - 1/15) portion = 1/30 portion
Empty 1/30 portion in 1 hour
Full cistern will empty in 30 hours.

১০,৮৬৩.

A bag contains 6 white and 4 black balls. 2 balls are drawn at random. Find the probability that they are of same color.

ক
ক) 1/2
খ
খ) 7/15
গ
গ) 8/15
ঘ
ঘ) 1/9
ঙ
ঙ) None of the above

ব্যাখ্যা

Let S be the sample space.
Then n(S) = no of ways of drawing 2 balls out of (6 + 4) = ¹⁰C₂
= (10 × 9)/(2 × 1) = 45
Let E = event of getting both balls of same colour
Then,
n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
= ⁶C₂ + ⁴C₂
= (6 × 5)/(2 × 1) + (4 × 3)/(2 × 1)
= 15 + 6
= 21
Therefore,
P(E) = n(E)/n(S)
= 21/45
= 7/15

১০,৮৬৪.

The L.C.M. of two numbers is 96. The numbers are in the ratio 2 : 3. Then the sum of the numbers is:

ক
82
খ
86
গ
80
ঘ
None of these

ব্যাখ্যা

Question: The L.C.M. of two numbers is 96. The numbers are in the ratio 2 : 3. Then the sum of the numbers is-

Solution:
Let the numbers be 2x and 3x
Then, their L.C.M. = 6x

So,
6x = 96
∴ x = 16

The numbers are 2x = 32 and 3x = 48

Hence, required sum = (32 + 48) = 80

১০,৮৬৫.

A mixture of 200 liters of wine and water contains 25% water. How much more water should be added so that water becomes 40% of the new mixture?

ক
50 liters
খ
40 liters
গ
30 liters
ঘ
45 liters

ব্যাখ্যা

Question: A mixture of 200 liters of wine and water contains 25% water. How much more water should be added so that water becomes 40% of the new mixture?

Solution:
Number of liters of water in 200 liters of the mixture = 25% of 200 = 1/4 of 200 = 50 liters
Let us Assume that another 'P' liters of water are added to the mixture to make water 40% of the new mixture.
So, the total amount of water becomes (50 + P) and the total volume of the mixture becomes (200 + P)
Thus, (50 + P) = 40% of (200 + P)
⇒ 50 + P = (40/100) × (200 + P)
⇒ 5000 + 100P = 8000 + 40P
⇒ 60P = 3000
∴ P = 50 liters

১০,৮৬৬.

A man's age is now 3 times his son's age. Eight years back, the man's age was 5 times his son's age. What is the present age of the son?

ক
ক) 15
খ
খ) 20
গ
গ) 18
ঘ
ঘ) 16

ব্যাখ্যা

Question: A man's age is now 3 times his son's age. Eight years back, the man's age was 5 times his son's age. What is the present age of the son?

Solution:
Let Man's son's present age = x
Man's present age = 3x

According to the question
5(x - 8) = 3x - 8
⇒ 5x - 40 = 3x - 8
⇒ 5x - 3x = 40 - 8
⇒ 2x = 32
x = 16

১০,৮৬৭.

A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.

ক
ক) 10
খ
খ) 12
গ
গ) 15
ঘ
ঘ) 18

ব্যাখ্যা

Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x + 5) = 4/5
⇒ 20x = 4(3x + 5)
⇒ 8x = 20
⇒ x = 2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.

১০,৮৬৮.

A, B, and C started a business by investing Tk. 24,000, Tk. 32,000 and Tk. 40,000 respectively. If the total profit at the end of the year is Tk. 18,900, what is B's share of the profit?

ক
Tk. 5990
খ
Tk. 6300
গ
Tk. 6660
ঘ
Tk. 6800

ব্যাখ্যা

Question: A, B, and C started a business by investing Tk. 24,000, Tk. 32,000 and Tk. 40,000 respectively. If the total profit at the end of the year is Tk. 18,900, what is B's share of the profit?

