Bank Math

PrepBank · পাতা ৫৮ / ১৬১ · ৫,৭০১–৫,৮০০ / ১৬,১২৪

৫,৭০১.

If 10 students run a mile in 10 minutes, how much time will 50 students take to run a mile?

ক
5 minutes
খ
10 minutes
গ
50 minutes
ঘ
500 minutes

ব্যাখ্যা

Question: If 10 students run a mile in 10 minutes, how much time will 50 students take to run a mile?

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

১০ জন ছাত্রের এক মাইল যেতে সময় লাগে ১০ মিনিট।
১ জনেরও এক মাইল যেতে সময় লাগে ১০ মিনিট।
৫০ জনেরও এক মাইল যেতে সময় লাগে ১০ মিনিট।

৫,৭০২.

How many ways can the word `MOTHER' be arranged with 2 letters each time?

ক
ক) 15
খ
খ) 30
গ
গ) 40
ঘ
ঘ) 60

ব্যাখ্যা

Question: How many ways can the word `MOTHER' be arranged with 2 letters each time?

Solution:
Total number of words, n = 6 and r = 2

∴ Arrangement = ⁿP_r
= ⁶P₂
= 30

৫,৭০৩.

There are 23 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12^th pole. How much more time will it take to reach the last pole?

ক
40 seconds
খ
44 seconds
গ
48 seconds
ঘ
46 seconds

ব্যাখ্যা

Question: There are 23 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12^th pole. How much more time will it take to reach the last pole?

Solution:
ধরি,
২টি পোলের মধ্যবর্তী দূরুত্ব = x মিটার
১ম পোল থেকে ১২তম পোলের মধ্যবর্তী দূরুত্ব = 11x মিটার
১২তম পোল থেকে ২৩তম পোলের মধ্যবর্তী দূরুত্ব = 11x মিটার

যেহেতু, প্রত্যেক পোলের দূরুত্ব সমান।
তাই ১ম পোল থেকে ১২তম পোলে যেতে যত সময় লাগবে ১২তম পোল থেকে ২৩তম পোলে যেতে একই সময় লাগবে।

১ম পোল থেকে ১২তম পোলে যেতে সময় লাগে = 24 সেকেন্ড
১২তম পোল থেকে ২৩তম পোলে যেতে সময় লাগে = 24 সেকেন্ড

মোট সময় লাগবে = (24 + 24) সেকেন্ড = 48 সেকেন্ড

৫,৭০৪.

If y < 0 and 4x > y, which of the following could be equal to x/y?

ক
1
খ
1/2
গ
0
ঘ
1/4

ব্যাখ্যা

Question: If y < 0 and 4x > y, which of the following could be equal to x/y?

Solution:
4x > y
x > y/4
x/y < 1/4 [y < 0; y একটি ঋণাত্মক সংখ্যা]

অপশনে 1/4 চেয়ে ছোট একমাত্র সংখ্যা 0।

৫,৭০৫.

Two trains of same length are running in parallel tracks in the same direction with speed 60 km/hr and 90 km/hr respectively. The latter completely crosses the former in 30 seconds. The length of each train (in meters) is-

ক
75m
খ
100m
গ
150m
ঘ
200m
ঙ
125m

ব্যাখ্যা

Let's take the length of each train = x,
total length of both trains = 2x,
Crossing time = 30 sec.
Relative speed = 90 - 60 = 30 km/hr
= 30 × 5/18
= 25/3 m/sec.
∴ Total length = Time × Relative speed
⇒ 2x = 30 × 25/3
⇒ 2x = 10 × 25
= 125 m.

৫,৭০৬.

Two numbers are in ratio 4 : 5 and their HCF is 9. The smaller number is-

ক
ক) 9
খ
খ) 24
গ
গ) 36
ঘ
ঘ) 45

ব্যাখ্যা

Question: Two numbers are in ratio 4 : 5 and their HCF is 9. The smaller number is-

Solution:
Let two numbers be 4x and 5x
Their HCF = 9

ATQ,
x = 9

Then, the smaller number = 4 × 9 = 36

৫,৭০৭.

A rectangular water reservoir cantains 72000 litres of water. If the length of reservoir is 8m and breadth of the reservoir is 4.5m, then the depth of the reservoir will be?

ক
2m
খ
4m
গ
5.5m
ঘ
3.25m

ব্যাখ্যা

Question: A rectangular water reservoir cantains 72000 litres of water. If the length of reservoir is 8m and breadth of the reservoir is 4.5m, then the depth of the reservoir will be?

Solution:
Given that,
Volume of the reservoir = 72,000 liters
Length = 8 m
Breadth = 4.5 m
Depth = ?

∴ 72,000 liters =72,000/1000 = 72 m³ [1 cubic meter = 1000 liters]

We know,
⇒ Volume = Length × Breadth × Depth
⇒ Depth = Volume/(Length × Breadth)
⇒ Depth = 72/(8 × 4.5)
⇒ Depth = 72/36
⇒ Depth = 2m
∴The depth of the reservoir is 2 meters.

৫,৭০৮.

The area of a rectangular field is 27500 sq. meters. This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 2.20 cm on the map. The breadth of the rectangular field in the map is -

ক
1.25 cm
খ
1.25 m
গ
12.5 cm
ঘ
125 cm
ঙ
None

ব্যাখ্যা

Question: The area of a rectangular field is 27500 sq. meters. This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 2.20 cm on the map. The breadth of the rectangular field in the map is -

Solution:
Length of the field = (2.20 × 100) m
= 220 m

We know,
Length × Breadth = 27500
Or, Breadth = 27500/220
∴ The breadth of the field = 125 m.

The breadth of the rectangular field in the map is = 125/100 cm
= 1.25 cm

৫,৭০৯.

The hypotenuse of an isosceles right angled triangle is 12 cm. Find its area in sq.cm.

ক
ক) 48 ‍cm²
খ
খ) 36 ‍cm²
গ
গ) 72 ‍cm²
ঘ
ঘ) 56 ‍cm²

ব্যাখ্যা

Question: The hypotenuse of an isosceles right angled triangle is 12 cm. Find its area in sq.cm.

Solution:
ধরি,
সমদ্বিবাহু সমকোণী ত্রিভুজের সমান বাহু a সে.মি.

আমরা জানি,
লম্ব² + ভূমি² = অতিভুজ²
বা, a² + a² = 12²
বা, 2a² = 144
বা, a² = 144/2
∴ a² = 72

∴ সমদ্বিবাহু ত্রিভুজের ক্ষেত্রফল = (1/2) × a × a
= (1/2) × a²
= (1/2) × 72
= 36 বর্গ সে.মি.

৫,৭১০.

A man goes half of a certain distance at 40 km/hr, and the other half 60 km/hr. His average speed for the whole journey is-

ক
ক) 50 kmph
খ
খ) 48 kmph
গ
গ) 45 kmph
ঘ
ঘ) 20 kmph
ঙ
ঙ) 15 kmph

ব্যাখ্যা

V = (2 × 40 × 60)/(40 + 60) = 48kmph

Alternative method:
Average speed is total distance travelled divided by total time taken.

Let the distance travelled is 2x or half of distance is x.

The first half of distance x is travelled with speed of 40km/hr, so time taken is x/40 hr.

Similarly time taken to travel the remaining x km is at speed of 60km/hr, so time taken for this 2nd half of distance is x/60.

Now, the total time taken to travel 2x distance is = x/40 + x/60 hr
= 3x/120 + 2x/120hr
= 5x/120 hr
= x/24 hr.

The average speed of car is 2x/(x/24) or 2 × 24 km/hr or 48km/hr.

৫,৭১১.

30° =?

ক
π/2 radian
খ
π/3 radian
গ
π/5 radian
ঘ
π/6 radian

ব্যাখ্যা

Question: 30° =?

Solution:
1° = π/180 radian
30° = (π/180) × 30°
= π/6 radian

৫,৭১২.

The sum of ages of 7 children born at the intervals of 5 years each is 154 years. What is the age of the youngest child?

ক
6
খ
7
গ
8
ঘ
9
ঙ
10

ব্যাখ্যা

Let the ages of children be x, (x + 5), (x + 10), (x + 15), (x + 20), (x + 25) and (x + 30) years.
Then, x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) + (x + 30) = 154
or, 7x + 105 = 154
or, 7x = 49
or, x = 7
∴ the age of the youngest child is 7 years.

৫,৭১৩.

What comes next in the series: 2, 6, 12, 20, 30, ...... ?

ক
36
খ
42
গ
44
ঘ
48

ব্যাখ্যা

Question: What comes next in the series: 2, 6, 12, 20, 30, ...... ?

Solution:
১ম পদ = 2
২য় পদ = 2 + 4 = 6
৩য় পদ = 6 + 6 = 12
৪র্থ পদ = 12 + 8 = 20
৫ম পদ = 20 + 10 = 30
৬ষ্ঠ পদ = 30 + 12 = 42

৫,৭১৪.

