Bank Math

PrepBank · পাতা ১৪৩ / ১৬১ · ১৪,২০১–১৪,৩০০ / ১৬,১২৪

১৪,২০১.

For many two numbers m, n ; (m + n) : (m - n) : mn = 7 : 1 : 60. Find the value of 1/m : 1/n

ক
ক) 4 : 3
খ
খ) 8 : 7
গ
গ) 3 : 4
ঘ
ঘ) 7 : 8

ব্যাখ্যা

(m+n)/(m−n) = 7x/x
⇒ m/n=4x/ 3x
Again mn=12x²
and mn =60x
so, 60x=12x²
⇒ x = 5
=> m = 20 and n= 15
Hence, 1/m : 1/n = 1/20 : 1/15 = 3 : 4

১৪,২০২.

A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?

ক
40 km/hr
খ
25 km/hr
গ
30 km/hr
ঘ
45 km/hr
ঙ
35 km/hr

ব্যাখ্যা

time = 1 hr 40 min 48 sec
= 1 hr + 40/60 hr + 48/3600 hr
= 1 + 2/3 + 1/75 = 126/75 hr
distance = 42 km
speed = distance/time = 42/( 126/75 ) = (42 × 75)/126 = 25 km/hr
⇒ 5/7 of the actual speed = 25
⇒ Actual speed = 25 × 7/5 = 35 km/hr

১৪,২০৩.

A, B and C together invest Tk. 53000 in a business. A invests Tk. 5000 more than B and B invests Tk. 6000 more than C. Out of a total profit of Tk. 31800, find the share of A.

ক
Tk. 12500
খ
Tk. 13800
গ
Tk. 12800
ঘ
Tk. 13500

ব্যাখ্যা

Question: A, B and C together invest Tk. 53000 in a business. A invests Tk. 5000 more than B and B invests Tk. 6000 more than C. Out of a total profit of Tk. 31800, find the share of A.

Solution:
Let C's investment = x
Then,
B invests Tk. 6,000 more than C
∴ B = x + 6000
A invests Tk. 5000 more than B
∴ A = (x + 6000) + 5000 = x + 11000

Total investment,
A + B + C = 53000
⇒ (x + 11000) + (x + 6000) + x = 53000
⇒ 3x + 17000 = 53000
⇒ 3x = 36000
∴ x = 12000

Now,
C = x = 12000
B = 12000 + 6000 = 18000
A = 12000 + 11000 = 23000

∴ Profit sharing ratio is,
A : B : C = 23000 : 18000 : 12000 = 23 : 18 : 12

∴ Share of A = 31800 × (23/53) = Tk. 13800

১৪,২০৪.

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
ক) 24 hours
খ
খ) 32 hours
গ
গ) 35 hours
ঘ
ঘ) 30 hours

ব্যাখ্যা

Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

Now
(1/x) + (2/x) + (4/x) = 1/5
(1 + 2 + 3)/x = 1/5
7/x = 1/5
x = 35

১৪,২০৫.

Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

ক
20
খ
5
গ
3
ঘ
13

ব্যাখ্যা

Question: Find a positive number which increased by 17 is equal to 60 times the reciprocal of the number.

Solution:
let the number be x

(x + 17) = 60 (1/x)
⇒ x² + 17x - 60 = 0
⇒ x²+ 20x - 3x - 60 = 0
⇒ x (x + 20) - 3 (x + 20) = 0
⇒ (x + 20) (x - 3) = 0
∴ x = - 20 , 3

as the number is positive, answer is 3

১৪,২০৬.

Sara covered a distance of 450 miles between city X and city Y in a total of 7 hours. If part of the distance was covered at 50 miles per hour speed and the remaining distance at 75 miles per hour speed, how many hours did she travel at 50 miles per hour?

ক
2 hours
খ
2 hours 20 minute
গ
3 hours
ঘ
3 hours 30 minute

ব্যাখ্যা

Question: Sara covered a distance of 450 miles between city X and city Y in a total of 7 hours. If part of the distance was covered at 50 miles per hour speed and the remaining distance at 75 miles per hour speed, how many hours did she travel at 50 miles per hour?

Solution:
2 hours were spent traveling at 50 miles per hour,
(7 - x) hours were spent traveling at 75 miles per hour.

ATQ,
50x + 75(7 - x) = 450
⇒ 50x + 525 - 75x = 450
⇒ - 25x + 525 = 450
⇒ - 25x = - 75
∴ x = 3

∴ Sara traveled 3 hours at 50 miles per hour.

১৪,২০৭.

What is the sum of two consecutive even numbers, the difference of whose squares is 84?

ক
ক) 40
খ
খ) 42
গ
গ) 44
ঘ
ঘ) 46

ব্যাখ্যা

Let
the numbers be x and x + 2.

Then,
(x + 2)² - x² = 84
x² + 2.x.2 + 2² - x² =84
4x + 4 = 84
4x = 80
x = 20.

The required sum = x + (x + 2)
= 2x + 2
= (2 × 20) + 2
= 42

১৪,২০৮.

α and β are the roots of 2x² + 5x + 2 = 0 then, the value of (1/α) + (1/β) is-

ক
- 3/2
খ
- 2
গ
- 5/2
ঘ
- 2/5

ব্যাখ্যা

Question: α and β are the roots of 2x² + 5x + 2 = 0 then, the value of (1/α) + (1/β) is-

Solution:
Here,
2x² + 5x + 2 = 0
where, a = 2, b = 5 and c = 2

∴ α + β = - (b/a) = - 5/2
and αβ = c/a = 2/2 = 1

∴ (1/α) + (1/β)
= (β + α)/αβ
= {- (5/2)}/1
= - 5/2

১৪,২০৯.

Questions (21-30 ) : Read the following questions carefully and choose the right answer.
21. Alam sold two vehicles for Tk 46000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

ক
ক) 2% loss
খ
খ) 1% profit
গ
গ) 1% loss
ঘ
ঘ) None of these

ব্যাখ্যা

Question: Alam sold two vehicles for Tk 46000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

Solution:
Let the profit be x% and loss be y%.
Net profit or loss% = {x + (- y) + x ×(- y)}/100 [Negative sign denotes that their is a loss]
Their is 10% loss and 10% profit then
∴ Net profit or loss% = {10 + (- 10) + 10 ×(- 10)}/100
= (10 - 10 - 100)/100
= - 1
∴ The net loss is 1%

১৪,২১০.

A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?

ক
3.5
খ
6
গ
8
ঘ
None of these

ব্যাখ্যা

Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?

Solution:
Let
the number is x

According to the given question-
3(2x + 9) = 75
⇒ 6x + 27 = 75
⇒ 6x = 75 - 27
⇒ 6x = 48
⇒ x = 48/6
x = 8

Hence, the number is 8.

১৪,২১১.

Twelve years ago, Babu was twice as old as Vuttu. If the ratio of their present ages is 4 : 3 respectively, find the difference between their present ages.

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

ব্যাখ্যা

Question: Twelve years ago, Babu was twice as old as Vuttu. If the ratio of their present ages is 4 : 3 respectively, find the difference between their present ages.

Solution:
Let 12 years ago age of Vuttu was x years and age of Babu was 2x.
So, present age of Vuttu = x + 12
And, present age of Babu = 2x + 12

As per question,
(2x + 12)/(x + 12) = 4/3
⇒ 6x + 36 = 4x + 48
⇒ 2x = 12
∴ x = 6

Present age of Vuttu = 6 + 12 = 18 years
Present age of Babu = 2 × 6 + 12 = 24 years

∴ Required difference between their ages = 24 - 18 = 6 years

১৪,২১২.

A football team lost 40% of the matches it played. If it won 75 matches, then find the number of matches it played.

ক
ক) 125
খ
খ) 115
গ
গ) 110
ঘ
ঘ) 120

ব্যাখ্যা

ম্যাচ হারে % = 40%
ম্যাচ জয় করে = 75 matches
ম্যাচ জয়ের হার = 100% - lost% = 100 - 40 = 60%

ধরি, ম্যাচ খেলার সংখ্যা 'x'

প্রশ্নমতে,
60% of x = 75
⇒ 60/100 × (x) = 75
⇒ x = (75/60) × 100
⇒ x = 5/4 × 100
⇒ x = 5 × 25 = 125

∴ ফুটবল দলটি ম্যাচ খেলে ১২৫টি।

১৪,২১৩.

A batsman makes a score of 84 runs in the 21^st inning and thus increases his average by 2 runs. His average after 21^st inning is-

ক
ক) 44
খ
খ) 38
গ
গ) 42
ঘ
ঘ) 48

ব্যাখ্যা

The average for 20 innings be x

Now
(20x + 84)/21 = x + 2
20x + 84 = 21x + 42
21x - 20x = 84 - 42
x = 42

∴ Average after 21^st innings
= 42 + 2
= 44

১৪,২১৪.