Solution:
A, B এবং C এর বিনিয়োগের অনুপাত,
A : B : C = 24000 : 32000 : 40000
= 24 : 32 : 40
= 3 : 4 : 5

অনুপাতগুলোর যোগফল = 3 + 4 + 5 = 12

মোট লাভ = 18900 টাকা
B এর লভ্যাংশ = (B এর অনুপাত/অনুপাতগুলোর যোগফল) × মোট লাভ
= (4/12) × 18900
= (1/3) × 18900
= 6300 টাকা

সুতরাং, B এর লভ্যাংশ হল 6300 টাকা।

১০,৮৬৯.

A train 108 metre long is moving at a speed of 50 km/hr. It crosses a train 112metre long coming from the opposite direction in 6seconds. What is the speed of the second train?

ক
82 kmph
খ
58 kmph
গ
44 kmph
ঘ
76 kmph

ব্যাখ্যা

Distance covered = (108 + 112)
= 220 meter.
Time = 6 seconds.
Relative speed = 220/6 = 110/3 m/s.
= (110/3) × (18/5) km/hr
= 132 km/hr.
50 + Speed of second train = 132 km/hr.
Speed of second train = (132 - 50)
= 82 km/hr.

১০,৮৭০.

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
ক) 12
খ
খ) 15
গ
গ) 18
ঘ
ঘ) 21

ব্যাখ্যা

Dividend on tk. 20 = tk.9/100x 20= 9/5
tk.12 is an income on tk.100.
Tk. 9/5 is an income on tk. 100/12 x 9/5 = tk.15

১০,৮৭১.

If 8% of x is the same as 4% of y, then 20% of x represents-

ক
50% of y
খ
10% of y
গ
70% of y
ঘ
40% of y

ব্যাখ্যা

Question: If 8% of x is the same as 4% of y, then 20% of x represents-

Solution:
Given that,
If 8% of x is the same as 4% of y

Now,
8% of x = 4% of y
⇒ (8/100)x = (4/100)y
⇒ x = 4y/8
⇒ x = y/2 .........(1)

Again,
We calculate,
= 20% of x
= 20% of y/2 ;[Substitute x = y/2]
= 20% × (y/2)
= 10% × y

Thus, 20% of x represents 10% of y.

১০,৮৭২.

The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.

ক
28 & 16
খ
28 & 17
গ
28 & 18
ঘ
28 & 19
ঙ
28 & 21

ব্যাখ্যা

Let, The numbers are x & y,
therefore, x - y = 11 ---- (1) and
1/5 (x + y) = 9
or, x + y = 45 ------ (2)
Adding two equation we got,
2x = 56 or, x = 28
Putting the value of x in equation 1,
We get, y = 17

১০,৮৭৩.

Ajay and Vijay started a business together with an investment of Tk. (1400 + x) and (1800 + 2x). After a year, Vijay received a profit of Tk. 3200 out of total profit of Tk.5600. What is the initial investment of Ajay?

ক
Tk.2000
খ
Tk.1600
গ
Tk.1800
ঘ
Tk.1500

ব্যাখ্যা

Question: Ajay and Vijay started a business together with an investment of Tk. (1400 + x) and (1800 + 2x). After a year, Vijay received a profit of
Tk. 3200 out of total profit of Tk.5600. What is the initial investment of Ajay?

Solution:
Ratio of profit share = Ajay : Vijay
⇒ (1400 + x) : (1800 + 2x) = (5600 - 3200) : 3200
⇒ (1400 + x) /(1800 + 2x) = (5600-3200)/3200
⇒ (1400 + x) /(1800 + 2x) = 2400 / 3200
⇒ (1400 + x) /(1800 + 2x) = 3 / 4
⇒ 5600 + 4x = 5400 + 6x
⇒ 6x - 4x = 5600 - 5400
⇒ 2x = 200
∴ x= 100

∴ Initial investment of Ajay = 1400 + 100 = Tk.1500

১০,৮৭৪.

800 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 50% in the solution?

ক
ক) 120 gm
খ
খ) 220 gm
গ
গ) 320 gm
ঘ
ঘ) 420 gm

ব্যাখ্যা

Question: 800 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 50% in the solution?