A man buys an article for 20% less than its value and sells it for 20% more than its value. What is his gain or loss percentage?

ক
No profit, no loss
খ
40% profit
গ
50% profit
ঘ
More than 50% Profit

ব্যাখ্যা

Questjion: A man buys an article for 20% less than its value and sells it for 20% more than its value. What is his gain or loss percentage?

Solution:
Let, the value of article is x Tk.

Buying price at 20% less,
= x - 20% of x
= x - (20x/100)
= x - 0.2x
= 0.8x Tk.

Selling Price at 20% more,
= x + 20% of x
= x + 0.2x
= 1.2x Tk.

Profit = 1.2x - 0.8x
= 0.4x Tk.

∴ Profit Percentage = (0.4x/0.8x) × 100%
= (40/0.8)%
= 50%

∴ The gain percentage is 50%.

৫,৭১৫.

The population of a town increases by 10% in the first year and decreases by 10% in the next year. What is the overall percentage change?

ক
0%
খ
1% increase
গ
1% decrease
ঘ
2% increase

ব্যাখ্যা

Question: The population of a town increases by 10% in the first year and decreases by 10% in the next year. What is the overall percentage change?

Solution:
Let the initial population = 100

Population after 1st year (10% increase)
Population = 100 + 10% of 100 = 100 + 10 = 110

Population after 2nd year (10% decrease)
Population = 110 - 10% of 110 = 110 - 11 = 99

Overall change = Final population - Initial population
= 99 - 100
= - 1

Overall percentage change = (- 1/100) × 100% = - 1%

∴ Population decreased by 1%

৫,৭১৬.

Q. (36-55): Choose the correct answer.

In a survey, 30% of the people surveyed owned a personal computer and 75% owned a cellular telephone. If 25% owned both a cellular telephone and a personal computer, then the percentage of the people who does not have either of the instrument?

ক
ক) 40%
খ
খ) 30%
গ
গ) 25%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: In a survey, 30% of the people surveyed owned a personal computer and 75% owned a cellular telephone. If 25% owned both a cellular telephone and a personal computer, then the percentage of the people who does not have either of the instrument?

Solution:
people surveyed owned a personal computer = n(P) = 30%
people surveyed owned a cellular telephone = n(C) = 75%
people surveyed owned both a cellular telephone and a personal computer = n(P ∩ C) = 25%

people surveyed owned both or anyone of them = n (P ∪ C)
= n(P) + n(C) - n(P ∩ C)
= 30% + 75% - 25%
= 80%

∴ then the percentage of the people who does not have either of the instrument = 100% - 80%
= 20%

৫,৭১৭.

If a^{2x - 5} = b² and a² = b, what is the value of x?

ক
4
খ
9
গ
9/2
ঘ
18

ব্যাখ্যা

Question: If a^{2x - 5} = b² and a² = b, what is the value of x?

Solution :
Given,
a^{2x - 5} = b² ,
a² = b

so, a^{2x - 5} = (a²)²
⇒ a^{2x - 5} = a⁴
⇒ 2x - 5 = 4
⇒ x = 9/2

৫,৭১৮.

Which of the following fraction is smaller than 3/4 and greater than 1/2?

ক
2/5
খ
5/8
গ
3/7
ঘ
4/9

ব্যাখ্যা

Question: Which of the following fraction is smaller than 3/4 and
greater than 1/2?

Solution:
3/4 = 0.75
1/2 = 0.5

ক) 2/5 = 0.4
খ) 5/8 = 0.625
গ) 3/7 = 0.428
ঘ) 4/9 = 0.444

∴ 5/8 is the required fraction.

৫,৭১৯.

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

ক
5/7
খ
2/7
গ
10/ 21
ঘ
3/5

ব্যাখ্যা

Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Solution:
Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7 =⁷C₂= 21
Let E = Event of drawing 2 balls, none of which is blue.
n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls = ⁵C₂= 10
Therefore, P(E) = n(E)/n(S)
= 10/ 21

৫,৭২০.

A number is doubled and 9 is added. If the resultant is trebled, it becomes 147. What is that number?

ক
12
খ
20
গ
16
ঘ
10

ব্যাখ্যা

Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 147. What is that number?

Solution:
Let the number be x

According to the question,
3(2x + 9) = 147
⇒ 6x + 27 = 147
⇒ 6x = 147 - 27
⇒ 6x = 120
⇒ x = 120/6
∴ x = 20

Hence, the number is 20.

৫,৭২১.

A man deposits Tk 600 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become Tk-

ক
660
খ
720
গ
160
ঘ
726
ঙ
None of these

ব্যাখ্যা

Question: A man deposits Tk 600 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become Tk-

Solution:
Given,
Principal, P = 600 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 600 × {1 + (1/10)}²
= 600 × (11/10)²
= 600 × (11/10) × (11/10)
= 726

৫,৭২২.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 4 ?

ক
ক) 2/5
খ
খ) 3/10
গ
গ) 1/5
ঘ
ঘ) 1/4

ব্যাখ্যা

Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 4 ?

Solution:
Here, S = {1, 2, 3, 4,........, 19, 20}
Let E = even of getting a multiple of 4 = {4, 8, 12, 16, 20}
∴P(E) = n(E)/n(S)
= 5/20
= 1/4

৫,৭২৩.

A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?

ক
6 days
খ
5 days
গ
10 days
ঘ
8 days

ব্যাখ্যা

Question: A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?

Solution:
A can complete the work in 8 × 6 = 48 hours
1 hour's work of A = 1/48 part

B can complete the work in 8 × 12 = 96 hours
1 hour's work of B = 1/96 part

(A + B)'s 1 hour's work = (1/48) + (1/96) part
= (2 + 1)/96 part
= 3/96 part
= 1/32

∴ Time taken by (A + B) working 4 hours daily = 32/(1 × 4)
= 8 days

৫,৭২৪.

There are two squares S₁ and S₂. The ratio of their areas is 9 : 16. If the side of S₁ is 12 cm. What is the side of S₂?

ক
17 cm
খ
21 cm
গ
14 cm
ঘ
16 cm

ব্যাখ্যা

Question: There are two squares S₁ and S₂. The ratio of their areas is 9 : 16. If the side of S₁ is 12 cm. What is the side of S₂?

Solution:
Given that,
Two squares S₁and S₂
Area of S₁ : Area of S₂ = 9 : 16
Side of S₁ = 12 cm

Now,
Let the side of S₂ be x cm.
Then,
(Side of S₁)² : (Side of S₂)² = 9 : 16
⇒ 12² : x² = 9 : 16
⇒ 144/x² = 9/16
⇒ x² = (144 × 16)/9
⇒ x² = 256
⇒ x² = 16²
∴ x = 16

So the side of S₂ is 16 cm.

৫,৭২৫.

A boat takes 38 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?

ক
ক) 180 km
খ
খ) 120 km
গ
গ) 360 km
ঘ
ঘ) 240 km

ব্যাখ্যা

Velocity of the stream = 4 km/hr.
The speed of the boat in still water is 14 km/hr.
Speed downstream = 14 + 4 = 18 km/hr.
Speed upstream = 10 km/hr.
Let the distance between A and B be x km.
Time taken to travel downstream from A to B + Time taken to travel upstream from B to C(mid of A and B)
= 38 hours.
⇒ x/18 + (x/2)/10 = 38
⇒ x/18 + x/20 = 38
⇒ 19x/180 = 38
⇒ x/180 = 2
⇒ x = 360 km.

৫,৭২৬.

What is the angle between the hour and minute hands of a clock when it is 3:15 pm?

ক
0°
খ
7.5°
গ
6.5°
ঘ
5°
ঙ
10°

ব্যাখ্যা

Question: What is the angle between the hour and minute hands of a clock when it is 3:15 pm?

Solution:
3টা 15 মিনিট = 3 + (15/60) ঘন্টা = 3 + 1/4 = 13/4 ঘন্টা

আমরা জানি, ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/4 ঘণ্টায় ঘোরে = (30° × 13)/4
= 390°/4
= 97.5°

আবার, মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 15 মিনিটে ঘোরে = 15 × 6° = 90°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |97.5° - 90°|
= 7.5°

৫,৭২৭.

A sum of money at simple interest amounts to Tk.815 in 3years and to Tk.854 in 4 years. What is the sum?

ক
Tk 720
খ
Tk 650
গ
Tk 698
ঘ
Tk 875
ঙ
Tk 659

ব্যাখ্যা

S.I. for 1 year = 854 - 815
= 39
S.I. for 3 years = 39 × 3
= 117
∴ Required Sum = 815 - 117
= Tk. 698.

৫,৭২৮.

If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube ?