A shopkeeper marks the price of an article at Tk. 80. What will be the selling price, if he allows two successive discounts of 5% each?

ক
Tk. 72.20
খ
Tk. 72
গ
Tk. 72.22
ঘ
Tk. 72.25

ব্যাখ্যা

At 5% discount for the first time = 80 × 95/100 = Tk. 76
At 5% discount for second time = 76 × 95/100 = Tk. 72.20

১৪,২১৫.

In an examination, 25% candidates failed in English and 35% students failed in Math. If 15% candidates failed in both, what is the percentage of candidates who passed in both the subjects?

ক
45%
খ
55%
গ
50%
ঘ
58%

ব্যাখ্যা

Question: In an examination, 25% candidates failed in English and 35% students failed in Math. If 15% candidates failed in both, what is the percentage of candidates who passed in both the subjects?

Solution:
Failed in both English and Math = 15%
Only failed in English = (25 - 15)% = 10%
Only failed in Math = (35 - 15)% = 20%

∴ Candidates who failed one or both subjects = 15% + 10% + 20%
= 45%

∴ Candidates who passed in both the subject = (100 - 45)% = 55%

১৪,২১৬.

A fair coin is tossed 3 times. What is the probability of getting exactly two tails?

ক
1/8
খ
2/3
গ
3/8
ঘ
1/4

ব্যাখ্যা

Question: A fair coin is tossed 3 times. What is the probability of getting exactly two tails?

Solution:
একটি মুদ্রা 3 বার ছুঁড়লে মোট সম্ভাব্য ফলাফল (Total outcomes) হলো 2³ = 8 টি।
মোট ফলাফল (S) = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
মোট ফলাফলের সংখ্যা, n(S) = 8

'ঠিক দুটি টেইল' (exactly two tails) এর অনুকূল ফলাফল, E = {HTT, THT, TTH}
∴ অনুকূল ফলাফলের সংখ্যা, n(E) = 3

∴ সম্ভাবনা (Probability) = অনুকূল ফলাফলের সংখ্যা/মোট ফলাফল
P(E) = n(E)/n(S)
P(E) = 3/8

অতএব, ঠিক দুটি টেইল পাওয়ার সম্ভাবনা হলো 3/8।

১৪,২১৭.

The angle measure of base angles of an isosceles triangle are represented by x and the vertex angle is 3x + 25. Find the measure of base angle.

ক
ক) 16°
খ
খ) 31°
গ
গ) 34°
ঘ
ঘ) 42°

ব্যাখ্যা

ATQ, x + x + 3x + 25 = 180°
Or, 5x = 155°
∴ x = 31°

১৪,২১৮.

What will be the difference of simple profit and compound profit of Tk. 8,000 in 2 years if the rate of profit is Tk. 10 percent per annum?

ক
Tk 150
খ
Tk 135
গ
Tk 115
ঘ
Tk 95
ঙ
Tk 80

ব্যাখ্যা

Question: What will be the difference of simple profit and compound profit of Tk. 8,000 in 2 years if the rate of profit is Tk. 10 percent per annum?

Solution:
Given,
P = 8000 Tk
n = 2 years
r = 10% = 10/100 = 1/10

We know,
Simple profit I = Prn
= 8000 × 1/10 × 2
= 1600

and,
Compound profit = P(1 + r)ⁿ - P
= P{(1 + r)ⁿ - 1}
= 8000{(1 + 1/10)² - 1}
= 8000{(11/10)² - 1}
= 8000(121/100 - 1)
= 8000 × (21/100)
= 1680

So the difference of simple profit and compound profit = (1680 - 1600) = Tk 80

১৪,২১৯.

In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

ক
0%
খ
15%
গ
25.5%
ঘ
35%

ব্যাখ্যা

Question: In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

Solution:
At the end of January,
The value of the stock is = Tk. 200 + 50% of (Tk. 200)
= Tk. 200 + Tk. 100 = Tk. 300.

At the end of February,
The value of the stock is = Tk. 300 - 20% of (Tk. 300)
= Tk. 300 - Tk. 60 = Tk. 240.

At the end of March,
The value of the stock is = Tk. 240 + 25% of (Tk. 240)
= Tk. 240 + Tk. 60 = Tk. 300.

At the end of April,
The value of the stock is = Tk. 300 - 10% of (Tk. 300)
= Tk. 300 - Tk. 30 = Tk. 270.

Now, the percentage change in price is,
= (Change in price/Original price) × 100%
= (270 - 200)/200 × 100%
= (70/200) × 100%
= 35%

১৪,২২০.

A pipe can fill a tank in p hours and another pipe can empty it in q hours (q > p). If both pipes are open together, in how many hours will the tank be filled?

ক
(q - p)/pq hours
খ
p + q hours
গ
pq/(q - p) hours
ঘ
None of these

ব্যাখ্যা

Question: A pipe can fill a tank in p hours and another pipe can empty it in q hours (q > p). If both pipes are open together, in how many hours will the tank be filled?

Solution:

Let the tank capacity = 1 unit.
Filling pipe rate = 1/p (tank per hour)
Emptying pipe rate = 1/q (tank per hour → negative)

Net rate when both pipes are open = 1/p – 1/q = (q – p) / (pq)
Time to fill the tank = Total tank ÷ Net rate = 1 ÷ [(q – p)/ (pq)] = pq / (q – p) hours

১৪,২২১.

x is a two digit number. The digits of the number differ by 2 and the square of the digits differ by 32. Which one of the following could x equal?

ক
ক) 75
খ
খ) 86
গ
গ) 97
ঘ
ঘ) 64

ব্যাখ্যা

9 - 7= 2 অর্থাৎ অঙ্কদ্বয়ের পার্থক্য 6 এবং
9²- 7² = 81 - 49 = 32 অর্থাৎ অক্ষদ্বয়ের বর্গের অন্তর 32
x এর মান হবে 97

১৪,২২২.

The average salary of 30 officers in an office is 120 tk and the average salary of laborers is 40 tk. Find the total number of laborers if the average salary of the office is 50 tk.

ক
180
খ
220
গ
210
ঘ
160

ব্যাখ্যা

Question: The average salary of 30 officers in an office is 120 tk and the average salary of laborers is 40 tk. Find the total number of laborers if the average salary of the office is 50 tk.

Solution:
The sum of the salary of officers will be = 30 × 120 = 3600
Let the number of laborers = L

ATQ,
3600 + 40L = 50(30 + L)
⇒ 2100 = 10L
∴ L = 210

১৪,২২৩.

The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What is the present age of the elder person?

ক
20 years
খ
30 years
গ
40 years
ঘ
10 years

ব্যাখ্যা

Let present age of the elder person = x
The present age of the younger person = x - 16
According to the question,
x - 6 = 3(x - 16 - 6)
⇒ x - 6 = 3x - 66
⇒ 2x = 60
⇒ x = 30
Hence, the present age of the elder person is 30 years.

১৪,২২৪.

A number consist of two digits, the sum of the digits is 10. If 72 is subtracted from the number, the digits are interchanged. Find the number.

ক
ক) 73
খ
খ) 82
গ
গ) 91
ঘ
ঘ) 95

ব্যাখ্যা

ধরি
একক স্থানীয় অংক x
দশক স্থানীয় অংক y

সংখ্যাটি = x + 10y

প্রশ্নমতে
x + y = 10 ....................(1)
আবার
x + 10y - 72 = 10x + y
10y - y = 10x - x + 72
9y - 9x = 72
9(y - x) = 72
y - x = 8
y = 8 + x......................(2)

(1) নং সমীকরণ হতে পাই
x + 8 + x = 10
2x + 8 = 10
2x = 10 - 8
2x = 2
x = 1

x এর মান (2) নং সমীকরণে বসিয়ে পাই
y = 8 + 1
y = 9

সংখ্যাটি = x + 10y
= 1 + 10 × 9
= 1 + 90

১৪,২২৫.

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

ক
450 kg
খ
560 kg
গ
600 kg
ঘ
720 kg

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

Solution:
Total quantity of sugar = 1000 kg

Let x kg be sold at 18% profit
Then (1000 - x) kg be sold at 8% profit

Profit from x kg at 18% = 18x/100
Profit from (1000 - x) kg at 8% = 8(1000 - x)/100

Total profit = 14% of 1000 = 14000/100 = 140

According to the question,
18x/100 + 8(1000 - x)/100 = 140
⇒ 18x + 8(1000 - x) = 14000
⇒ 18x + 8000 - 8x = 14000
⇒ 10x = 14000 - 8000
⇒ 10x = 6000
⇒ x = 600

∴ 600 kg of sugar was sold at 18% profit.

বিকল্প সমাধান:
By the rule of alligation,

Ration of 1^st and 2^nd parts = 4 : 6 = 2 : 3
∴ Quantity of 2^nd kind = (3/5) × 1000 = 600 kg

১৪,২২৬.