Solution:
amount of sugar = 800 × 30/100
= 240 grams

let, x gm sugar to be added
ATQ,
(240 + x)/(800 + x) = 50%
⇒ (240 + x)/(800 + x) = = 1/2
⇒ 480 + 2x = 800 + x
⇒ 2x - x = 800 - 480
∴ x = 320 gm

১০,৮৭৫.

The mean of the five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Then the mean of the first three observations is?

ক
9
খ
12
গ
8
ঘ
15

ব্যাখ্যা

Question: The mean of the five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Then the mean of the first three observations is?

Solution:
Given that,
The mean of the five observations = 11
Number of observations = 5
The observations = x, x + 2, x + 4, x + 6, x + 8

We know,
Mean or Average = Sum of observations ÷ Number of observations
Sum of observations = x + x + 2 + x + 4 + x + 6 + x + 8
⇒ 5x + 20 = 5(x + 4)

∴ Mean = [5(x + 4)] ÷ 5
⇒ 11 = x + 4
⇒ x = 7

∴ First three observations,
x = 7, x + 2 = 9, x + 4 = 11

∴ Mean of first three = (7 + 9 + 11)/ 3
= 27/3
= 9

১০,৮৭৬.

If 8 men can reap 40 acres in 12 days, then how many acres can 30 men reap in 20 days?

ক
270 acres
খ
250 acres
গ
180 acres
ঘ
230 acres
ঙ
None of the above

ব্যাখ্যা

Question: If 8 men can reap 40 acres in 12 days, then how many acres can 30 men reap in 20 days?

Solution:
8 men can reap in 12 days 40 acres
1 man can reap in 1 day 40/(12 × 8) acres

∴ 30 men reap in 20 days = (40 × 600)/96
= 250 acres

১০,৮৭৭.

If a = 3 + 2√2, then the value of (√a − 1/√a) is?

ক
2
খ
√2
গ
2√2
ঘ
0

ব্যাখ্যা

Question: If a = 3 + 2√2, then the value of (√a − 1/√a) is?

Solution:
a = 3 + 2√2
⇒ a = 2 + 1 + 2√2
⇒ a = (√2)² + 2 . √2 . 1 + 1²
⇒ a = (√2 + 1)²
⇒ √a = √2 + 1
⇒ 1/√a = 1/(√2 + 1)
⇒ 1/√a = 1(√2 - 1)/(√2 + 1)(√2 - 1)
⇒ 1/√a = √2 - 1

∴√a - 1/√a =√2 + 1 - √2 + 1 = 2

১০,৮৭৮.

A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any?

ক
ক) 2% loss
খ
খ) 2% profit
গ
গ) 1% profit
ঘ
ঘ) 1% loss

ব্যাখ্যা

Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any?

Solution:
Let cost price of goods = Tk. 100
Market price of goods
=110% of 100
=(110/100)×100
=Tk. 110

After discount selling price of goods
= 90% of 110
= (90/100) × 110
=Tk. 99

Loss = 100 - 99 = Tk. 1

Loss % = (1/100) × 100 = 1%

১০,৮৭৯.

3 pumps, working 4 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work, to empty the tank in one day?

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

ব্যাখ্যা

We are given that,
3 pumps, working 4 hours a day, can empty a tank in 2 days. Therefore, it means that:
3 pumps take a total of 8 hours to empty the tank.
Hence, 1 pump will take 8 x 3 = 24 hours

As the number of pumps decreases, the time required increases.
So, if 4 pumps work, the time required decreases.
∴ 24/4 = 6hrs. needed to empty the tank in 1 day.

১০,৮৮০.

For which of the following value of m is (30 + 2m)/m an integer?

ক
ক) 40
খ
খ) 25
গ
গ) 20
ঘ
ঘ) 15

ব্যাখ্যা

m = 15; (30 + 2m)/m = (30 + 2 × 15)/15 = 4 which is an integer.
For m = 40, 25 or 20; (30 + 2m)/m is not a integer.

১০,৮৮১.

The daily rate for a hotel room that sleeps 4 people is Tk. 390 for one person and X taka for each additional person. If 3 people take the room for one day and each pays Tk 210 for the room, then what is the value of X?

