Bank Math

PrepBank · পাতা ১৪৬ / ১৬১ · ১৪,৫০১–১৪,৬০০ / ১৬,১২৪

১৪,৫০১.

The average marks of four subjects is 120. If 33 was misread as 13 during the calculation, what will be the correct average?

ক
ক) 125
খ
খ) 134
গ
গ) 167
ঘ
ঘ) 178

ব্যাখ্যা

The average marks of four subjects is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to total.
Then average = 20/4 = 5
Correct average = 120 + 5 = 125

১৪,৫০২.

The ratio of two numbers is 2 : 3 and their sum is 250. The smaller one of the numbers is-

ক
50
খ
100
গ
150
ঘ
None of these

ব্যাখ্যা

Question: The ratio of two numbers is 2 : 3 and their sum is 250. The smaller one of the numbers is-

Solution:
let, the numbers be 2x, 3x

2x + 3x = 250
⇒ 5x = 250
⇒ x = 250/5
∴ x = 50

numbers are 100, 150

১৪,৫০৩.

B is twice as old as A but twice younger than F. C is half the age of A, but twice older than d. Who is the second oldest?

ক
F
খ
C
গ
B
ঘ
D
ঙ
A

ব্যাখ্যা

Let, A = x

Then B = 2x and F = 4x, C = x/2, D = x

Thus the second oldest is B.

১৪,৫০৪.

A man sells a watch for 960 Taka and loses 20%. What was the cost price?

ক
1100
খ
1000
গ
1200
ঘ
1150

ব্যাখ্যা

Question: A man sells a watch for 960 Taka and loses 20%. What was the cost price?

Answer: Here, Given Selling Price = 960 Taka
- With Loss 20 % If,
The Selling Price is 80 Taka then Cost Price is =100 Taka
The Selling Price is 1 Taka then Cost Price is =100/80 Taka
The Selling Price is 960 Taka then Cost Price is = (100×960)/80 Taka = 1200 Taka

১৪,৫০৫.

A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. How many times can it go round a cylinder with radius 20 cm?

ক
ক) 39
খ
খ) 49
গ
গ) 59
ঘ
ঘ) 69

ব্যাখ্যা

Let the required number of rounds be x
More radius, Less rounds (Indirect proportion)
∴ 20:14::70:x
⇔(20×x)=(14×70)
⇔ x= (14×70)/ 20
⇔ x=49

১৪,৫০৬.

Arif started a business with Tk. 60,000. After some months, Nehal joined with Tk. 40,000. At the end of the year, the profit was divided in the ratio 9 : 5. For how many months was Nehal in the business?

ক
10 months
খ
9 months
গ
8 months
ঘ
7 months

ব্যাখ্যা

Question: Arif started a business with Tk. 60,000. After some months, Nehal joined with Tk. 40,000. At the end of the year, the profit was divided in the ratio 9 : 5. For how many months was Nehal in the business?

Solution:
Let,
Nehal joined for x months.

ATQ,
(60,000 × 12)/(40,000 × x) = 9/5
⇒ x = (60,000 × 12 × 5)/(40,000 × 9)
∴ x = 10

∴ Nehal joined for 10 months.

১৪,৫০৭.

If log⁡₁₀x + log⁡₁₀(x + 3) = 1, find the value of x.

ক
2
খ
4
গ
5
ঘ
6

ব্যাখ্যা

Question: If log⁡₁₀x + log⁡₁₀(x + 3) = 1, find the value of x.

Solution:
log⁡₁₀x + log⁡₁₀(x + 3) = 1
⇒ log₁₀{x(x + 3)} = log₁₀10
⇒ x² + 3x = 10
⇒ x² + 3x - 10 = 0
⇒ x + 5x - 2x - 10 = 0
⇒ x(x + 5) - 2(x + 5) = 0
⇒ (x + 5)(x - 2) = 0
∴ x = - 5, 2

১৪,৫০৮.

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
30%
খ
15%
গ
20%
ঘ
10%

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:
A dishonest milkman professes to sell his milk at cost price, but he mixes it with water and gains 25%

We know,
Profit = SP - CP
Let milk bought (cost price) be 1 litres at Tk. 100 and profit = 25

∴ Selling price = 100 + 25 = Tk. 125

As the selling price of 1 litre was Tk. 100(same as cost)

Quantity sold = 125/100 = 5/4 = 1.25 litre

Hence, water added = 1.25 - 1 = 0.25 litres

∴ Percentage of water = (0.25/1.20) × 100 = 20%

১৪,৫০৯.