Raju drove 8 miles west, 6 miles north, 3 miles east, and 6 more miles north. How far was Raju from his starting place?

ক
ক) 12 miles
খ
খ) 13 miles
গ
গ) 17 miles
ঘ
ঘ) 19 miles

ব্যাখ্যা

Question: Raju drove 8 miles west, 6 miles north, 3 miles east, and 6 more miles north. How far was Raju from his starting place?

Solution:

AE = √(AF² + EF²)
= √{(8 - 3)²+(6 + 6)²}
= √( 25 + 144)
= √169
= 13

১৪,২২৭.

The average marks of a student in 4 subjects is 75. If the student obtained 85 marks in the fifth subject, then the new average is

ক
ক) 76
খ
খ) 77
গ
গ) 78
ঘ
ঘ) 79

ব্যাখ্যা

Sum of marks in 4 Subjects = 75 × 4 = 300
Sum of marks in 5 Subjects = 300 + 85 = 385
New Average = 385/5 = 77

১৪,২২৮.

Painter A can paint a house in 16 days, and painter B can do the same work in 20 days. With the help of painter C, they paint the house in 8 days only. Then, Painter C alone can do this task in -

ক
ক) 80 Days
খ
খ) 85 Days
গ
গ) 79 Days
ঘ
ঘ) 76 Days

ব্যাখ্যা

A paints in 20 days;
B paints in 30 days;
Let C paint in c days.

1/20 + 1/16 + 1/c = 1/8
1/c = 1/8 – 1/20 – 1/16
1/c = (10 – 4 – 5)/80 = 1/80
Hence, C alone should paint the house in 80 days.

১৪,২২৯.

A clock loses (falls behind) 15 minutes each day. How many days will it take to reach a point where the clock will indicate the correct time?

ক
36 days
খ
48 days
গ
54 days
ঘ
72 days

ব্যাখ্যা

Question: A clock loses (falls behind) 15 minutes each day. How many days will it take to reach a point where the clock will indicate the correct time?

Solution:
একটি ঘড়িকে পুনরায় সঠিক সময় দেখাতে হলে তাকে 12 ঘণ্টা সময় হারাতে হবে। কারণ একটি 12 ঘণ্টার ঘড়িতে যখন সঠিক সময় থেকে 12 ঘণ্টা সময় পিছিয়ে পড়বে, তখন এটি আবার সঠিক সময় নির্দেশ করবে।
12 ঘণ্টা = 12 × 60 মিনিট = 720 মিনিট

এখন, যেহেতু ঘড়িটি প্রতিদিন 15 মিনিট করে সময় হারায়,

15 মিনিট সময় হারায় 1 দিনে
∴720 মিনিট সময় হারাবে = (1/15) × 720 দিনে
= 48 দিনে
সুতরাং, 48 দিন পর ঘড়িটি আবার সঠিক সময় দেখাবে।

১৪,২৩০.

3 horses cost is equal to 5 cows cost. If 4 horses and 6 cows total cost is Tk. 19000, then what is the cost of each horse?

ক
ক) Tk. 2500
খ
খ) Tk. 1500
গ
গ) Tk. 2000
ঘ
ঘ) Tk. 5000

ব্যাখ্যা

Question: 3 horses cost is equal to 5 cows cost. If 4 horses and 6 cows total cost is Tk. 19000, then what is the cost of each horse?

Solution:
Let,
cost of one horse = Tk. x
cost of one cow = Tk. y

ATQ,
3x = 5y
x = 5y/3 ............ (1)

Again,
4x + 6y = 19000
⇒ 4 × (5y/3) + 6y = 19000
⇒ (20y + 18y)/3 = 19000
⇒ 38y = 19000 × 3
⇒ 38y = 57000
⇒ y = 57000/38
∴ y = 1500

From (1) we get,
x = (5 × 1500)/3
∴ x = 2500

∴ Cost of one horse = Tk. 2500

১৪,২৩১.

A box contains 5 red, 6 green and 7 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or white?

ক
ক) 1/2
খ
খ) 1/4
গ
গ) 2/3
ঘ
ঘ) 3/5

ব্যাখ্যা

Question: A box contains 5 red, 6 green and 7 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or white?

Solution:
Total number of balls = (5 + 6 + 7) = 18

P(drawing a red ball or a white ball) = P(red) + P(white)
= 5/18 + 7/18
= 12/18
= 2/3

১৪,২৩২.

If 25% of 1200 + 35% of 600 = x% of 4000, find the value of x.

ক
14.65
খ
10.50
গ
12.75
ঘ
11.50

ব্যাখ্যা

Question: If 25% of 1200 + 35% of 600 = x% of 4000, find the value of x.

Solution:
25% of 1200 + 35% of 600 = x% of 4000
⇒ (25/100) × 1200 + (35/100) × 600 = (x/100) × 4000
⇒ 300 + 210 = 40x
⇒ 40x = 510
⇒ x = 510/40
∴ x = 12.75

১৪,২৩৩.

A boat sailing against a stream of river takes 6 hours to travel 36 km while sailing with the stream it takes 3 hours to travel the same distance. What is the speed of the stream?

ক
3 km/h
খ
3.5 km/h
গ
4 km/h
ঘ
5 km/h

ব্যাখ্যা

Question: A boat sailing against a stream of river takes 6 hours to travel 36 km while sailing with the stream it takes 3 hours to travel the same distance. What is the speed of the stream?

Solution:
Let,
Speed of boat = x km/h and,
Speed of stream = y km/h

ATQ,
x - y = 36/6 = 6 ......... (i)
x + y = 36/3 = 12 ....... (ii)

From,
(ii) - (i)
x + y - x + y = 12 - 6
⇒ 2y = 6
∴ y = 3

So, Speed of the stream = 3 km/h

১৪,২৩৪.

Two outlet pipes A and B are connected to a full tank. Pipe A alone can empty the tank in 10 minutes and pipe B alone can empty the tank in 30 minutes. If both are opened together, how much time will it take to empty the tank completely?

ক
7 minutes
খ
7 minutes 30 seconds
গ
6 minutes
ঘ
6 minutes 3 seconds

ব্যাখ্যা

Question: Two outlet pipes A and B are connected to a full tank. Pipe A alone can empty the tank in 10 minutes and pipe B alone can empty the tank in 30 minutes. If both are opened together, how much time will it take to empty the tank completely?

Solution:
Let the capacity of the tank be LCM(10, 30) = 30 units
Efficiency of pipe A = 30/10 = 3 units/minute
Efficiency of pipe B = 30/30 = 1 units/minute

∴ Combined efficiency of pipe A and pipe B = 4 units/minute

Therefore, time required to empty the tank if both pipes work = 30/4 minutes = 7.5 minutes = 7 minutes 30 seconds

১৪,২৩৫.

The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is:

ক
20°
খ
25°
গ
30°
ঘ
40°

ব্যাখ্যা

Question: The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is:

Solution:

Let,
AB = height of tree
BC= Shadow of tree
angle of elevation = C
∴ BC = √3 AB

We know,
tan∠C = AB/BC
⇒ tan∠C = AB/√3AB
⇒ tan∠C = 1/√3
⇒ tan∠C = tan30°
∴ ∠C = 30°

১৪,২৩৬.

Rahim buys a Tk. 50 share of a company that pays 12% profit. He buys the share at such a price that he earns 20% on his investment. At what price did Rahim buy the share?

ক
Tk. 36
খ
Tk. 35
গ
Tk. 32
ঘ
Tk. 30

ব্যাখ্যা

Question: Rahim buys a Tk. 50 share of a company that pays 12% profit. He buys the share at such a price that he earns 20% on his investment. At what price did Rahim buy the share?

Solution:
Here
profit given by the company on 1 share = 12% of 50
= Tk. 6

Let
Rahim buys one share for x Tk

ATQ,
20% of x = 6
20x/100 = 6
⇒ 20x = 600
⇒ x = 600/20
∴ x = 30

Rahim bought the share at Tk. 30

১৪,২৩৭.

One army camp had ration for 560 soldiers for 20 days, 560 soldiers reported for the camp, and after 12 days, 112 soldiers were sent to another camp. For how many days, the remaining soldiers can stay in the camp without getting any new ration?

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

ব্যাখ্যা

Question: One army camp had ration for 560 soldiers for 20 days, 560 soldiers reported for the camp, and after 12 days, 112 soldiers were sent to another camp. For how many days, the remaining soldiers can stay in the camp without getting any new ration?

Solution:
After 12 days, there was ration for 560 soldiers for 8 days.
Remaining persons = (560-112) = 448
Less soldiers, more days (inverse proportion)
Let the x is the required number of days
Then, 448 : 560 = 8 : x
Or, x = (560 × 8)/ 448 = 10
Hence, the required number of days is 10.

১৪,২৩৮.

What will come at the place of question mark?
3, 6, 11, 18, 27, ?