ক
60
খ
120
গ
80
ঘ
240

ব্যাখ্যা

Question: The daily rate for a hotel room that sleeps 4 people is Tk. 390 for one person and X taka for each additional person. If 3 people take the room for one day and each pays Tk 210 for the room, then what is the value of X?

Solution:
The daily rate for 1 person is Tk. 390
For each additional person daily rate X taka
The total cost for 3 people is = 390 + 2X

If 3 people take the room for one day and each pays Tk 210 for the room
Total cost = 210 × 3 = Tk. 630

According to the question
390 + 2X = 630
⇒ 2X = 630 - 390
⇒ 2X =240
∴ X = 120

১০,৮৮২.

ক
98
খ
101
গ
96
ঘ
108

ব্যাখ্যা

Question:

Solution:

১০,৮৮৩.

If A : B = 2 : 3 and B : C = 4 : 5 then A : C is -

ক
ক) 6 : 15
খ
খ) 8 : 20
গ
গ) 8 : 15
ঘ
ঘ) 8 : 12

ব্যাখ্যা

Question: If A : B = 2 : 3 and B : C = 4 : 5 then A : C is -

Solution:
A : B = 2 : 3
= (2 × 4 ) : (3 × 4)
= 8 : 12

B : C = 4 : 5
= (4 × 3) : (5 × 3)
= 12 : 15

∴ A : B : C = 8 : 12 : 15
∴ A : C = 8 : 15

১০,৮৮৪.

What is the probability that an integer selected at random from those between 20 and 100 inclusive is a multiple of 15?

ক
ক) 5/79
খ
খ) 2/27
গ
গ) 5/81
ঘ
ঘ) 6/79

ব্যাখ্যা

Multiple of 15 from 20 to 100 is 30, 45, 60, 75, 90 = 5
∴ Probability = 5/81

১০,৮৮৫.

If p and q are positive integers such that 2^p × 4^q = 32, then 2p + q =?

ক
1 or 3
খ
3 or 5
গ
4 or 5
ঘ
4 or 7
ঙ
None of them

ব্যাখ্যা

Question: If p and q are positive integers such that 2^p × 4^q = 32, then 2p + q =?

Solution:
Given, 2^p × 4^q = 32
⇒ 2^p × 2^2q = 2⁵
⇒ 2^{p + 2q} = 2⁵
⇒ p + 2q = 5

Since p and q are positive integers, test values of q :

If q = 1 then p = 3
If q = 2 then p = 1

Now compute 2p + q :
For (p, q)=(3, 1)
2p + q= 2(3) + 1 = 7

For (p, q)=(1, 2)
2p + q = 2(1) + 2 = 4

১০,৮৮৬.

The number of two digit prime numbers which remain prime even inverting the position of its digits is:

ক
4
খ
5
গ
9
ঘ
10

ব্যাখ্যা

Question: The number of two digit prime numbers which remain prime even inverting the position of its digits is:

Solution:
These numbers are 11, 13, 31, 17, 71, 37, 73, 79, 97.

∴ There are 9 such number.

১০,৮৮৭.

What is the least perfect square that is a multiple of 7, 11 and 12?

ক
ক) 421231
খ
খ) 242131
গ
গ) 223121
ঘ
ঘ) 213444

ব্যাখ্যা

Let us assume the least perfect square be X
⇒ 7 = 7 × 1
⇒ 11 = 11 × 1
⇒ 12 = 2²× 3 ⇒

The LCM of (7, 11, 12) = 2² × 3 × 11 × 7
⇒ The least perfect square = 2² × 3² × 11² × 7² = 213444
∴ The required result will be 213444.

১০,৮৮৮.

What is the area of a square field whose diagonal is 40 meters?

ক
750 sq. m.
খ
950 sq. m.
গ
900 sq. m.
ঘ
800 sq. m.

ব্যাখ্যা

Question: What is the area of a square field whose diagonal is 40 meters?

Solution:
Area of a square = (1/2) × (diagonal)²
= (1/2) × (40)²
= (1/2) × 1600
= 800 sq. m.

১০,৮৮৯.

The area of this triangle is 24cm².

Work out the perimeter of the triangle.