ক
12√3 cm
খ
2√3 cm
গ
12√2 cm
ঘ
2√2 cm

ব্যাখ্যা

Since a cube has 4 diagonals, we have :
Length of a diagonal
= (12/4)cm = 3cm

Let the length of each edge of the cube be 'a' cm
Then, √3a = 3
or, a = √3

A cube has total 12 edges.
Therefore, total length of the edges of the cube = 12√3 cm

৫,৭২৯.

15% monthly salary increase resulted in a Tk. 14400 per year increase in salary for an employee. What was his monthly salary before the increase?

ক
Tk. 7850
খ
Tk. 8980
গ
Tk. 6000
ঘ
Tk. 8000
ঙ
Tk. 7500

ব্যাখ্যা

Question: 15% monthly salary increase resulted in a Tk. 14400 per year increase in salary for an employee. What was his monthly salary before the increase?

Solution:
Increasing in 12 months = 14400 taka
So, Increasing in 1 month = (14400/12) = Tk. 1200

Now,
15% of original salary = 1200
1% of original salary = 1200/15
∴ 100% of original salary = (1200 × 100)/15 = 8000 taka.

So the monthly salary before the increase was Tk. 8,000.

৫,৭৩০.

Tk. 6000 becomes Tk. 7200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of same principal in 5 years will be -

ক
Tk. 8000
খ
Tk. 8250
গ
Tk. 9000
ঘ
Tk. 9250

ব্যাখ্যা

Question: Tk. 6000 becomes Tk. 7200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of same principal in 5 years will be -

Solution:
৬০০০ টাকা ৪ বছরে ৭২০০ টাকা হয়।
৪ বছরে সুদ = ৭২০০ - ৬০০০ টাকা
= ১২০০ টাকা
১ বছরে সুদ = ১২০০/৪ = ৩০০ টাকা

১.৫ গুণ বৃদ্ধিতে ১ বছরে সুদ = ৩০০ × ১.৫ টাকা
= ৪৫০ টাকা

৫ বছরে সুদ = ৪৫০ × ৫ টাকা
= ২২৫০ টাকা

∴ ৫ বছর পর সুদাসলে হবে = ৬০০০ + ২২৫০ টাকা
= ৮২৫০ টাকা

৫,৭৩১.

Himel is throwing a bachelorette party for his best friend with x guests total. All of the guests plan to split the cost of renting a limo for y taka. The day before, z guests cancel. Which of the following represents the percent increase in the amount each guest must pay towards the limo rental?

ক
{100x/y(z - x)}%
খ
{100z/(x - z)}%
গ
(y/x)%
ঘ
None of these

ব্যাখ্যা

Question: Himel is throwing a bachelorette party for his best friend with x guests total. All of the guests plan to split the cost of renting a limo for y taka. The day before, z guests cancel. Which of the following represents the percent increase in the amount each guest must pay towards the limo rental?

Solution:
first, each guest pays y/x taka

after z guests cancel, y/(x - z) taka

increase = { y/(x - z)} - (y/x)
= yz/x(x - z)

%increase = (yz/x(x - z)) × (x/y) × 100%
= 100z/(x - z) %

৫,৭৩২.

Area of a rectangular field is 400 square meter. If its length is 16 meter. What is his circumference of the field?

ক
ক) 16
খ
খ) 25
গ
গ) 41
ঘ
ঘ) 82

ব্যাখ্যা

একটি আয়তাকার মাঠের ক্ষেত্রফল ৪০০ বর্গফুট।
এর দৈর্ঘ্য ১৬ মিটার হলে প্রস্থ ৪০০/১৬ = ২৫ মিটার।
অতএব, এর পরিসীমা = ২(১৬+২৫) = ৮২ ফুট

৫,৭৩৩.

A book sold at a discounted price. If it had a regular price of tk. 300 and was sold for tk. 276, how much discount was applied?

ক
7%
খ
8%
গ
9%
ঘ
10%
ঙ
None

ব্যাখ্যা

প্রশ্ন: A book sold at a discounted price. If it had a regular price of tk. 300 and was sold for tk. 276, how much discount was applied?

সমাধান:
দেওয়া আছে,
বইয়ের প্রকৃত মূল্য = 300 টাকা
বিক্রয়মূল্য = 276 টাকা
ছাড়ের পরিমাণ = 300 - 276 = 24 টাকা

300 টাকায় ছাড় দেয় = 24 টাকা
1 টাকায় ছাড় দেয় = 24/300 টাকা
∴ 100 টাকায় ছাড় দেয় = (24 × 100)/300 টাকা
= 8 টাকা বা 8%

৫,৭৩৪.

AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is

ক
5 cm
খ
10 cm
গ
20 cm
ঘ
15 cm

ব্যাখ্যা

AD is the median and 'O' is the centroid
Therefore, AO = 2 × OD

AO = 10 cm.
OD = 10/2 cm
= 5 cm

৫,৭৩৫.

Due to reduction in the bus price by 15%, the number of passengers on a certain route increased by 40%. What will be the percentage increase in revenue?

ক
ক) 17
খ
খ) 18
গ
গ) 19
ঘ
ঘ) 20
ঙ
ঙ) None

ব্যাখ্যা

ধরি,১০০ জন যাত্রী পরিবহন হত যখন ভাড়া ছিল ১০০ টাকা।
রাজস্ব = ১০০×১০০ = ১০০০০ টাকা
ভাড়া কমার পরে,
১৪০ জন যাত্রী পরিবহন হত যখন ভাড়া ৮৫ টাকা।
রাজস্ব = ১৪০×৮৫ = ১১৯০০ টাকা
রাজস্ব বৃদ্ধি = (১১৯০০ - ১০০০০) টাকা = ১৯০০ টাকা
১০০০০ টাকায় রাজস্ব বৃদ্ধি = ১৯০০ টাকা
১ টাকায় রাজস্ব বৃদ্ধি = ১৯০০/১০০০০ টাকা
১০০ টাকায় রাজস্ব বৃদ্ধি = ১৯০০×১০০/১০০০০ টাকা
= ১৯ টাকা বা ১৯%

৫,৭৩৬.

The average weight of 40 students in a class is 45 kg. If three students weighing 52 kg, 48 kg, and 50 kg leave the class, what is the new average weight of the remaining students?

ক
44.6 kg
খ
43.7 kg
গ
42.3 kg
ঘ
41.9 kg

ব্যাখ্যা

Question: The average weight of 40 students in a class is 45 kg. If three students weighing 52 kg, 48 kg, and 50 kg leave the class, what is the new average weight of the remaining students?

Solution:
Total weight = 45 × 40 = 1800 kg

Students leaving = 52 kg + 48 kg + 50 kg = 150 kg
Remaining total weight = 1800 - 150 = 1650 kg

Remaining students = 40 - 3 = 37 students
New average = 1650/37
= 44.59 kg

Therefore, the new average weight is approximately 44.6 kg.

৫,৭৩৭.

The population of a village is 25000. One-fifth are females and the rest are males, 5% of males and 40% of females are uneducated. What percentage on the whole are educated?

ক
ক) 88%
খ
খ) 65%
গ
গ) 85%
ঘ
ঘ) 78%

ব্যাখ্যা

Question: The population of a village is 25000. One-fifth are females and the rest are males, 5% of males and 40% of females are uneducated. What percentage on the whole are educated?

Solution:
Number of females = 25000 × 1/5
= 5000
Number of males = (25000 - 5000)
= 20000

Number of educated females = 5000 × 60/100
= 3000
Number of educated males = 20000 × 95/100
= 19000

Total educated population = 22000
Percentage of educated population = (22000/25000) × 100
= 88%

৫,৭৩৮.

If the cost of q metres of wire is Tk. k, then what is the cost of p metres of wire at the same rate (in Tk)?

ক
pq/k
খ
kp/q
গ
q/kp
ঘ
kq/p

ব্যাখ্যা

Question: If the cost of q metres of wire is Tk. k, then what is the cost of p metres of wire at the same rate (in Tk)?

Solution:
Cost of q metres = Tk. k
Cost of 1 metre = Tk. k/q
Cost of p metres = Tk. (k × p/q) = Tk. kp/q

৫,৭৩৯.

A trapezium has parallel sides of length 15 m and 35 m. The distance between the sides is 12 m. Calculate the area of the trapezium.

ক
300 m²
খ
420 m²
গ
196 m²
ঘ
260 m²

ব্যাখ্যা

Question: A trapezium has parallel sides of length 15 m and 35 m. The distance between the sides is 12 m. Calculate the area of the trapezium.

Solution:
Given that,
Parallel sides of trapezium, a = 15 m and b = 35 m
Distance (height) between parallel sides, h = 12 m

We know,
Area of a trapezium =(1/2) × (sum of parallel sides) × height
= (1/2) × (a + b) × h
= (1/2) × (15 + 35) × 12
= 50 × 6
= 300 m²

So the area of the trapezium is 300 m².

৫,৭৪০.

A fair die is thrown once. What is the probability of getting a prime number?