ক
48
খ
41
গ
36
ঘ
43
ঙ
38

ব্যাখ্যা

Question: What will come at the place of question mark?
3, 6, 11, 18, 27, ?

Solution:
Look at the differences between consecutive terms.
6 - 3 = 3
11 - 6 = 5
18 - 11 = 7
27 - 18 = 9
The first differences are 3, 5, 7, 9
These increase by + 2 each time (3 ⇒ 5 ⇒ 7 ⇒ 9).
So the next difference should be = 9 + 2 = 11

Therefore next number = 27 + 11 = 38

১৪,২৩৯.

A password consists of 2 letters (A-Z only) followed by 2 digits (0-9).
How many such passwords can be formed if no repetition is allowed?

ক
60500
খ
65000
গ
60000
ঘ
58500

ব্যাখ্যা

Question: A password consists of 2 letters (A-Z only) followed by 2 digits (0-9). How many such passwords can be formed if no repetition is allowed?

Solution:

First letter: 26 choices

Second letter: 25 remaining choices

Total letter arrangements = 26 × 25 = 650

First digit: 10 choices

Second digit: 9 remaining choices

Total digit arrangements = 10 × 9 = 90

Total passwords = 650 × 90 = 58500

১৪,২৪০.

A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included?

ক
196
খ
186
গ
190
ঘ
200
ঙ
250

ব্যাখ্যা

When at least 2 women are included.
The committee may consist of 3 women, 2 men : It can be done in ⁴C₃ × ⁶C₂ : ⁴C₃ × ⁶C₂ ways.
or, 4 women, 1 man : It can be done in ⁴C₄ × ⁶C₁ : ⁴C₄ × ⁶C₁ ways.
or, 2 women, 3 men : It can be done in ⁴C₂ × ⁶C₃ : ⁴C₂ × ⁶C₃ ways.
Total number of ways of forming the committees,
= ⁴C₂ × ⁶C₃ + ⁴C₃ × ⁶C₂ + ⁴C₄ × ⁶C₁
= 6 × 20 + 4 × 15 + 1 × 6
= 120 + 60 + 6
= 186

১৪,২৪১.

A pipe can fill a tank in x hours and another pipe can empty it in y (y > x) hours. If both pipes are open, in how many hours will the tank is filled?

ক
xy/(x - y) hours
খ
xy/(y - x) hours
গ
(x - y) hours
ঘ
(x + y) hours
ঙ
None of the above

ব্যাখ্যা

Question: A pipe can fill a tank in x hours and another pipe can empty it in y (y > x) hours. If both pipes are open, in how many hours will the tank is filled?

Solution:
Net part filled in 1 hour
= (1/x) - (1/y)
= (y - x)/xy hours

∴ The tank will be filled in = xy/(y - x) hours.

১৪,২৪২.

A man takes 20 minutes to row 12 km upstream which is one-third more than the time he takes on his way downstream. What is his speed in still water?

ক
ক) 72 km/hr
খ
খ) 42 km/hr
গ
গ) 36 km/hr
ঘ
ঘ) 48 km/hr

ব্যাখ্যা

Question: A man takes 20 minutes to row 12 km upstream which is one-third more than the time he takes on his way downstream. What is his speed in still water?

Solution:
Let,
His speed in still water is x km/hr
The speed of stream is y km/hr
Time taken downstream is t min
ATQ,
t + (t/3) = 20 min
⇒ (3t + t)/3 = 20
⇒ 4t = 20 × 3
⇒ t = 60/4
∴ t = 15 min

In 20 minutes he rows in upstream 12 km
∴ In 60 minutes he rows in upstream (12 × 60)/20 km
= 36 km

∴ x - y = 36 ..............(1)

In 15 minutes he rows In downstream 12 km
∴ In 60 minutes he rows In downstream (12 × 60)/15 km
= (720 × 3)/40 km
= 48 km

∴ x + y = 48 ................(2)

From (2) + (1) we get,
x + y + x - y = 48 + 36
⇒ 2x = 84
∴ x = 42

∴ His speed in still water is 42 km/hr

১৪,২৪৩.

Which of the following lines passes through the point (2, 5)?

ক
y = 2x - 1
খ
y = 2x + 1
গ
y = 4x - 2
ঘ
y = 2x + 5

ব্যাখ্যা

Question: Which of the following lines passes through the point (2, 5)?

Solution:
At the point (2, 5), x is 2 and y is 5. We can check which equation works when we substitute in these values:
y = 2x - 1 ⇒ 5 = 2 × 2 - 1 False
y = 2x + 1 ⇒ 5 = 2 × 2 + 1 True
y = 4x - 2 ⇒ 5 = 4 × 2 - 2 False
y = 2x + 5 ⇒ 5 = 2 × 2 + 5 False

১৪,২৪৪.

Armaan and Ghalib started a cafe with Tk. 40000 and Tk. 80000, respectively. Ghalib got married to someone in another town and left after 7 months. But Jishan immediately replaced him with an investment of Tk. 144000. At the end of the year, the business performed well and registered a profit of Tk. 50600.What is Ghalib’s share in this profit?

ক
ক) Tk. 13800
খ
খ) Tk. 16100
গ
গ) Tk. 16500
ঘ
ঘ) Tk. 16866.67

ব্যাখ্যা

We know,
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment x Time) : (B's investment x Time) = Profit of A : Profit of B

The total value of investment of Arman, Ghalib, and Jishan after 12 months is =
Tk. 40000 x 12 months : Tk. 80000 x 7 months : Tk. 144000 x (12 - 7)months = 480000 : 560000 : 720000
∴ Profit ratio = 240000 : 280000 : 360000 = 6 : 7 : 9
∴ Share of Ghalib = 7/(6 + 7 + 9) x 50600 = Tk. 16100

১৪,২৪৫.

The volume of a cuboid with length, breadth and height as 5x, 3x² and 7x⁴ respectively is:

ক
105x⁷
খ
105x²
গ
105x⁴
ঘ
105x

ব্যাখ্যা

Question: The volume of a cuboid with length, breadth and height as 5x, 3x² and 7x⁴ respectively is:

Solution:
দেওয়া আছে
আয়তাকার ঘনবস্তুর (cuboid) দৈর্ঘ্য = 5x
আয়তাকার ঘনবস্তুর (cuboid) প্রস্থ = 3x²
আয়তাকার ঘনবস্তুর (cuboid) উচ্চতা = 7x⁴

আয়তাকার ঘনবস্তুর আয়তন = 5x × 3x² × 7x⁴
= 105x⁷

১৪,২৪৬.

Given n = 1 + x and x is the product of four consecutive integers. Then which of the following us true?
I. n is an odd integer.
II. n is prime.
III. n is a perfect square

ক
Only I is correct
খ
Only II is correct
গ
Only III is correct
ঘ
Both I and II are correct
ঙ
Both I and III are correct

ব্যাখ্যা

Question: Given n = 1 + x and x is the product of four consecutive integers. Then which of the following us true?
I. n is an odd integer.
II. n is prime.
III. n is a perfect square

Solution:
Out of four consecutive integers, two are even and therefore, their product is even, and on adding 1 to it, we get an odd integer. So, n is odd. Some possible values of n are as follows:
n = 1 + (1 × 2 × 3 × 4) = (1 + 24) = 25 = 5²
n = 1 + (2 × 3 × 4 × 5) = (1 + 120) = 121 = 11²
n = 1 + (3 × 4 × 5 × 6) = (1 + 360) = 361 = 19²
n = 1 + (4 × 5 × 6 × 7) = (1 + 840) = 841 = 29²
And so on.....
Hence, n is odd and a perfect square.

১৪,২৪৭.

Bimol started a business investing Tk. 9000. After five months, Sifat joined with a capital of Tk 8000. If at the end of the year, they earn a profit of Tk 6970, then what will be the share of Sifat in the profit?

ক
2380 Tk
খ
2240 tk
গ
2420 Tk
ঘ
2160 Tk

ব্যাখ্যা

Question: Bimol started a business investing Tk. 9000. After five months, Sifat joined with a capital of Tk 8000. If at the end of the year, they earn a profit of Tk 6970, then what will be the share of Sifat in the profit?

Solution:
Bimol invested for 12 months and Sifat invested for 7 months.
So Bimol : Sifat = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14

Sifat Ratio in profit will be = 6970 × (14/41)
= Tk 2380

১৪,২৪৮.

If annual income from 6% stock at 80 is Tk. 50 more than 7% stock at 120, then the investment is-

ক
Tk. 2500
খ
Tk. 3000
গ
Tk. 4500
ঘ
Tk. 5000

ব্যাখ্যা

Question: If annual income from 6% stock at 80 is Tk. 50 more than 7% stock at 120, then the investment is-

Solution:
Let,
The investment is Tk. x

6% stock at 80,
income from Tk. 80 is 6
∴ income from Tk. x is 6x/80

7% stock at 120,
income from Tk. 120 is 7
∴ income from Tk. x is 7x/120

ATQ,
6x/80 - 7x/120 = 50
⇒ 18x - 14x = 50 × 240
⇒ 4x = 50 × 240
∴ x = 3000

১৪,২৪৯.