ক
16 cm
খ
12 cm
গ
9 cm
ঘ
24 cm
ঙ
None of these

ব্যাখ্যা

Question: The area of this triangle is 24cm².

Work out the perimeter of the triangle.

Solution:
The area of a triangle is = (1/2) × b × h.
24 = (1/2) × 6× (3x - 1)
⇒ 3x - 1 = 8
⇒ 3x = 9
∴ x = 3

Since x = 3, the side lengths are 6 cm, 8 cm and10 cm.
The perimeter is 6 + 8 + 10 = 24 cm

১০,৮৯০.

A box contains a total of 300 coins, some worth 25 paise and others worth 50 paise. If the total value of these coins is Tk 120, how many 50 paise coins are there?

ক
200
খ
180
গ
160
ঘ
140

ব্যাখ্যা

Question: A box contains a total of 300 coins, some worth 25 paise and others worth 50 paise. If the total value of these coins is Tk 120, how many 50 paise coins are there?

Solution:
Let the number of 50 paise coins be = x
So, the number of 25 paise coins is = 300 - x

According to the question,
50x + {25 × (300 - x)} = 120 × 100
⇒ 50x + 7500 - 25x = 12000
⇒ 25x = 4500
∴ x = 180

১০,৮৯১.

The greatest number that divides 86, 182, and 366 leaving the same remainder of 6 in each case is:

ক
12
খ
16
গ
8
ঘ
4

ব্যাখ্যা

Question: The greatest number that divides 86, 182, and 366 leaving the same remainder of 6 in each case is:

Solution:
Given that,
Numbers are 86, 182, 366
And remainder is 6

Now, numbers leaving remainder 6:
86 - 6 = 80
182 - 6 = 176
366 - 6 = 360

HCF of 80, 176, and 360:
Prime factorization:
80 = 2⁴ × 5
176 = 2⁴ × 11
360 = 2³ × 3² × 5
∴ Common factor = 2³ = 8

So the greatest number is 8.

১০,৮৯২.

Vikas and Mohan working together can complete a work in 6 days. If Vikas alone completes the same work in 10 days, in how many days Mohan alone can complete the same work?

ক
13 days
খ
14 days
গ
16 days
ঘ
15 days

ব্যাখ্যা

Question: Vikas and Mohan working together can complete a work in 6 days. If Vikas alone completes the same work in 10 days, in how many days Mohan alone can complete the same work?

Solution:
Vikas and Mohan together can complete the task in 6 days.
So, in one day, they will complete 1/6 part of the task.

Therefore, (Vikas + Mohan)'s one day work will be = 1/6
Similarly, Vikas's one day work = 1/10
Therefore, Mohan's one day work = 1/6 - 1/10 = (5 - 3)/30 = 2/30 = 1/15

In one day Mohan completes the 1/15 part of the work so he will complete the entire work in 15 days.

১০,৮৯৩.

The average age of A, B and C is 30 years. If the difference between B’s age and A’s age is the same as the difference between C’s age and B’s age. If D is 40 years older than B then what is the sum of the age of B and D?

ক
ক) 130 years
খ
খ) 60 years
গ
গ) 75 years
ঘ
ঘ) 100 years

ব্যাখ্যা

A + B + C = 30×3 = 90 yrs ...... (1)
ATQ,
B - A = C - B
Or, A+C = 2B
From (1),
B + 2B = 90
Or, B = 30
∴ D = B + 40 = 30 + 40 = 70
So, B + D = 30+70 = 100 yrs

১০,৮৯৪.

If A381 is divisible by 11, find the value of the smallest natural number A?

ক
5
খ
6
গ
7
ঘ
9

ব্যাখ্যা

Question: If A381 is divisible by 11, find the value of the smallest natural number A?

Solution:
A number is divisible by 11 if the difference of the sum of the digits in the odd places and sum of the digits in even place is zero or divisible by 11.
Hence, (A + 8) - (3 + 1) = 0 or multiple of 11.
To get the difference 0 or multiple of 11, we need 7 at the place of A.
So, sum of odd place - sum of even place
= 15 - 4 = 11. And this is divisible by 11.

১০,৮৯৫.