If X and Y are in the ratio 13 : 4, and Y and Z in the ratio 13 : 4, then X and Z will be in the ratio-

ক
169 : 16
খ
13 : 4
গ
4 : 13
ঘ
13 : 16

ব্যাখ্যা

Question: If X and Y are in the ratio 13 : 4, and Y and Z in the ratio 13 : 4, then X and Z will be in the ratio-

Solution:
X : Y = 13 : 4
⇒ X/Y = 13/4

Y : Z = 13 : 4
⇒ Y/Z = 13/4

(X/Y) × (Y/Z) = (13/4) × (13/4)
⇒ X/Z = 169/16
∴ X : Z = 169 : 16

১৪,৫১০.

On 8th feb, 2005 it was tuesday. What was the day of the week on 8Th feb, 2004?

ক
ক) Tuesday
খ
খ) Monday
গ
গ) Sunday
ঘ
ঘ) Wednesday

ব্যাখ্যা

The year 2004 is a leap year. It has 2 odd days.
∴ The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday.

১৪,৫১১.

Sunday, Monday, Wednesday, Saturday, Wednesday, Monday, .....

ক
Sunday, Monday
খ
Sunday, Sunday
গ
Sunday, Wednesday
ঘ
Sunday, Saturday

ব্যাখ্যা

Question: Sunday, Monday, Wednesday, Saturday, Wednesday, Monday, .....

Solution:
Sunday to Monday = no gap
Monday to Wednesday = One day gap.
Wednesday to Saturday = Two days gap.
Saturday to Wednesday = Three days gap.
Wednesday to Monday = Four days gap.
In the next term there must be five days and six days gap.
So, Next term would be Sunday, Sunday.

১৪,৫১২.

If x = √5 + 2 what is the value of x² + 1/x² ?

ক
ক) 18
খ
খ) 10
গ
গ) 20
ঘ
ঘ) 26

ব্যাখ্যা

দেয়া আছে,
x =√5 + 2
1/x = 1/(√5 + 2)
= (√5 - 2)/(√5 + 2)(√5 - 2)
= (√5 - 2)/{(√5)² - (2)²}
= (√5 - 2)/(5 - 4)
= √5 - 2

x + 1/x = √5 + 2 + √5 - 2
= 2√5

x² + 1/x² = (x + 1/x)² - 2x. (1/x)
= (2√5)² - 2
= 4 × 5 - 2
= 20 - 2
= 18

১৪,৫১৩.

A can finish the job at the same time in which B and C together do it. If A and B together can finish the work in 10 days and C alone can do the work in 50 days, how many days B will take to complete the same job?

ক
20 days
খ
22 days
গ
22.5 days
ঘ
25 days

ব্যাখ্যা

Question: A can finish the job at the same time in which B and C together do it. If A and B together can finish the work in 10 days and C alone can do the work in 50 days, how many days B will take to complete the same job?

Solution:
The efficiency of A = B + C
(A + B) can finish the work in 10 days,
and C can finish the work in 50 days.

Now,
A + B = 10 days
C = 50 days

Assume the total work = LCM of the given days
∴ LCM of days = LCM of (10 and 50) = 50
Let the total work = 50

C's one day work = 50/50 = 1
(A + B)'s one day work = 5
i.e., (A + B + C)'s one day work = 5 +1=6
i.e., A + A = 6
⇒ 2A = 6
Or, A's one day work efficiency = 3

A + B = 5,
i.e., 3 + B = 5
Or, B's one day efficiency = 2

Hence, B alone can work in 50/2 = 25 days

১৪,৫১৪.

A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

ক
9 sec
খ
11 sec
গ
15 sec
ঘ
18 sec

ব্যাখ্যা

Question: A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

Solution:
Speed of train = 54 km/hr
= 54 × 5/18 m/sec
= 15 m/sec

Length of the train = 165 meters

Therefore, time taken by the train to cross a pole = length of train/speed of train
= 165/15 sec
= 11 sec

Thus, train takes 11 seconds to cross the pole.

১৪,৫১৫.

The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14 : 5. What is daughter's present age ?

ক
12 years
খ
18 years
গ
52 years
ঘ
None of these

ব্যাখ্যা

Question: The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14 : 5. What is daughter's present age ?