A person borrows Tk.5000 for 2years at 4% per annum simple interest. He immediately lends it to another person at 6(1/4)%per annum for 2 years. Find his gain in the transaction per year.

ক
ক) Tk. 112.50
খ
খ) Tk. 167.50
গ
গ) Tk. 228
ঘ
ঘ) Tk. 160

ব্যাখ্যা

The difference in interest rate = 6(1/4)% - 4%
= (25/4)% - 4%
= (9/4)%
Gain per year
= simple interest on Tk. 5000 at = (9/4)% for 1 year.
= {5000 × (9/4) × 1}/100
= 225/2
= Tk. 112.5

১৪,২৫০.

A train moving at speed of 108 km/hr crosses a pole in 12 seconds. Find the length of the train.

ক
250 meters
খ
280 meters
গ
300 meters
ঘ
360 meters

ব্যাখ্যা

Question: A train moving at speed of 108 km/hr crosses a pole in 12 seconds. Find the length of the train.

Solution:
Length of the train is equal to the distance covered by train to cross the pole.
So, we will find the distance travelled by the train in 12 seconds.

Now,
Speed is given in Km/hr so we will convert it into m/s
Speed = 108 × (5/18) = 30 m/s
Time = 12 seconds

We know,
Distance = Speed × Time
∴ Length of train = 30 × 12 = 360 meters

১৪,২৫১.

In how many years will Tk. 15,000 amount to Tk. 18,600 at 12% per annum simple interest?

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

ব্যাখ্যা

Question: In how many years will Tk. 15,000 amount to Tk. 18,600 at 12% per annum simple interest?

Solution:
Principal, P = Tk. 15,000
Amount, A = Tk. 18,600

∴ Simple interest, I = A - P
= 18,600 - 15,000
= Tk. 3600

Rate of interest, r = 12%

We know,
I = Pnr
⇒ 3,600 = 15,000 × n × (12/100)
⇒ 3,600 = 15,000 × n × (3/25)
⇒ 3,600 = 1,800n
⇒ n = 3,600/1,800
∴ n = 2 years

১৪,২৫২.

An inspector notices a thief from a distance of 200 meters after this thief starts running and the inspector chases him. The inspector and the thief run at the speed of 11 km/hr and 10 km/hr respectively. The distance between them after 6 minutes is?

ক
120 m
খ
110 m
গ
100 m
ঘ
90 m

ব্যাখ্যা

Question: An inspector notices a thief from a distance of 200 meters after this thief starts running and the inspector chases him. The inspector and the thief run at the speed of 11 km/hr and 10 km/hr respectively. The distance between them after 6 minutes is?

Solution:
চোর ও ইন্সপেক্টরের আপেক্ষিক গতি = (11 - 10) km/hr
= 1 km/hr
6 মিনিটে অতিক্রম করে = {(1/60) × 6}km
= 1/10 km
= 100 m

∴ চোর ও ইন্সপেক্টরের মধ্যবর্তী দূরত্ব = (200 - 100) m
= 100 m

১৪,২৫৩.

If x² - 2ax + a² = 0 , find the value of x/a.

ক
3
খ
2/3
গ
1
ঘ
0

ব্যাখ্যা

Question: If x² - 2ax + a² = 0 , find the value of x/a.

Solution:
a is obviously a non-zero number.
Given that,
⇒ x² - 2ax + a² = 0
⇒ (x - a)² = 0
⇒ x - a = 0
⇒ x = a
⇒ x/a = a/a ; [divide by a]
∴ x/a = 1

∴ So the value x/a is 1.

১৪,২৫৪.

What is the median of the modes in the dataset {-5, 4, 3, 7, 2, 1, 3, 4, 5,-1, 7, 8, -4, 2, 6}?

ক
ক) 2
খ
খ) 2.5
গ
গ) 3
ঘ
ঘ) 3.5

ব্যাখ্যা

Question: What is the median of the modes in the dataset {- 5, 4, 3, 7, 2, 1, 3, 4, 5,- 1, 7, 8, - 4, 2, 6}?

Solution:
প্রদত্ত ডাটা সেটকে আমরা ক্রমানুসারে সাজিয়ে পাই,
- 5, - 4, -1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8

2, 3, 4, 7 প্রত্যেকে দুইবার করে বিদ্যমান।
প্রচুরক গুলো হলো: 2, 3, 4, 7

এখানে
n = 4
মধ্যক = {4/2 তম ও ((4/2) + 1) তম পদের মানের যোগফল} / 2
= {2 ও 3 তম পদের মানের যোগফল}/2
= (3 + 4)/2
= 3.5

১৪,২৫৫.

If 75% students of a class answered the 1st question on a certain test correctly, 55% answered the 2nd question on the test correctly and 20% answered neither of the questions correctly, what percent answered both correctly?

ক
10%
খ
20%
গ
30%
ঘ
50%

ব্যাখ্যা

Question: If 75% students of a class answered the 1st question on a certain test correctly, 55% answered the 2nd question on the test correctly and 20% answered neither of the questions correctly, what percent answered both correctly?

Solution:
Let,
x% students answered both correctly

∴ (75 - x)% + (55 - x)% + x% + 20% = 100%
⇒ 75% + 55% + 20% - x% = 100%
⇒ 150% - x% = 100%
∴ x% = 150% - 100% = 50%

১৪,২৫৬.

If each photocopy of a manuscript costs 4 cents per page, what is the cost, in cents, to reproduce x copies of an x-page manuscript?

ক
4x
খ
4x²
গ
x²
ঘ
16x²

ব্যাখ্যা

Question: If each photocopy of a manuscript costs 4 cents per page, what is the cost, in cents, to reproduce x copies of an x-page manuscript?

Solution:
Cost to reproduce 1 page of a manuscript = 4 cents
∴ Cost to reproduce x pages of a manuscript= 4x cents

Cost to reproduce x copies of a x page manuscript= x × 4x cents = 4x²cents

১৪,২৫৭.

If a shopkeeper buys eggs at Tk. 42 per sext (six eggs) and sells them at Tk. 56 per two quads (eight eggs), what percentage profit does he make?

ক
5%
খ
1%
গ
7%
ঘ
None

ব্যাখ্যা

Question: If a shopkeeper buys eggs at Tk. 42 per sext (six eggs) and sells them at Tk. 56 per two quads (eight eggs), what percentage profit does he make?

Solution:
Cost price of 6 eggs = Tk. 42
Cost price of 1 egg = 42/6
= 7 Tk.

Cost price of 8 eggs = 8 × 7
= 56
Selling price of 8 eggs = Tk. 56

∴ Profit = 56 − 56
= 0

∴ As the selling and cost prices are the same, there is no profit.

১৪,২৫৮.

The square root of (7 + 3√5) (7 - 3√5) is ?

ক
2
খ
4
গ
3
ঘ
6

ব্যাখ্যা

Question: The square root of (7 + 3√5) (7 - 3√5) is ?

Solution:
Given that,
{(7 + 3√5) (7 - 3√5)}
= √{(7)² - (3√5)²}
= √(49 - 45)
= √4
= 2

১৪,২৫৯.

Tk. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

ক
Tk. 1320
খ
Tk. 1380
গ
Tk. 1360
ঘ
Tk. 1390
ঙ
None

ব্যাখ্যা

Question: Tk 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Solution:
Here,
p = Tk. 1200
r% = 5%
n = 3 years

Now,
A = p[1 + (nr/100)]
= 1200[1 + (3 × 5)/100]
= 12000 × (115/100)
= 1380

Hence, the amount after 3 years is Tk. 1380

১৪,২৬০.

A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

ক
10√5
খ
25
গ
50
ঘ
60
ঙ
None of these

ব্যাখ্যা

Question: A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

Solution:
x = Side of Square Playground
∴ x² = the area of the Square Playground

Now,
The rectangle sides are x + 30 and x - 20
Therefore the Area of the rectangle will be (x + 30)(x - 20)

Considering area of the two are the same
x² = (x + 30)(x - 20)
⇒ x² = x² +10x - 600
⇒ 10x = 600
∴ x = 60

১৪,২৬১.

A pipe can fill 1/6th of a tank in 30 minutes. How much time will it take to fill two tanks?

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

ব্যাখ্যা

Question: A pipe can fill 1/6th of a tank in 30 minutes. How much time will it take to fill two tanks?

Solution:
full tank is filled in = (6 × 30) = 180 minutes = 3 hours.

two tanks is filled in = 6 hours

১৪,২৬২.

In a circle, if the radius r is increased to (r + n) then its area is doubled. Find the value of r.