ক
1/6
খ
2/3
গ
1/3
ঘ
1/2

ব্যাখ্যা

Question: A fair die is thrown once. What is the probability of getting a prime number?

Solution:
A standard fair die has 6 faces numbered: 1, 2, 3, 4, 5, 6.
The prime numbers from 1 to 6 are: 2, 3, and 5.

Probability = (Number of favorable outcomes)/(Total number of outcomes)
= 3/6
= 1/2

৫,৭৪১.

The sum of the age of father and son is 50. Five years back their ratio was 7 : 1. After five years son's age will be -

ক
ক) 45 years
খ
খ) 10 years
গ
গ) 20 years
ঘ
ঘ) 15 years

ব্যাখ্যা

Question: The sum of the age of father and son is 50. Five years back their ratio was 7 : 1. After five years son's age will be -

Solution:
ধরি,
৫ বছর পূর্বে পিতা ও পুত্রের বয়স ছিলো যথাক্রমে ৭ক এবং ক
প্রশ্নমতে,
৭ক + ক + ৫ + ৫ = ৫০
৮ক = ৪০
ক = ৫

৫ বছর পূর্বে পিতা ও পুত্রের বয়স ছিলো যথাক্রমে ৩৫ বছর এবং ৫ বছর।
৫ বছর পর বয়স হবে যথাক্রমে ৪৫ বছর ও ১৫ বছর।

৫,৭৪২.

The capital stock of a company is Tk. 500,000 and is divided into 5,000 shares. If the company declares a total dividend of Tk. 75,000, how much will Rahim receive for his 80 shares?

ক
Tk. 800
খ
Tk. 1,000
গ
Tk. 1,200
ঘ
Tk. 1,500

ব্যাখ্যা

Question: The capital stock of a company is Tk. 500,000 and is divided into 5,000 shares. If the company declares a total dividend of Tk. 75,000, how much will Rahim receive for his 80 shares?

Solution:
5,000 shares income Tk. 75,000
∴ 1 share income = Tk. 75,000 / 5,000
∴ 80 shares income = Tk. (75,000 × 80)/5,000
= Tk. 1,200

∴ Rahim will receive Tk. 1,200 as his share of the dividend.

৫,৭৪৩.

What is the highest power of 3 in the prime factorization of 234?

ক
1
খ
5
গ
4
ঘ
2

ব্যাখ্যা

Question: What is the highest power of 3 in the prime factorization of 234?

Solution:
Given that,
Highest power of 3 in the prime factorization of 234

Now,
The prime factorization of 234 = 2 × 3² × 13

∴ Highest power of 3 = 2

∴ The highest power of 3 is 2.

৫,৭৪৪.

If X and Y are prime numbers then which of the following cannot be the sum of X and Y?

ক
ক) 5
খ
খ) 10
গ
গ) 23
ঘ
ঘ) 26

ব্যাখ্যা

Question: If X and Y are prime numbers then which of the following cannot be the sum of X and Y?

Solution:
The prime numbers which are less than 23 ⇒ 2, 3, 5, 7, 11, 13, 17, 19

Now,
5 = 2 + 3
10 = 3 + 7
26 = 7 + 19

But we can not write 23 as sum of two different prime numbers.

৫,৭৪৫.

Find the probability that a leap year has 52 Sundays.

ক
2/7
খ
5/7
গ
2/9
ঘ
4/7
ঙ
None of these

ব্যাখ্যা

Question: Find the probability that a leap year has 52 Sundays.

Solution:
A leap year can have 52 Sundays or 53 Sundays.
In a leap year, there are 366 days out of which there are 52 complete weeks & remaining 2 days.

Now, these two days can be (Sat, Sun) (Sun, Mon) (Mon, Tue) (Tue, Wed) (Wed, Thur) (Thur, Friday) (Friday, Sat).
So there are total 7 cases out of which (Sat, Sun) (Sun, Mon) are two favorable cases.
So, P(53 Sundays) = 2/7

Now,
P(52 Sundays) + P(53 Sundays) = 1
So, P(52 Sundays) = 1 - P(53 Sundays) = 1 - (2/7) = 5/7

৫,৭৪৬.

A pupil's marks were wrongly entered as 83 instead of 63. Due to that, the average marks for the class got increased by half. The number of pupils in the class is:

ক
40
খ
30
গ
25
ঘ
17

ব্যাখ্যা

Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that, the average marks for the class got increased by half. The number of pupils in the class is:

Solution:
Let there be 'p' pupils in the class.

Total increase in marks = p × 1/2= p/2
∴ p/2 = (83 - 63)
⇒ p/2 = 20
⇒ p = 40

Hence, The number of pupils in the class is = 40

৫,৭৪৭.

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

ক
4%
খ
6.25%
গ
20%
ঘ
25%

ব্যাখ্যা

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

Solution:
Let C.P. of 1 litre milk be Tk. 1
Then,
S.P. of 1 litre of mixture = Tk. 1,
Gain = 25%.

C.P. of 1 litre mixture = Tk. (100/125) × 1 = Tk. 4/5

By the rule of alligation, we have:

⇒ Quantity of water : Quantity of milk = (1 - 4/5) : (4/5 - 0) = 1/5 : 4/5 = 1 : 4

Hence, percentage of water in the mixture = (1/5) × 100% = 20%

৫,৭৪৮.

In what ratio must a grocer mix two varieties of sugar costing Tk.18 and Tk.24 per kg respectively so as to get a mixture worth Tk.19.5 per kg?

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

ব্যাখ্যা

Question: In what ratio must a grocer mix two varieties of sugar costing Tk.18 and Tk.24 per kg respectively so as to get a mixture worth Tk.19.5 per kg?

Solution:
Let 18 Tk kg sugar = x kg
and 24 Tk kg sugar = y kg
ATQ,
18x + 24y = 19.5(x + y)
⇒ 18x + 24y = 19.5x + 19.5y
⇒ 1.5x = 4.5y
⇒ x/y = 4.5/1.5
⇒ x/y = 3
⇒ x : y = 3 : 1

৫,৭৪৯.

What percentage of the whole week does Sagor spend in school except lunch time, if his school times are 8 am to 4 pm from Monday to Saturday, with 2 hours for lunch each day?

ক
11%
খ
20%
গ
21%
ঘ
25%

ব্যাখ্যা

Question: What percentage of the whole week does Sagor spend in school except lunch time, if his school times are 8 am to 4 pm from Monday to Saturday, with 2 hours for lunch each day?

Solution:
Time spent by Sagor in a day = 4 pm - 8 am = 8 hours

Except lunch time, Sagor spends in a day = 8 - 2 = 6 hours

Number of school days in a week = 6

Total school hours in a week = 6 × 6 = 36 hours

Total hours in a week = 7 × 24 = 168 hours

Percentage time spent in a week = (36/168) × 100%
= 21%

৫,৭৫০.

Tamim and Sakib can do a piece of work in 20 days and 12 days respectively. Tamim started the work alone and then after 4 days, Sakib joined him till the completion of the work. How long did the work last?

ক
8 days
খ
9 days
গ
10 days
ঘ
12 days

ব্যাখ্যা

Question: Tamim and Sakib can do a piece of work in 20 days and 12 days respectively. Tamim started the work alone and then after 4 days, Sakib joined him till the completion of the work. How long did the work last?

Solution:
Work done by Tamim in 4 days = (1/20) × 4 = 1/5
∴ Remaining work = 1 - (1/5) = 4/5

(Tamim + Sakib)'s 1day's work = (1/20) + (1/12)
= 8/60 = 2/15

Now, 2/15 work is done by Tamim and Sakib in 1 day.
So, 4/5 work will be done by Tamim and Sakib in = (15/2) × (4/5)
= 6 days

∴ Total time taken = (6 + 4) days = 10 days

৫,৭৫১.

When bent in the form of a circle a wire has a radius of 28 cm. If it is bent in the form of a square, what will be its area in cm²?

ক
ক) 7744
খ
খ) 5808
গ
গ) 1936
ঘ
ঘ) 3872

ব্যাখ্যা

Given, Radius of circle, r=28 cm
then the circumference = 2πr
= 2 × 22/7 × 28
= 176 cm

Let 'a' be the side of the square,

circumference of circle = perimeter of the square
Or, 176=4a
Or, a = 176/4 = 44 cm
∴ area of square = a²
= 44²
= 1936 cm²

৫,৭৫২.

X can do a work in 15 days, and Y in 10 days. They work together for 3 days. How much of the work is left?

ক
1/4
খ
1/2
গ
2/5
ঘ
3/4

ব্যাখ্যা

Question: X can do a work in 15 days, and Y in 10 days. They work together for 3 days. How much of the work is left?