Solution:
Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years. Then, daughter age = (68 - x) years
∴ (x + 4)/(68 - x + 4) = 14/5
⇒ 5(x + 4) = 14(72 - x)
⇒ 5x + 20 = 1008 - 14x
⇒ 19x = 988
⇒ x = 52

∴ Daughter's present age = (68 - 52) = 16 years.

১৪,৫১৬.

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

ক
8
খ
10
গ
12
ঘ
15

ব্যাখ্যা

Question: The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

Solution:
Let,
The number of students is 30x
The number of teachers is x

ATQ,
(30x + 50)/(x + 5) = 25/1
⇒ 30x + 50 = 25x + 125
⇒ 30x - 25x = 125 - 50
⇒ 5x = 75
∴ x = 15

∴ The present number of teachers is 15

১৪,৫১৭.

In the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent.

ক
ক) 25%
খ
খ) 40%
গ
গ) 33.33%
ঘ
ঘ) 15%

ব্যাখ্যা

Question: In the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent.

Solution:
Let the C.P. of 1 pen =Tk. 1
∴ C.P of 12 pens=Tk. 12×1 =Tk. 12

C.P. of 12 pens = S.P of 16 pens
∴ S.P of 16 pens= Tk. 12
∴ C.P of 16 pens= Tk. 16

∴ Loss = C.P - S.P
=16- 12
=4 Tk.

Loss = {(4/16) × 100}%
= 25%.

১৪,৫১৮.

The perimeter of an equilateral triangle is 84√3 cm. Find its height.

ক
32 cm
খ
35 cm
গ
39 cm
ঘ
43 cm
ঙ
None

ব্যাখ্যা

Question: The perimeter of an equilateral triangle is 84√3 cm. Find its height.

Solution:
Given,
The perimeter of the equilateral triangle = 84√3 cm.
∴ Each side of the equilateral triangle = (84√3/3) = 28√3 cm.

We know,
The height of the equilateral triangle will be = (√3/2) × (28√3) = 42 cm

১৪,৫১৯.

A 70 metres long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

ক
230 m
খ
240 m
গ
260 m
ঘ
320 m

ব্যাখ্যা

Relative speed = (120 + 80) km/hr
(200 times; 5/18) m/s
(500/9) m/s

Let the length of other train x meter
Then, (x +270)/9 = 500/9
⇒ x + 270 = 500
⇒ x = 230

Answer : 230 m

১৪,৫২০.

In a shower, 2 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

ক
30000 m³
খ
3000 m³
গ
300 m³
ঘ
30 m³

ব্যাখ্যা

Question: In a shower, 2 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Solution:
1 hectare = 10000 m²
⇒ 1.5 hectare = 10000 × 1.5 m² = 15000 m²

The volume of water = 15000 × 2/100
= 300 m³

১৪,৫২১.

In a T-20 cricket match, the number of boundaries scored was twice the number of over boundaries by a team. The team took 22 single runs, no two or three runs and could not score from 38 deliveries. How many runs did the team score?

ক
124
খ
144
গ
150
ঘ
302

ব্যাখ্যা

Question: In a T-20 cricket match, the number of boundaries scored was twice the number of over boundaries by a team. The team took 22 single runs, no two or three runs and could not score from 38 deliveries. How many runs did the team score?

Solution:
T-20 cricket match এ
Total Ball = 120
boundaries and over boundaries = 120 - (22 + 38)
= 60

Again
boundaries = 2(over boundaries)

2(over boundaries) + over boundaries = 60
3(over boundaries) = 60
over boundaries = 60/3 = 20

boundaries = 60 - 20 = 40

The team score = 1 × 22 + 40 × 4 + 20 × 6
= 22 + 160 + 120
= 302

১৪,৫২২.

Which of the following integers has the most divisors?

ক
88
খ
91
গ
95
ঘ
99

ব্যাখ্যা

Question: Which of the following integers has the most divisors?

Solution:
• For 88:
Prime factorization: 88 = 2³ × 11
Number of divisors = (3 + 1) × (1 + 1) = 4 × 2 = 8 divisors
Divisors are: 1, 2, 4, 8, 11, 22, 44, 88

• For 91:
Prime factorization: 91 = 7 × 13
Number of divisors = (1 + 1) × (1 + 1) = 2 × 2 = 4 divisors
Divisors are: 1, 7, 13, 91

• For 95:
Prime factorization: 95 = 5 × 19
Number of divisors = (1 + 1) × (1 + 1) = 2 × 2 = 4 divisors
Divisors are: 1, 5, 19, 95

• For 99:
Prime factorization: 99 = 3² × 11
Number of divisors = (2 + 1) × (1 + 1) = 3 × 2 = 6 divisors
Divisors are: 1, 3, 9, 11, 33, 99

Therefore, 88 has the most divisors.