ক
ক) n/(√2 - 1)
খ
খ) n/(√2 + 1)
গ
গ) (√2 - 1)/n
ঘ
ঘ) √2(n - 1)

ব্যাখ্যা

Question: In a circle, if the radius r is increased to (r + n) then its area is doubled. Find the value of r.

Solution:
ধরি,
ব্যাসার্ধ = r
ক্ষেত্রফল = πr²

ব্যাসার্ধ (r + n) হলে ক্ষেত্রফল = π(r + n)²

প্রশ্নমতে,
2 × πr² = π(r + n)²
বা, 2r² = (r + n)²
বা, (√2r)² = (r + n)²
বা, √2r = r + n
বা, √2r - r = n
বা, r(√2 - 1) = n
∴ r = n/(√2 - 1)

১৪,২৬৩.

What is the minimum value of sin θ?

ক
0
খ
- 1
গ
1
ঘ
- 1/2

ব্যাখ্যা

Question: What is the minimum value of sin θ?

Solution:
sinθ এর সর্বনিম্ন মান - 1 এবং সর্বোচ্চ মান 1
cosθ এর সর্বনিম্ন মান - 1 এবং সর্বোচ্চ মান 1

১৪,২৬৪.

A person deposited Tk. 400 for 2 years, Tk. 550 for 4 years and Tk. 1200 for 6 years. He received the total simple interest of Tk. 1020. The rate of interest per annum is

ক
ক) 5%
খ
খ) 10%
গ
গ) 15%
ঘ
ঘ) 20%

ব্যাখ্যা

ধরি, সুদের হার r %
প্রশ্নমতে, (400 × 2 × r)/100 + (550 × 4 × r)/100 + (1200 × 6 × r)/100 = 1020
⇒ 8r + 22r + 72r = 1020
⇒ 102r = 1020
⇒ r = 10%

১৪,২৬৫.

If a > b > 1, then which of the following is true?

ক
ক) a² > b²
খ
খ) a² < ab
গ
গ) (a - b) < 0
ঘ
ঘ) (b + a) > 2a

ব্যাখ্যা

Suppose
a = 3, b = 2
Option a) a² > b² = (3)² > (2)² = 9 > 4; True
Option b) a² < ab = (3)² < 3×2 = 9 < 6; False
Option c) a - b < 0 = 3 - 2 < 0 = 1 < 0; False
Option d) b + a > 2a = 2 + 3 > 2×3 = 5 > 6; False

১৪,২৬৬.

The total of the ages of Ali , Gazi and Masud is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Masud?

ক
ক) 24 years
খ
খ) 38 years
গ
গ) 34 years
ঘ
ঘ) 32 years

ব্যাখ্যা

Let the age of Ali, Gazi and Masud be respectively 2x, 3x and 4x years

ATQ, 10 years ago, 2x + 3x + 4x = 93 - 30
9x = 63
x = 7
So, 10 years ago Masud's age was, 4x = 28 years

Now, Masud's age is = 38 years

১৪,২৬৭.

If þ is defined for all positive real numbers a and b by aþb = ab/(a+b), then 10þ2 = ?

ক
ক) 5/3
খ
খ) 5/2
গ
গ) 5
ঘ
ঘ) 20/3

ব্যাখ্যা

যেহেতু aþb = ab/(a + b)
∴ 10þ2 = (10 × 2)/(10 + 2)
= 20/12
= 5/3

১৪,২৬৮.

A two-digit number has 6 in its ten's digit. The sum of its digits is one seventh of the number itself. What is the number?

ক
ক) 65
খ
খ) 63
গ
গ) 68
ঘ
ঘ) 69

ব্যাখ্যা

Question: A two-digit number has 6 in its ten's digit. The sum of its digits is one seventh of the number itself. What is the number?

Solution:
দশক স্থানীয় অঙ্ক ৬
একক স্থানীয় অঙ্ক x
সংখ্যাটি = ৬ × ১০ + x
= ৬০ + x

প্রশ্নমতে,
৬ + x = (৬০ + x)/৭
⇒ ৪২ + ৭x = ৬০ + x
⇒ ৭x - x = ৬০ - ৪২
⇒ ৬x = ১৮
∴ x = ৩

সংখ্যাটি ৬৩

১৪,২৬৯.

Dean of a business school distributed Tk. 100000 scholarships among 36 students giving 3000 to each male student and Tk. 2500 tk each female student. How many female students received scholarships?

ক
ক) 20
খ
খ) 22
গ
গ) 16
ঘ
ঘ) 13

ব্যাখ্যা

ধরি, ছাত্রীর সংখ্যা x জন, তাহলে ছাত্রের সংখ্যা 36-X জন
প্রশ্নমতে, 2500x + 3000(36-x) = 100000
বা, 2500x+108000-3000x = 10000
বা, 500x = 8000
বা, X = 16

১৪,২৭০.

In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is

ক
52
খ
50
গ
45
ঘ
42

ব্যাখ্যা

Question: In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is

Solution:
Let, total staff 100

female = 40
male = 100 - 40
= 60

married staff = 40 × 0.7 + 60 × 0.5
= 28 + 30
= 58

∴ unmarried staff = 100 - 58
= 42

১৪,২৭১.

Six people Nitro, Nemesis, Nick Fury, Viper, Kronos and Hulk are attending a hexagonal table conference. All the sides of the hexagon table so formed are of same length. Nitro is not adjacent to Nemesis or Nick Fury, Viper is not adjacent to Nick Fury or Kronos. Nemesis and Nick Fury are adjacent, Hulk is in the middle of Viper and Nick Fury. Who is placed exactly opposite to Kronos?

ক
Nemesis
খ
Nick Fury
গ
Viper
ঘ
Hulk

ব্যাখ্যা

Question: Six people Nitro, Nemesis, Nick Fury, Viper, Kronos and Hulk are attending a hexagonal table conference. All the sides of the hexagon table so formed are of same length. Nitro is not adjacent to Nemesis or Nick Fury, Viper is not adjacent to Nick Fury or Kronos. Nemesis and Nick Fury are adjacent, Hulk is in the middle of Viper and Nick Fury. Who is placed exactly opposite to Kronos?

Solution:
Hulk is in the middle of Viper and Nick Fury.
Nemesis and Nick Fury are adjacent.
Nitro is not adjacent to Nick Fury.

Thus, two arrangements are possible.

Hulk is exactly opposite to Kronos.

১৪,২৭২.

There is a dishonest shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, a policeman finds that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

ক
23.3% profit
খ
15% loss
গ
23.3% loss
ঘ
15% profit

ব্যাখ্যা

Question: There is a dishonest shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, a policeman finds that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution:
selling price of 0.8 kg = 23 taka

selling price of 1 kg = 23/0.8 taka
= 115/4 taka
= 28.75 taka

percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15%

১৪,২৭৩.

If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

ক
22
খ
32
গ
36
ঘ
40

ব্যাখ্যা

Question: If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

Solution:
Seventh term, a₇ = 9
Number of terms,n = 8
a_n = a₁ + (n - 1)d
∴ a₇ = a₁ + 6d
⇒ 9 = a₁ + 12
∴ a₁ = - 3

8th term , a₈ = 9 + 2 = 11

Sum of terms of the sequence = (n/2)[2a₁ + (n - 1)d]
= 4 × [- 6 + 14]
= 4 × 8
= 32

১৪,২৭৪.

A wheel of an engine of 450 cm in circumference makes 20 revolutions in 6 seconds. What is the speed of the wheel in km/h?

ক
48 km/h
খ
54 km/h
গ
36 km/h
ঘ
60 km/h

ব্যাখ্যা

Question: A wheel of an engine of 450 cm in circumference makes 20 revolutions in 6 seconds. What is the speed of the wheel in km/h?

Solution:
Total distance = (450 × 20) cm
= 9000 cm
= 9000/100 m
= 90 m

We know,
Speed = (Total distance ÷ Time)
= (90 ÷ 6) m/sec
= 15 m/sec
= (15 × 18/5) km/h
= 54 km/h

১৪,২৭৫.

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

ক
ক) 1/8
খ
খ) 1/6
গ
গ) 1/4
ঘ
ঘ) 1/2

ব্যাখ্যা

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

Solution:
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

১৪,২৭৬.

If a runner takes as much time in running 20 metres as the car takes in covering 50 metres. The distance covered by the runner during the time the car covers 1 km is -

ক
ক) 400 metres
খ
খ) 40 metres
গ
গ) 440 metres
ঘ
ঘ) None of these

ব্যাখ্যা

According to the question,
∴ 50 m = 20 m
∴ 1m = 20/50 m
∴ 1000 m = (20/50)×1000 m
= 400 metres

১৪,২৭৭.

A mixture of 72 kg contains 17 parts A, 3 Parts of B, 4 parts of C. Find the quantity of B?