A train 300 metres long is running at a speed of 90 km/hr. How many seconds will it take cross a 200 metres long train running in the same direction at a speed of 60 km/hr?

ক
70 s
খ
60 s
গ
50 s
ঘ
12 s

ব্যাখ্যা

Question: A train 300 metres long is running at a speed of 90 km/hr. How many seconds will it take cross a 200 metres long train running in the same direction at a speed of 60 km/hr?

Solution:
Length of 1st train 300 metres
Length of 2nd train 200 metres

∴ Total distance to cross each other = 300 + 200 metres
= 500 metres

Relative speed for travelling same direction = 90 - 60 km/hr
= 30 km/hr
= (30 × 1000)/3600 m/s
= 300/36 m/s

Required time to cross = 500/(300/36) s
= (500 × 36)/300 s
= 60 s

১০,৮৯৬.

If principal P becomes Q in 2 years when interest R% is compounded half-yearly. And if the same principal P becomes Q in 2 years when interest S% is compound annually, then which of the following is true ?

ক
ক) R > S
খ
খ) R = S
গ
গ) R < S
ঘ
ঘ) None

ব্যাখ্যা

Since interest is compounded half yearly at R% p.a. the value of R will be lesser than the value of S

১০,৮৯৭.

A company pays rent of Tk. 20000 per month for office space to its owner. But if the company pays the annual rent at the beginning of the year the owner gives a discount of 5% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

ক
ক) Tk. 225000
খ
খ) Tk. 228000
গ
গ) Tk. 227000
ঘ
ঘ) Tk. 226000

ব্যাখ্যা

Question: A company pays rent of Tk. 20000 per month for office space to its owner. But if the company pays the annual rent at the beginning of the year the owner gives a discount of 5% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

Solution:
Total annual rent = Tk. (20000 × 12) = Tk. 240000
Discount = 5% of tk. 240000
= Tk. 12000
∴ Annual rent paid after discount = Tk. (240000 - 12000)
= Tk. 228000

১০,৮৯৮.

tan³60° - 2sin60° = ?

ক
√3
খ
1/√3
গ
2
ঘ
2√3

ব্যাখ্যা

Question: tan³60° - 2sin60° = ?

Solution:
Given that,
tan³60° - 2sin60°
= (√3)³ - 2(√3/2)
= 3√3 - √3
= 2√3

১০,৮৯৯.

Find the equation of the line with x- intercept = 4 and y- intercept = 3.

ক
3x - 4y - 12 = 0
খ
4x + 3y - 12 = 0
গ
3x + 4y - 12 = 0
ঘ
3x + 4y + 12 = 0

ব্যাখ্যা

Question: Find the equation of the line with x- intercept = 4 and y- intercept = 3.

Solution:
x- intercept = 4, so, the line passes through (4, 0)
y- intercept = 3, so, the line passes through (0, 3)

we know, The intercept form of a line is:
(x/a) + (y/b) = 1, where a = x- intercept and b = y- intercept
or, (x/4) + (y/3) = 1
or, (3x + 4y)/12 = 1
or, 3x + 4y = 12
∴ 3x + 4y - 12 = 0

so, the equation of the line is 3x + 4y - 12 = 0

১০,৯০০.

If θ be a positive acute angle satisfying cos²θ + cos⁴θ = 1, then the value of tan²θ + tan⁴θ is?

ক
3/2
খ
0
গ
1
ঘ
1/2
ঙ
None of these

ব্যাখ্যা

Question: If θ be a positive acute angle satisfying cos²θ + cos⁴θ = 1, then the value of tan²θ + tan⁴θ is?

Solution:
Given that,
cos²θ + cos⁴θ = 1
⇒ cos⁴θ = 1 - cos²θ
⇒ cos⁴θ = sin²θ ; [sin²θ = 1 - cos²θ]
⇒ cos²θ.cos²θ = sin²θ
⇒ cos²θ = sin²θ/cos²θ
⇒ cos²θ = tan²θ

Now,
cos²θ + cos⁴θ = 1
⇒ cos²θ + (cos²θ)² = 1
⇒ tan²θ + (tan²θ)² = 1
∴ tan²θ + tan⁴θ = 1