Solution:
X, 15 দিনে করতে পারে কাজটির 1 অংশ
∴ X ,1 দিনে করতে পারে কাজটির 1/15 অংশ

Y, 10 দিনে করতে পারে কাজটির 1 অংশ
∴ Y, 1 দিনে করতে পারে কাজটির 1/10 অংশ

X ও Y 1 দিনে একত্রে করতে পারে কাজটির = {(1/15) + (1/10)} অংশ
= (2 + 3)/30 অংশ
= 5/30 অংশ
= 1/6 অংশ

X ও Y 3 দিনে করতে পারে কাজটির (3 × 1/6) অংশ
= 1/2 অংশ

কাজ বাকি থাকে = 1 - (1/2) অংশ
= (2 - 1)/2 অংশ
= 1/2 অংশ

∴ কাজটির 1/2 অংশ বাকি থাকে।

৫,৭৫৩.

If an article is sold for Tk. 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

ক
Tk. 222
খ
Tk. 224
গ
Tk. 228
ঘ
Tk. 232

ব্যাখ্যা

Question: If an article is sold for Tk. 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

Solution:

SP of the article = Tk. 178

Loss % = 11%

∴ CP = {100/(100 - 11)} × 178

= (178 × 100)/89 = 200

Now CP = Tk. 200 and Profit% = 11%

∴ New SP = {(100 + 11)/100} × 200 = (111 × 200)/100 = 222

Therefore, the article should be sold at Tk. 222

৫,৭৫৪.

If x + y + z = 9 and both y and z are positive integers greater than zero, then the maximum value x can take is-

ক
ক) 6
খ
খ) 0
গ
গ) 7
ঘ
ঘ) 9

ব্যাখ্যা

y and z are positive integers greater than zero.
so, y > 0 and z > 0
now here you have to find maximum value of x so value of (y + z) must be minimum.
we know, after zero , 1 is the smallest positive integer
we should take y = z = 1

Here, x + y + z = 9
⇒x = 9 - (y + z)
x = 9 - (1 + 1)
x = 7

Therefore the maximum value of x can take, is 7.

৫,৭৫৫.

The 2^nd and 8^th term of an arithmetic progression are 17 and - 1 respectively. What is the 14^th term?

ক
- 22
খ
- 25
গ
- 19
ঘ
- 28

ব্যাখ্যা

Question: The 2^nd and 8^th term of an arithmetic progression are 17 and - 1 respectively. What is the 14^th term?

Solution:
Let the first term be a and the common difference be d.

We know,
n term of arithmetic progression = a + (n - 1)d
Then,
2^nd term, a + d = 17 ……(i)
8^th term, a + 7d = - 1 ……(ii)

Now, Subtract (i) from (ii),
(a + 7d) - (a + d) = - 1 - 17
⇒ 6d = - 18
∴ d = - 3
From (i) we get,
⇒ a + ( - 3) = 17 ; [d = - 3]
⇒ a - 3 = 17
∴ a = 20

Now, 14^th term = a + 13d
= 20 + 13( - 3)
= 20 - 39
= - 19

So the 14th term of the arithmetic progression is - 19.

৫,৭৫৬.

Find the surface area of a cuboid 16 m long, 14 m broad and 7 m high.

ক
900 m²
খ
434 m²
গ
1000 m²
ঘ
868 m²

ব্যাখ্যা

Question: Find the surface area of a cuboid 16 m long, 14 m broad and 7 m high.

Solution:
Where,
length, l = 16 m
breadth, b = 14 m
height, h = 7 m

We know,
total surface area of a cuboid
= 2(lb + bh + hl)
= [2 (16 × 14 + 14 × 7 + 16 × 7)]
= 2 (224 + 98 + 112)
= (2 × 434)
= 868 m²

So the surface area of the cuboid is 868 square metres.

৫,৭৫৭.

If the monthly salary of an employee is increased by (8/3)%, he gets tk.88 more. His monthly salary (in TK.) is

ক
ক) 2700
খ
খ) 2800
গ
গ) 3000
ঘ
ঘ) 3300

ব্যাখ্যা

Let
The monthly salary be x

Now
(8/3)% of x = 88
(8/3) × (1/100) × x = 88
8x/(3 × 100) = 88
x = (88 × 3 × 100)/8
x = 3300

৫,৭৫৮.

If cotθ = 3/4, then secθ = ?

ক
5/3
খ
4/5
গ
3/5
ঘ
5/4

ব্যাখ্যা

Question: If cotθ = 3/4, then secθ = ?

Solution:
দেওয়া আছে,
cotθ = 3/4 = ভূমি/লম্ব
∴ ভূমি = 3, লম্ব = 4

পিথাগোরাসের উপপাদ্য অনুযায়ী,
অতিভুজ = √(লম্ব² + ভূমি²)
= √(4² + 3²)
= √(16 + 9)
= √25
= 5

এখন,
secθ = অতিভুজ/ভূমি
∴ secθ = 5/3

৫,৭৫৯.

বিক্রয় করসহ একটি দ্রব্যের বিক্রয়মূল্য ৩০৮ টাকা। বিক্রয় করের হার ১০%। যদি দ্রব্যটি বিক্রয়ে দোকানদারের ১২% লাভ হয়, তবে দ্রব্যটির ক্রয়মূল্য কত?

ক
২৩০ টাকা
খ
২২০ টাকা
গ
২৫০ টাকা
ঘ
২৬০ টাকা
ঙ
২৪০ টাকা

ব্যাখ্যা

প্রশ্ন: বিক্রয় করসহ একটি দ্রব্যের বিক্রয়মূল্য ৩০৮ টাকা। বিক্রয় করের হার ১০%। যদি দ্রব্যটি বিক্রয়ে দোকানদারের ১২% লাভ হয়, তবে দ্রব্যটির ক্রয়মূল্য কত?

সমাধান:
বিক্রয় কর ১০% হলে, কর সংযোজন মূল্য = ১০০ + ১০ = ১১০ টাকা

কর সংযোজন মূল্য ১১০ টাকা হলে কর বাদে মূল্য = ১০০ টাকা
∴ কর সংযোজন মূল্য ১ টাকা হলে কর বাদে মূল্য = ১০০/১১০ টাকা
∴ কর সংযোজন মূল্য ৩০৮ টাকা হলে কর বাদে মূল্য = (১০০ × ৩০৮)/১১০ টাকা
= ২৮০ টাকা

১২% লাভে, বিক্রয়মূল্য = ১০০ + ১২ = ১১২ টাকা

বিক্রয়মূল্য ১১২ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
∴ বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/১১২ টাকা
∴ বিক্রয়মূল্য ২৮০ টাকা হলে ক্রয়মূল্য = (১০০ × ২৮০)/১১২ টাকা
= ২৫০ টাকা

৫,৭৬০.

Given,

ক
4/3
খ
4
গ
4^4/3
ঘ
4⁵

ব্যাখ্যা

Question: Given,

Solution:

৫,৭৬১.

A factory has two machines, X and Y. Machine X can produce 6,000 items in 10 days, working 6 hours per day. Machine Y can produce 8,000 items in 8 days, working 10 hours per day. If both machines work together for 8 hours per day, how many days will they take to produce 24,000 items?

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

ব্যাখ্যা

Question: A factory has two machines, X and Y. Machine X can produce 6,000 items in 10 days, working 6 hours per day. Machine Y can produce 8,000 items in 8 days, working 10 hours per day. If both machines work together for 8 hours per day, how many days will they take to produce 24,000 items?

Solution:
Total hours worked by Machine X = 10 days × 6 hours/day = 60 hours.
Rate of X = (6000/60) = 100 items/hour

Total hours worked by Machine Y = 8 days × 10 hours/day = 80 hours.
Rate of Y = (8000/80) = 100 items/hour

Combined rate = Rate of X + Rate of Y = 100 + 100 = 200 items/hour.

So, time required = {24000/(200 × 8)} = 15 days.

৫,৭৬২.

The base of a rectangle is three times as long as the height. If the perimeter is 64, what is the area of the rectangle?

ক
ক) 24
খ
খ) 64
গ
গ) 96
ঘ
ঘ) 192

ব্যাখ্যা

মনে করি, আয়তক্ষেত্রের উচ্চতা x এবং ভূমি 3x
প্রশ্নমতে, 2(3x + x) = 64
⇒ 8x = 64
⇒ x = 8
∴ আয়তক্ষেত্রের উচ্চতা 8 এবং ভূমি 8×3 = 24 একক
∴ ক্ষেত্রফল = 8 × 24 = 192 একক

৫,৭৬৩.

A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 13 meter². The area of the whole room is 49 meter². What is the length of the one side of the carpet?

ক
8 meter
খ
6 meter
গ
4 meter
ঘ
2 meter

ব্যাখ্যা

Question: A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 13 meter². The area of the whole room is 49 meter². What is the length of the one side of the carpet?

Solution:
মনে করি,
কার্পেটের এক বাহুর দৈর্ঘ্য x মিটার

প্রশ্নমতে,
49 - 13 = x²
⇒ 36 = x²
⇒ 6² = x²
∴ x = 6

৫,৭৬৪.

A train 240 meters long passes a pole in 15 seconds. How long will it take to pass through a platform 300 meters long?