ক
ক) 9 kg
খ
খ) 10 kg
গ
গ) 12 kg
ঘ
ঘ) 14 kg
ঙ
ঙ) 15 kg

ব্যাখ্যা

Parts of B = 72 × (3/24) kg
= 9 kg

১৪,২৭৮.

(1.49 × 14.9 - 0.51 × 5.1)/(14.9 - 5.1) is equal to-

ক
ক) 1
খ
খ) 2
গ
গ) 0
ঘ
ঘ) 4

ব্যাখ্যা

Question: (1.49 × 14.9 - 0.51 × 5.1)/(14.9 - 5.1) is equal to-
Solution:
(1.49 × 14.9 - 0.51 × 5.1)/(14.9 - 5.1)
= 10(1.49 × 1.49 - 0.51 × 0.51)/ 10(1.49 - 0.51)
=(1.49²- 0.51²)/(1.49 - 0.51)
= (1.49 + 0.51)(1.49 - 0.51)/(1.49 - 0.51)
= 1.49 + 0.51
= 2

১৪,২৭৯.

The average of runs of a cricket player of 10 innings was 32. How many runs must be made in his next innings so as to increase his average of runs by 4?

ক
20
খ
76
গ
86
ঘ
29

ব্যাখ্যা

Question: The average of runs of a cricket player of 10 innings was 32. How many runs must be made in his next innings so as to increase his average of runs by 4?

Solution:

Average after 11 innings = 36

Required number of runs,

= ( 36 × 11) - (32 × 10)

= 396 - 320

= 76

১৪,২৮০.

Which of the following is irrational?

ক
0.75
খ
√289
গ
3/5
ঘ
√18

ব্যাখ্যা

Question: Which of the following is irrational?

Solution:
একটি সংখ্যা অমূলদ (irrational) হয় যদি এটি p/q আকারে প্রকাশ করা না যায়, যেখানে p এবং q পূর্ণসংখ্যা এবং q ≠ 0।

ক) 0.75 = 75/100 = 3/4 = এটি p/q আকারে প্রকাশ করা যায়, তাই এটি মূলদ সংখ্যা।

খ) √289 = 17 একটি পূর্ণবর্গ সংখ্যা (17² = 289), তাই √289 = 17 একটি মূলদ সংখ্যা।

গ) 3/5 = এটি ইতিমধ্যে p/q আকারে আছে, তাই এটি মূলদ সংখ্যা।

ঘ) √18 = √(9 × 2) = 3√2 একটি পূর্ণবর্গ সংখ্যা নয়, তাই √18 একটি অমূলদ সংখ্যা। এটি p/q আকারে প্রকাশ করা যায় না।

উত্তর: ঘ) √18 একটি অমূলদ (irrational) সংখ্যা।

১৪,২৮১.

The angle of elevation of a tower becomes 60° from 45° by moving 60 metres towards a Minar. Find the height of the Minar.

ক
(3 + √3) m
খ
20 (3 + √3) m
গ
30 (3 + √3) m
ঘ
30 m

ব্যাখ্যা

Question: The angle of elevation of a tower becomes 60° from 45° by moving 60 metres towards a Minar. Find the height of the Minar.

Solution:

let, height AB
In triangle ABD,
tan60 = AB/BD
⇒ √3 = AB/BD
⇒ BD = AB/√3

In triangle ABC,
tan45 = AB/BC
⇒ 1 = AB/BC
⇒ AB = BC
⇒ AB = BD + DC
⇒ AB = BD + 60
⇒ AB = (AB/√3) + 60
⇒ AB - (AB/√3) = 60
⇒ AB . (√3 - 1)/√3 = 60
⇒ AB = 60√3/(√3 - 1)
= 60√3 (√3 + 1)/(√3 - 1)(√3 + 1)
= 30 (3 + √3) m

১৪,২৮২.

Parimal purchased 10 calculators and 16 watches for Tk. 56100 and sold them so as to earn an overall profit of 20%. At what total price should he sell 15 calculators and 24 watches together so as to earn the same percentage profit?

ক
Tk. 100980
খ
Tk. 116176
গ
Tk. 121176
ঘ
Tk. 100660

ব্যাখ্যা

Question: Parimal purchased 10 calculators and 16 watches for Tk. 56100 and sold them so as to earn an overall profit of 20%. At what total price should he sell 15 calculators and 24 watches together so as to earn the same percentage profit?

Solution:
Calculators = 10
Watches = 16
Total Item = 10 + 16 = 26
Total Cost price = Tk. 56,100
Average price of Each item = 56100/26
= Tk. 2157.69

Second Time total item = 15 + 24 = 39
So, Total cost price of 39 items = 2157.69 × 39 = 84,150
thus, the selling price of 39 items with 20% profit,
= 84,150 + 20% of 84,150
= Tk 84,150 + 16,830
= Tk. 100,980

১৪,২৮৩.

The sum of money is divided among 160 males and some females in the ratio 16 : 21. Individually, each male gets Tk 4 and a female Tk 3. The number of females is-

ক
285
খ
220
গ
240
ঘ
280

ব্যাখ্যা

Question: The sum of money is divided among 160 males and some females in the ratio 16 : 21. Individually, each male gets Tk 4 and a female Tk 3. The number of females is-

Solution:
Let the number of females be x.
Then,
(160 × 4)/3x = 16/21
→ 48x = 160 × 4 × 21
→ x = 280

১৪,২৮৪.

A manager has Tk. 6000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?

ক
Tk. 750
খ
Tk. 1000
গ
Tk. 1200
ঘ
Tk. 1500

ব্যাখ্যা

Question: A manager has Tk. 6000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?

Solution:
Let each part time employee receive a raise of y
Then each full time employee receives a raise of 2y
There are 4 full- time employees and 2 part- time employees
The total budget is 6000
So, the equation is
4(2y) + 2y = 6000
⇒10y = 6000
∴ y = 600

Raise for each full-time employee = 2y = 1200

১৪,২৮৫.

If the radius of a circle is tripled, the circumference is -

ক
ক) multiplied by 3
খ
খ) multiplied by 6
গ
গ) multiplied by 9
ঘ
ঘ) multiplied by 12

ব্যাখ্যা

Circumference of circle, C = 2πr
If the radius of a circle is tripled, the circumference is multiplied by 3.

১৪,২৮৬.

It is impossible for the earth to

ক
move round the sun
খ
have lights on it
গ
be the most important planet of the solar system
ঘ
be the nearest planet of the sun

ব্যাখ্যা

অপশন ক) পৃথিবী সর্বদা সূর্যের চার দিকে ঘুরে। সুতরাং, ক অসম্ভব হতে পারে না।

অপশন খ) have something on এর অর্থ হচ্ছে- বস্তুর উপরে কোন কিছু পড়া। পৃথিবীর নিজস্ব আলো নেই। তবে পৃথিবীর উপর সূর্য থেকে আলো পড়ে। সুতরাং, খ অসম্ভব হতে পারে না।

অপশন গ) পৃথিবী একমাত্র গ্রহ যা প্রাণীর বসবাস উপযোগী। তাছাড়া আরো অনেক কারণেই পৃথিবী সূর্যের সবচেয়ে গূরুত্বপূর্ন গ্রহ। সুতরাং, গ অসম্ভব হতে পারে না।

অপশন ঘ) পৃথিবী সূর্যের নিকটতম গ্রহ হতে পারে না। বুধ হলো সূর্যের নিকটতম গ্রহ এবং এটি পৃথিবীর প্রায় ৫৮ মিলিয়ন কিলোমিটার দূরে থাকে। পৃথিবী আমাদের সৌর জগতের তৃতীয় গ্রহ হিসাবে পরিচিত। প্রকৃতির নিয়ম অনুযায়ী, পৃথিবী একটি গ্রহ হিসাবে পর্যায়ক্রমে সূর্যকে ঘিরে ঘুরে চলে যাচ্ছে এবং এর মাঝখানে আরও অন্যান্য গ্রহগুলি অবস্থিত আছে। তাই পৃথিবী সূর্যের নিকটতম গ্রহ হতে পারে না। সুতরাং ঘ অসম্ভব।

১৪,২৮৭.

If the length of each of the sides of a square garden plots is increased by 10 percent , by what percent is the sum of the areas of this plots increased?

ক
ক) 15%
খ
খ) 16%
গ
গ) 21%
ঘ
ঘ) 24%

ব্যাখ্যা

বর্গক্ষেত্রের একবাহু = 100 একক
বর্গক্ষেত্রের ক্ষেত্রফল = (100)² = 10,000 বর্গ একক

50% বৃদ্ধিতে বর্গক্ষেত্রের একবাহু দৈর্ঘ্য = (100 +100 এর 10%) একক
= 110 একক

বর্গক্ষেত্রের নতুন ক্ষেত্রফল = (110)² বর্গ একক
= 12,100বর্গ একক

ক্ষেত্রফল বৃদ্ধি পায় = (12,100 - 10,000) বর্গ একক
= 2100 বর্গ একক
শতকরা ক্ষেত্রফল বৃদ্ধি পায় = {(2100/10,000) × 100}%
= 21%

১৪,২৮৮.