ক
31.25 seconds
খ
33.75 seconds
গ
35 seconds
ঘ
37.5 seconds

ব্যাখ্যা

Question: A train 240 meters long passes a pole in 15 seconds. How long will it take to pass through a platform 300 meters long?

Solution:
Train length = 240 meters
Time to pass a pole = 15 seconds

Speed = (240/15) m/s = 16 m/s

Total distance to be covered (train + platform) = 240 + 300 = 540 meters
So, Time = 540/16
= 33.75 seconds

৫,৭৬৫.

The average of three consecutive multiples of 5 is 50. What is the largest of these multiples?

ক
45
খ
65
গ
58
ঘ
50
ঙ
55

ব্যাখ্যা

Question: The average of three consecutive multiples of 5 is 50. What is the largest of these multiples?

Solution:
Let the three consecutive multiples of 5 are, 5x, 5x + 5, 5x + 10

Average = 5x + (5x + 5) + (5x + 10)/3
= (15x + 15)/3

As per question;
⇒ (15x + 15)/3 = 50
⇒ 15x + 15 = 150
⇒ 15x = 135
⇒ x = 135/15 = 9
∴ x = 9

So, the largest multiple is = 5x + 10 = 45 + 10 = 55.

৫,৭৬৬.

A pair of trains set off at the same moment from opposite ends: one from Rajshahi to Dhaka and the other from Dhaka to Rajshahi. After passing each other, one takes 9 hours and the other 16 hours to complete their trips. Find the speed ratio of the two trains.

ক
2 : 3
খ
1 : 3
গ
4 : 5
ঘ
4 : 3
ঙ
None of the above

ব্যাখ্যা

Question: A pair of trains set off at the same moment from opposite ends: one from Rajshahi to Dhaka and the other from Dhaka to Rajshahi. After passing each other, one takes 9 hours and the other 16 hours to complete their trips. Find the speed ratio of the two trains.
(একটি ট্রেন রাজশাহী থেকে ঢাকার দিকে এবং আরেকটি ঢাকা থেকে রাজশাহীর দিকে একই সময়ে যাত্রা শুরু করে। তারা যখন মিলিত হয়, তখন দেখা যায় একটির গন্তব্যে পৌঁছাতে ৯ ঘণ্টা এবং অন্যটির ১৬ ঘণ্টা লাগে। এই অনুযায়ী, তাদের গতি অনুপাতে কত?)

Solution:
দুটি ট্রেন একই সময়ে যাত্রা শুরু করেছে - একটি রাজশাহী থেকে ঢাকা, অন্যটি ঢাকা থেকে রাজশাহী।

পথে এক সময় তারা একে অপরকে অতিক্রম করেছে।
সেই অতিক্রম করার পর, এক ট্রেন ৯ ঘণ্টা, অন্যটি ১৬ ঘণ্টা সময় নিয়ে নিজ নিজ গন্তব্যে পৌঁছেছে।

ধরা যাক:
ট্রেন A যাচ্ছে রাজশাহী থেকে ঢাকা (গতিবেগ = v₁)
ট্রেন B যাচ্ছে ঢাকা থেকে রাজশাহী (গতিবেগ = v₂)

তারা যখন মাঝ পথে দেখা করে (ধরা যাক M পয়েন্টে), তখন তারা একই সময় নিয়ে সেই পয়েন্টে পৌঁছায় (যেহেতু একসাথে শুরু করেছে)।

মিলনের পর:

ট্রেন A বাকি পথ যেতে ৯ ঘণ্টা নেয়, দূরত্ব = 9 × v₁ট্রেন B বাকি পথ যেতে ১৬ ঘণ্টা নেয়, দূরত্ব = 16 × v₂এই দূরত্ব দুটি সমান নয়, কিন্তু এদের অনুপাতই বলে দেবে গতির অনুপাত।

দুটি ট্রেন একসাথে শুরু করে এক পয়েন্টে দেখা করলে, যে ট্রেনটি অতিক্রমের পরে কম সময় নেয়, তার গতি বেশি।

গতির অনুপাত নির্ণয়ের সূত্র:
গতির অনুপাত = √(দ্বিতীয় ট্রেনের সময় / প্রথম ট্রেনের সময়)
অর্থাৎ:
v1/v2 = √(16/9) = 4/3

দুটি ট্রেনের গতির অনুপাত = ৪ : ৩

৫,৭৬৭.

A takes twice as long to do a piece of work, as B takes. A & B together can finish a piece of work in 20 days. A alone can do it in-

ক
ক) 25 days
খ
খ) 30 days
গ
গ) 35 days
ঘ
ঘ) 60 days

ব্যাখ্যা

ধরি,
B কাজটি করতে সময় নেয় = x দিন
A কাজটি করতে সময় নেয় = 2x দিন

A এবং B 1 দিনে করতে পারে কাজটির = (1/x) + (1/2x) অংশ
= (2 + 1)/2x
= 3/2x
A এবং B 3/2x অংশ কাজ করতে সময় লাগে = 1 দিন
A এবং B 1 অংশ কাজ করতে সময় লাগে = 1/(3/2x) দিন
= 2x/3

প্রশ্নমতে,
2x/3 = 20
x = (20 × 3)/2
x = 30

A কাজটি করতে সময় নেয় = 2 × 30 দিন = 60 দিন

৫,৭৬৮.

If (3x + 2y) = 8 and (2x - y) = 3 find the value of 'x'.

ক
2
খ
3
গ
4
ঘ
6
ঙ
None of these

ব্যাখ্যা

Question: If (3x + 2y) = 8 and (2x - y) = 3 find the value of 'x'.

Solution:
3x + 2y = 8 ........(1)
2x - y = 3 ........(2)

From (1) + (2) × 2 we get,
3x + 2y + 4x - 2y = 8 + 6
⇒ 7x = 14
∴ x = 2

৫,৭৬৯.

A tank can be filled by pipe A in 2 hours and pipe B in 6 hours. At 10 A.M. pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?

ক
ক) 11 A.M.
খ
খ) 11.45 A.M.
গ
গ) 12 A.M.
ঘ
ঘ) 12.45 A.M.

ব্যাখ্যা

Question: A tank can be filled by pipe A in 2 hours and pipe B in 6 hours. At 10 A.M. pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?

Solution:
A ২ ঘণ্টায় পূর্ণ করে ১ অংশ
১ ঘণ্টায় পূর্ণ করে ১/২ অংশ

বাকি থাকে (১ - ১/২) অংশ
= ১/২ অংশ ; যা A, B একসাথে সম্পন্ন করে।

B ৬ ঘণ্টায় করে ১ অংশ কাজ
১ ঘণ্টায় করে ১/৬ অংশ কাজ

A, B ১ ঘণ্টায় করে (১/৬) + (১/২) অংশ
= ৪/৬ অংশ
= ২/৩ অংশ

A, B ২/৩ অংশ পূর্ণ করে ১ ঘণ্টায়
১/২ অংশ পূর্ণ করে ৩/(২ × ২)
= ৩/৪ ঘণ্টায়

মোট সময় = ১ + (৩/৪) = ৭/৪ ঘন্টা = ১ ঘণ্টা ৪৫ মিনিট
∴ ট্যাঙ্ক পূর্ণ হবে = ১০ টা + ১ ঘণ্টা ৪৫ মিনিট
= ১১ টা ৪৫ মিনিট

৫,৭৭০.

Find the value of 9⁵ × 9^-3 × 9⁴

ক
ক) 9¹²
খ
খ) 9⁶
গ
গ) 9^{- 60}
ঘ
ঘ) 9⁴

ব্যাখ্যা

Question: Find the value of 9⁵ × 9^-3 × 9⁴

Solution:
9⁵ × 9^-3 × 9⁴
=9^{5 + (- 3) + 4}
=9^{5 - 3 + 4}
=9⁶

৫,৭৭১.

A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio -

ক
ক) 3 : 4
খ
খ) 13 : 15
গ
গ) 4 : 5
ঘ
ঘ) 16 : 15

ব্যাখ্যা

For an income of Tk. 1 in 9% stock at 96,
investment = Tk. (96/9)
= Tk. 32/3

For an income of Tk. 1 in 12% stock at 120,
investment = Tk. (120/12)
= Tk. 10

Ratio of investments = (32/3) : 10
= 32 : 30
= 16 : 15.

৫,৭৭২.

When you looked at a clock, it was showing 6 : 00 in the morning. By how much angle will the hour’s hand rotate when you again look at the clock at 12 : 00 in the noon?

ক
120°
খ
180°
গ
150°
ঘ
110°

ব্যাখ্যা

Question: When you looked at a clock, it was showing 6 : 00 in the morning. By how much angle will the hour’s hand rotate when you again look at the clock at 12 : 00 in the noon?