The average monthly income of Abir and Sabbir is Tk. 8000. The average monthly income of Sabbir and Rana is Tk. 9500 and the average monthly income of Abir and Rana is Tk. 9000. What is the monthly income of Abir?

ক
Tk. 7000
খ
Tk. 7500
গ
Tk. 6500
ঘ
Tk. 6000
ঙ
None of these

ব্যাখ্যা

Question: The average monthly income of Abir and Sabbir is Tk. 8000. The average monthly income of Sabbir and Rana is Tk. 9500 and the average monthly income of Abir and Rana is Tk. 9000. What is the monthly income of Abir?

Solution:
Abir + Sabbir (total income) = (8000 × 2) = 16000 .......... (1)
Sabbir + Rana (total income) = (9500× 2) = 19000 ........ (2)
Abir + Rana (total income) = (9000 × 2) = 18000 ......... (3)

(1) + (2) + (3) ⇒
2(Abir + Sabbir+ Rana) = 16000 + 19000 + 18000
⇒ 2(Abir + Sabbir + Rana) = 53000
⇒ Abir + Sabbir + Rana = 26500 ....... (4)

(4) - (2) ⇒
Abir = 26500 - 19000 = 7500
∴ Abir's monthly income Tk. 7500.

১৪,২৮৯.

If a³ - b³ = 513 and a - b = 3, What is the value of ab?

ক
45
খ
46
গ
36
ঘ
54

ব্যাখ্যা

Question: If a³ - b³ = 513 and a - b = 3, What is the value of ab?

Solution:
given,
a³ - b³ = 513
a - b = 3

we know that,
a³ - b³ = (a - b)³ + 3ab(a - b)
or, (a - b)³ + 3ab(a - b) = 513
or, 3³ + 3ab(3) = 513
or, 9ab = 513 - 27
or, ab = 486/9
∴ ab = 54

১৪,২৯০.

A two-digit number has 3 in its unit digit. The sum of its digits is one seventh of the number itself. What is the number?

ক
ক) 73
খ
খ) 53
গ
গ) 63
ঘ
ঘ) 83

ব্যাখ্যা

Question: A two-digit number has 3 in its unit digit. The sum of its digits is one seventh of the number itself. What is the number?

Solution:
ধরি,
দশক স্থানীয় অংকটি = ক

∴ সংখ্যাটি = ১০ক + ৩

প্রশ্নমতে,
১/৭(১০ক + ৩) = (ক + ৩)
১০ক + ৩ = ৭ক + ২১
৩ক = ১৮
ক = ৬

∴ সংখ্যাটি = ৬৩

১৪,২৯১.

The cost of 8 pens and 4 notebooks is equal to the cost of 12 pens and 2 notebooks. Find the ratio between the cost of 1 pen and the cost of 1 notebook.

ক
3 : 5
খ
1 : 2
গ
1 : 4
ঘ
2 : 5

ব্যাখ্যা

Question: The cost of 8 pens and 4 notebooks is equal to the cost of 12 pens and 2 notebooks. Find the ratio between the cost of 1 pen and the cost of 1 notebook.

Solution:
Let,
The price of 1 pen = x taka
The price of 1 notebook = y taka

ATQ,
8x + 4y = 12x + 2y
⇒ 12x - 8x = 4y - 2y
⇒ 4x = 2y
⇒ x/y = 2/4
⇒ x/y = 1/2
∴ x : y = 1 : 2

১৪,২৯২.

An observer who is 1.5 meters tall is standing 10√3 meters away from a flagpole. If the angle of elevation from his eye to the top of the flagpole is 30°, what is the height of the flagpole?

ক
12 m
খ
7.5 m
গ
11.5 m
ঘ
10 m

ব্যাখ্যা

Question: An observer who is 1.5 meters tall is standing 10√3 meters away from a flagpole. If the angle of elevation from his eye to the top of the flagpole is 30°, what is the height of the flagpole?

Solution:

এখানে,
পর্যবেক্ষকের উচ্চতা, CD = 1.5 মিটার
এখানে, CD = EB
পতাকা দণ্ডের (Flagpole) উচ্চতা, = AB

Now,
tan∠C = AE/CE
⇒ tan30° = AE/10√3
⇒ 1/√3 = AE/10√3
∴ AE = 10

∴ AB = AE + BE
= 10 + 1.5
= 11.5 m

১৪,২৯৩.

If 25 is 25 percent of 40 percent of a certain number, what is the number?

ক
250
খ
50
গ
350
ঘ
280

ব্যাখ্যা

Question: If 25 is 25 percent of 40 percent of a certain number, what is the number?

Solution:
Let, The number be x then
25 = 25% of 40% of x
or, 25 = (25/100) × (40/100) × x
or, x = (25 × 100 × 100)/(25 × 40)
or, x = 250

So the number is 250.

১৪,২৯৪.

If 2x = 3y and x + 2y = 7, what is the value of y?

ক
ক) 3
খ
খ) 2
গ
গ) 1
ঘ
ঘ) 0

ব্যাখ্যা

Question: If 2x = 3y and x + 2y = 7, what is the value of y?

Sloution:
Given that,
2x = 3y........(1)
x + 2y = 7........(2)

From (1) ⇒
2x = 3y
x = 3y/2

From (2) ⇒
(3y/2) + 2y = 7
(3y + 4y)/2 = 7
7y/2 = 7
y/2 = 1
y = 2

১৪,২৯৫.

What is the greatest number which divides 639, 1065 and 1491 exactly?

ক
193
খ
183
গ
223
ঘ
213

ব্যাখ্যা

Question: What is the greatest number which divides 639, 1065 and 1491 exactly?

Solution:
H.C.F. of 639 and 1065 is 213.
H.C.F. of 213 and 1491 is 213.

১৪,২৯৬.

What is the average (arithmetic mean) of the values 36, 42, 40, 38, 44, 40, and 40?

ক
25
খ
40
গ
37
ঘ
17

ব্যাখ্যা

Question: What is the average (arithmetic mean) of the values 36, 42, 40, 38, 44, 40, and 40?

Solution:
Find the sum of all values:
36 + 42 + 40 + 38 + 44 + 40 + 40 = 280

Divide the sum by the total number of values:
Average = 280 ÷ 7 = 40

১৪,২৯৭.

If 75% of the students in a school are boys and the number of girls is 420, the number of boys is:

ক
1170
খ
1680
গ
1555
ঘ
1260

ব্যাখ্যা

Question: If 75% of the students in a school are boys and the number of girls is 420, the number of boys is:

Solution:
75% of the students in a school are boys
girls = 25%

25% of total students = 420
⇒ total students = 420/0.25
= 1680

∴ the number of boys is = 1680 - 420
= 1260

১৪,২৯৮.

If 12 men or 18 women can do a work in 14 days, then in how many days will 8 men and 16 women do the same work?

ক
ক) 7 days
খ
খ) 8 days
গ
গ) 9 days
ঘ
ঘ) 6 days

ব্যাখ্যা

Question: If 12 men or 18 women can do a work in 14 days, then in how many days will 8 men and 16 women do the same work?

Solution:
Let the required number of days be x.
12 men = 18 women
8 men = (18 × 8)/12 women = 12 women

Total women = (12 + 16) = 28

More women , Less days.
∴ 28 : 18 = 14 : x
⇒ 28/18 = 14/x
⇒ x = (18 × 14)/28
∴ x = 9

∴ Hence, required number of days = 9

১৪,২৯৯.

The cost of Type 1 rice is Tk. 15 per kg and Type 2 rice is Tk. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

ক
Tk. 18
খ
Tk. 18.5
গ
Tk. 19
ঘ
Tk. 19.5

ব্যাখ্যা

Question: The cost of Type 1 rice is Tk. 15 per kg and Type 2 rice is Tk. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

Solution:
Let,
Quantity of type 1 rice is 2x kg.
Quantity of type 2 rice is 3x kg.
The price per kg of the mixed variety of rice is y taka

∴ Total price of type 1 rice is 15 × 2x = 30x Taka
∴ Total price of type 2 rice is 20 × 3x = 60x Taka

ATQ,
30x + 60x = y(2x + 3x)
⇒ 90x = y × 5x
⇒ y = (90x)/(5x)
∴ y = 18

১৪,৩০০.

The sum of a positive number and its reciprocal is thrice the difference of the number and its reciprocal. The number is-

ক
ক) 1/2
খ
খ) 1/√2
গ
গ) 2
ঘ
ঘ) √2

ব্যাখ্যা

Let
The number is x

Now
x + 1/x = 3(x - 1/x)
x + 1/x = 3x - 3/x
3x - x = 1/x + 3/x
2x = (1 + 3)/x
2x = 4/x
x = 2/x
x² = 2
x = √2