Solution:
In 12 hours, the hour’s hand turns 360°

Hence, the difference between time 12 : 00 - 6 : 00 = 6 hours

Therefore, the required angle = (360°/12) × 6 = 180°

৫,৭৭৩.

If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.

ক
± 9
খ
± 6
গ
± 7
ঘ
± 8

ব্যাখ্যা

Question: If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.

Solution:
a² + b² + c² = 16
ab + bc + ca = 10

We know that,
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (a + b + c)² = 16 + 2 × 10
⇒ (a + b + c)² = 36
⇒ a + b + c = √36
⇒ a + b + c = ± 6

∴ The value of (a + b + c) is ± 6.

৫,৭৭৪.

The difference of 13/12 and its reciprocal is equal to-

ক
169/144
খ
15/16
গ
4/3
ঘ
None

ব্যাখ্যা

Question: The difference of 13/12 and its reciprocal is equal to-

Solution:
The reciprocal of 13/12 is 12/13
Now, calculate the difference between 13/12 and 12/13
= (13/12) - (12/13)
= (169 - 144)/156
= 25/156

∴ The difference between 13/12 and its reciprocal is 25/156.

৫,৭৭৫.

What is the volume of a cylinder with diameter 8 and height 14 unit?

ক
704
খ
650
গ
890
ঘ
690

ব্যাখ্যা

Question: What is the volume of a cylinder with diameter 8 unit and height 14 unit?

Solution:
Given,
Height = 14 unit
Diameter = 8 unit
∴ radius = 8 ÷ 2
= 4 unit

We know,
The volume of a cylinder = πr²h
= (22/7) × 4² × 14
= 22 × 16 × 2
= 704

৫,৭৭৬.

Labib wants to arrange four out of his five saplings in a row on a shelf. If each sapling is in a pot of a different color, in how many different ways can he arrange the four saplings?

ক
24
খ
60
গ
78
ঘ
120

ব্যাখ্যা

Question: Labib wants to arrange four out of his five saplings in a row on a shelf. If each sapling is in a pot of a different color, in how many different ways can he arrange the four saplings?

Solution:
যেহেতু প্রতিটি চারাগাছ ভিন্ন ভিন্ন রঙের পাত্রে আছে এবং সেগুলোকে একটি সারিতে সাজাতে হবে, তাই এটি একটি বিন্যাসের (Permutation) সমস্যা।

∴ পাঁচটি চারাগাছ হতে চারটি নিয়ে সাজানো যায় = ⁵P₄ উপায়ে
= 5!/(5 - 4)! উপায়ে
= 5! উপায়ে
= 5 × 4 × 3 × 2 × 1 উপায়ে
= 120 উপায়ে

∴ লাবিব মোট 120টি ভিন্ন উপায়ে চারাগাছগুলো সাজাতে পারবে।

৫,৭৭৭.

If on a Sale there is 40% discount on the marked price of Tk. 1000, but the sale is done at Tk. 510 only then what additional discount % did the customer get?

ক
ক) 10%
খ
খ) 15%
গ
গ) 28%
ঘ
ঘ) 9%

ব্যাখ্যা

Question: If on a Sale there is 40% discount on the marked price of Tk. 1000, but the sale is done at Tk. 510 only then what additional discount % did the customer get?

Solution:

Marked price = Tk. 1000
First discount = 40%
After first discount selling price is = 1000 - (40% of 100) = 600

Let the second discount is = x%

ATQ,
600 - (x% of 600) =510
⇒ 600 - 6x = 510
⇒ 6x = 90
⇒ x = 15

৫,৭৭৮.

The sum of odd numbers up to 240 is -

ক
11400
খ
12400
গ
13400
ঘ
14400

ব্যাখ্যা

Question: The sum of odd numbers up to 240 is -

Solution:
Number of odd numbers up to 240 = 240/2 = 120
Sum of first n odd numbers = n²
n = 120
∴ Required sum = 120² = 14400

৫,৭৭৯.

The number 2272 and 875 are divided by a 3 digit number N, giving the same remainders. The sum of the digit is-

ক
12
খ
22
গ
18
ঘ
10

ব্যাখ্যা

Question: The number 2272 and 875 are divided by a 3 digit number N, giving the same remainders. The sum of the digit is-

Solution:
Let the remainder in each case be x
Then, (2272 - x) and (875 - x) are exactly divisible by three digit number
Difference :
= (2272 - x) - (875 - x)
= 1397
Factor of 1397 = 11 × 127
Since, both 11 and 127 are prime number
Three digit number is 127

∴ Sum of digits = 1 + 2 + 7 = 10

৫,৭৮০.

How many different numbers of two digits can be formed with the digits 1, 2, 3, 4, 5, 6; no digit being repeated?

ক
36
খ
30
গ
25
ঘ
24

ব্যাখ্যা

Question: How many different numbers of two digits can be formed with the digits 1, 2, 3, 4, 5, 6; no digit being repeated?

Solution:
different numbers of two digits can be formed = 6 × 5
= 30

৫,৭৮১.

An amount of money in invested in a saving account for two years. It increases by Tk. 645 in two years after annual compounding at the rate of 15% per year. What is the amount in Tk. invested initially?

ক
Tk. 1500
খ
Tk. 2000
গ
Tk. 2200
ঘ
Tk. 1800

ব্যাখ্যা

Question: An amount of money in invested in a saving account for two years. It increases by Tk. 645 in two years after annual compounding at the rate of 15% per year. What is the amount in Tk. invested initially?

Solution:
Let, the principal be p

ATQ,
p + 645 = p(1 + 15/100)²
⇒ p + 645 = p(1 + 3/20)²
⇒ p + 645 = p(23/20)²
⇒ p + 645 = (529p)/400
⇒ 529p = 400p + 258000
⇒ 129p = 258000
⇒ p = 258000/129
∴ p = 2000

৫,৭৮২.

If CAFE = FACE, then TALE = ?

ক
TAEL
খ
LTEA
গ
LATE
ঘ
ELAT

ব্যাখ্যা

Question: If CAFE = FACE, then TALE = ?

Solution:
এখানে,
CAFE = FACE এর C আর F পরস্পরের স্থান পরিবর্তন করেছে, A আর E এর কোনো পরিবর্তন হয়নি।

একইভাবে,
TALE শব্দের A আর E এর কোনো পরিবর্তন হবে না, T আর L পরস্পরের স্থান পরিবর্তন করবে।
∴ TALE = LATE

৫,৭৮৩.

2100 Taka is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

ক
Tk. 2315.25
খ
Tk. 2325.25
গ
Tk. 2425
ঘ
Tk. 2575
ঙ
None

ব্যাখ্যা

Question: 2100 Taka is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

Solution:
Here,
p = Tk. 2100
r% = 5%
n = 2 years

C = p[1 + (r/100)]ⁿ
= 2100 [1 + (5/100)]2
= 2100 × [105/100]²
= (2100 × 11025)/10000
= 2315.25

Hence, the amount after two years is Tk. 2315.25

৫,৭৮৪.

The length of a box is 3 meters, breadth is 2 meters 50 centimeters and height is 2 meters. What is the volume of the box?

ক
ক) 9 cubic meters
খ
খ) 15 cubic meters
গ
গ) 25 cubic meters
ঘ
ঘ) 12 cubic meters

ব্যাখ্যা

প্রশ্ন: The length of a box is 3 meters, breadth is 2 meters 50 centimeters and height is 2 meters. What is the volume of the box?

সমাধান:
দৈর্ঘ্য = ৩ মিটার
প্রস্থ = ২ মিটার ৫০ সেন্টিমিটার
= ২ মিটার + (৫০/১০০) মিটার
= (২ + ১/২) মিটার
= ৫/২ মিটার
উচ্চতা = ২ মিটার

∴ আয়তন = দৈর্ঘ্য × প্রস্থ × উচ্চতা
= ৩ × (৫/২) × ২ ঘনমিটার
= ১৫ ঘনমিটার

৫,৭৮৫.

The area of a circle is increased by 22 square cm if its radius is increased by 1 cm. The original radius of the circle is -

ক
1.5 cm
খ
3 cm
গ
3.5 cm
ঘ
6 cm

ব্যাখ্যা

Question: The area of a circle is increased by 22 square cm if its radius is increased by 1 cm. The original radius of the circle is -

Solution:
Let the original radius of the circle be r cm.

ATQ,
π(r + 1)² - πr² = 22
⇒ π{(r + 1)² - r²} = 22
⇒ π(r² + 2r + 1 -r²) = 22
⇒ 2r + 1 = 22/π
⇒ 2r + 1 = (22 × 7)/22
⇒ 2r + 1 = 7
⇒ 2r = 6
⇒ r = 3 cm

৫,৭৮৬.

There are Tiger and peacock in zoo. The total number of their heads is 60 and the total number of their legs is 180. How many peacocks are there?

ক
35
খ
25
গ
40
ঘ
30

ব্যাখ্যা

Question: There are Tiger and peacock in zoo. The total number of their heads is 60 and the total number of their legs is 180. How many peacocks are there?

Solution:
Let,
There are x peacocks

So the number of tiger = (60 - x)

ATQ,
2x + 4(60 - x) = 180
⇒ 2x + 240 - 4x = 180
⇒ 240 - 2x = 180
⇒ 240 - 180 = 2x
⇒ 60 = 2x
⇒ x = 60/2
∴ x = 30

৫,৭৮৭.

If a² + b² = 45 and ab = 18, find (1/a) + (1/b)

ক
1/3
খ
1/2
গ
2/3
ঘ
1/4

ব্যাখ্যা

Question: If a² + b² = 45 and ab = 18, find (1/a) + (1/b)

Solution:
Given that,
ab = 18
a² + b² = 45
⇒ (a + b)² - 2ab = 45
⇒ (a + b)² - 36 = 45
⇒ (a + b)² = 81
∴ a + b = 9

Now,
(1/a) + (1/b)
=(b + a)/ab
= 9/18
= 1/2

৫,৭৮৮.

If the list price of a book is Tk. 50, and a Tk. 10 discount is offered on the book, then what is the discount percentage?

ক
5%
খ
10%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: If the list price of a book is Tk. 50, and a Tk. 10 discount is offered on the book, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100

Marked Price = Tk. 50
Discount= Tk. 10

Discount (%) = (10/50) ×100%

= 100/5 %

= 20%

∴ Therefore, the discount percentage is calculated as 20%.

৫,৭৮৯.

Find the wrong term in the following series.
1200, 1188, 1164, 1116, 1020, 828, 484

ক
1200
খ
1188
গ
1020
ঘ
484
ঙ
828

ব্যাখ্যা

Question: Find the wrong term in the following series.
1200, 1188, 1164, 1116, 1020, 828, 484

Solution:
Given series:
1200, 1188, 1164, 1116, 1020, 828, 484
The series decreases with multiples of 12, doubling each time.
1^st term = 1200
2^nd term = 1200 - 12 = 1188
3^rd term = 1188 - 24 = 1164
4^th term = 1164 - 48 = 1116
5^th term = 1116 - 96 = 1020
6^th term = 1020 - 192 = 828
7^th term = 828 - 384 = 444

The series has 484 as the last term, but it should be 444.

Hence the wrong term in the series is 484.

৫,৭৯০.

A person subscribes to LiveMCQ for a year pack Tk. 1200. If the monthly subscription is Tk. 200, how much discount does a yearly subscriber get?

ক
70%
খ
65%
গ
50%
ঘ
25%

ব্যাখ্যা

Question: A person subscribes to LiveMCQ for a year pack Tk. 1200. If the monthly subscription is Tk. 200, how much discount does a yearly subscriber get?

Solution:
The monthly subscription is Tk. 125, so for a year pack should be = (12 × 200) taka
= Tk.2400

Discount = 2400 - 1200
= 1200 taka

%discount = (1200/2400) × 100%
= 50%

৫,৭৯১.

Simon rowing against the current can go 2 km per hour. If the speed of the current is 3 km per hour, how much time will he take to cover 32 km, rowing along the current?

ক
3 hr
খ
4 hr
গ
5 hr
ঘ
6 hr

ব্যাখ্যা

Question: Simon rowing against the current can go 2 km per hour. If the speed of the current is 3 km per hour, how much time will he take to cover 32 km, rowing along the current?

Solution:
ধরি, সায়মনের বেগ x কিমি/ঘণ্টা
স্রোতের বেগ ৩ কিমি/ঘণ্টা

সায়মন স্রোতের বিপরীতে ২ কিমি/ঘণ্টা বেগে যায়।

x - ৩ = ২
∴ x = ৫ কিমি/ঘণ্টা

স্রোতের অনুকূলে বেগ = ৩ + ৫ কিমি/ঘণ্টা
= ৮ কিমি/ঘণ্টা

স্রোতের অনুকূলে যেতে সময় লাগে = ৩২/৮ ঘণ্টা
= ৪ ঘন্টা

৫,৭৯২.

Rahim and Karim started a business investing Tk. 26000 and Tk. 30000 respectively. Out of a total profit of Tk. 7000, Rahim's share is -

ক
Tk. 3050
খ
Tk. 3150
গ
Tk. 3250
ঘ
Tk. 3450

ব্যাখ্যা

Question: Rahim and Karim started a business investing Tk. 26000 and Tk. 30000 respectively. Out of a total profit of Tk. 7000, Rahim's share is -

Solution:
Given,
Investment ratio = 26000 : 30000
= 13 : 15
Sum of the ratio's = 13 + 15 = 28

∴ Rahim's share = 7000 × (13/28)
= Tk. 3250

৫,৭৯৩.

If √x = √7 - √5 then the value of x² - 24x + 8 = ?

ক
5
খ
4
গ
2
ঘ
0

ব্যাখ্যা

Question: If √x = √7 - √5 then the value of x² - 24x + 8 = ?

Solution:
Given,
√x = √7 - √5
⇒ x = 7 + 5 - 2.√7.√5 (Squaring both sides)
⇒ x = 12 - 2√35
⇒ x - 12 = - 2√35
⇒ x² + 144 - 24x = 140 (Squaring both sides)
⇒ x² + 4 - 24x = 0
⇒ x² + 8 - 24x = 4
∴ x² - 24x + 8 = 4

৫,৭৯৪.

A starts a business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

ক
ক) 7000 Tk
খ
খ) 9000 Tk
গ
গ) 8000 Tk
ঘ
ঘ) 12000 Tk

ব্যাখ্যা

Question: A starts a business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

Solution:
Let B's capital be Tk x
∴ A's share in 12 months = 3500 × 12
And, B's share in 7 months = 7x

Then,
(3500 × 12)/7x = 2/3
⇒ 14x = 126000
⇒ x = 9000

৫,৭৯৫.

If m and n are whole numbers such that mⁿ = 121, then the value of (m - 1)^{n + 1} is = ?

ক
1000
খ
676
গ
121
ঘ
10
ঙ
None of these

ব্যাখ্যা

প্রশ্ন: If m and n are whole numbers such that mⁿ = 121, then the value of (m - 1)^{n + 1} is = ?

সমাধান:
দেওয়া আছে,
mⁿ = 121
⇒ mⁿ = 11²
এখানে, m = 11 এবং n = 2

∴ (m - 1)^{n + 1} = (11 - 1)^{2 + 1}
= 10³
= 1000

৫,৭৯৬.

If a 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

৫,৭৯৭.

A train 150 meters long takes 40 seconds to cross a 350-meter-long bridge. How much time will the train take to cross a 250-meter-long platform?

ক
32 seconds
খ
28 seconds
গ
19 seconds
ঘ
22 seconds

ব্যাখ্যা

Question: A train 150 meters long takes 40 seconds to cross a 350-meter-long bridge. How much time will the train take to cross a 250-meter-long platform?

Solution:
Length of train = 150 m
Length of bridge = 350 m
∴ Total distance to cross bridge = 150 + 350 = 500 m
Time taken = 40 seconds
∴ Speed of train = Total distance/Time
= 500/40 = 12.5 m/s

Length of platform = 250 m
∴ Total distance to cross platform = 150 + 250 = 400 m

∴ Time taken = Total distance/Speed
= 400/12.5 seconds
= 32 seconds

৫,৭৯৮.

6, 7, 9, 13, ___, ___. What are the two missing numbers in the series?

ক
ক) 21, 37
খ
খ) 17, 21
গ
গ) 21, 39
ঘ
ঘ) 17, 19

ব্যাখ্যা

6 7 9 13 21 37
1 2 4 8 16

৫,৭৯৯.

The incomes of X and Y are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. If each of them saves Tk. 1000, then, X’s income can be

ক
Tk. 1000
খ
Tk. 2000
গ
Tk. 4000
ঘ
Tk. 6000

ব্যাখ্যা

Question: The incomes of X and Y are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. If each of them saves Tk. 1000, then, X’s income can be

Solution:
The incomes of X and Y are 3x, 2x
their expenditures are 5y, 3y

3x - 5y = 1000
2x - 3y = 1000

3x - 5y = 2x - 3y
⇒ x = 2y

3 × 2y - 5y = 1000
⇒ y = 1000
x = 2 × 1000 = 2000 taka

∴ X’s income = 3x
= 3 × 2000
= Tk. 6000

৫,৮০০.

A trader mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

ক
ক) 5%
খ
খ) 15%
গ
গ) 12%
ঘ
ঘ) 8%

ব্যাখ্যা

প্রশ্ন: A trader mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

সমাধান:
C.P. of 56 kg rice = (26 × 20 + 30 × 36)
= (520 + 1080)
=1600

S.P. of 56 kg rice = (56 × 30)
= 1680.

∴ Profit = 1680 - 1600
= 80

∴ Profit percentage = (80/1600) × 100% = 5%