১৪,৫২৩.

The area of a rhombus is 36cm². The length of one of its diagonals is 8 cm. The length of the other diagonal is -

ক
ক) 10 cm
খ
খ) 9 cm
গ
গ) 7 cm
ঘ
ঘ) 6 cm

ব্যাখ্যা

Area of rhombus =36cm²
First diagonal =d₁=8 cm
Second diagonal = d₂
Now,
Area of rhombus = (1/2) × d₁ × d₂
36 = (1/2) × d₁ × d₂
36 = (1/2) × 8 × d₂
36 = 4 × d₂
d₂ = 36/4
d₂ = 9 cm

১৪,৫২৪.

If sec²θ + tan²θ = 5/3, then what is the value of tan2θ?

ক
2√3
খ
√3
গ
1/√3
ঘ
Cannot be determined

ব্যাখ্যা

Question: If sec²θ + tan²θ = 5/3, then what is the value of tan2θ?

Solution:
We know that,
sec²θ = 1 + tan²θ

Given that,
sec²θ + tan²θ = 5/3
⇒ 1 + tan²θ + tan²θ = 5/3
⇒ 2tan²θ = 5/3 - 1
⇒ 2tan²θ = 2/3
⇒ tan²θ = 1/3
⇒ tanθ = 1/√3
∴ θ = 30°

Now,
tan2θ = tan(2 × 30°) = tan60° = √3

১৪,৫২৫.

A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

ক
X gains Tk. 4250
খ
X loses Tk. 2750
গ
X loses Tk. 3740
ঘ
X gains Tk. 3150
ঙ
None

ব্যাখ্যা

Question: A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

Solution:
Here,

Money spent by X = Tk. 150000

Money received by X = 105% of Tk. 150000 = Tk. 157500

Cost Price to X = 98% of Tk. 157500 = Tk. 154350

∴ X gains = Tk. (157500 - 154350) = Tk. 3150

১৪,৫২৬.

The difference of the two numbers is 20% of the large number, if the smaller number is 20, then the larger number is-

ক
22
খ
25
গ
30
ঘ
45

ব্যাখ্যা

Question: The difference of the two numbers is 20% of the large number, if the smaller number is 20, then the larger number is-

Solution:
Let the large number be x.
Then,
x - 20 = 20% of x = 20x/100 = x/5
⇒ x - x/5 = 20
⇒ 5x - x = 100
⇒ 4x = 100
∴ x = 25

১৪,৫২৭.

If a biker rides at 70 km/hr instead of 50 km/hr, he would have ride 100 km more. The actual distance travelled by biker is:

ক
250 km
খ
225 km
গ
200 km
ঘ
175 km

ব্যাখ্যা

Question: If a biker rides at 70 km/hr instead of 50 km/hr, he would have ride 100 km more. The actual distance travelled by biker is:

Solution:
Let,
the actual distance travelled be x km.

Then,
x/50 = (x + 100)/70
⇒ x/5 = (x + 100)/7
⇒ 7x = 5x + 500
⇒ 7x - 5x = 500
⇒ 2x = 500
⇒ x = 500/2
∴ x = 250 km

১৪,৫২৮.

Three pipes A, B and C can fill a tank in 8 hours. After working together for 2 hours B is closed and then A and C can fill in the remaining part in 8 hours. The number of hours taken by B alone to fill the cistern, is:

ক
ক) 30 hours
খ
খ) 32 hours
গ
গ) 60 hours
ঘ
ঘ) 24 hours

ব্যাখ্যা

Question: Three pipes A, B and C can fill a tank in 8 hours. After working together for 2 hours, B is closed and then A and C can fill in the remaining part in 8 hours. The number of hours taken by B alone to fill the cistern, is:

Solution:
(A + B + C )'s 1 hour's work = 1/8 parts.

Part filled in 2 hours = 2/8 = 1/4 part.
Remaining part = 1- (1/4) = 3/4

Now,
(A + C)'s 8 hour's work = 3/4
∴ (A + C)'s 1 hour's work = 3/(4 × 8) = 3/32

∴ B's 1 hour's work = (1/8) - (3/32) parts [ এখানে (A + B + C ) - (A + C) বিয়োগ করে ]
= (4 - 3)/32
= 1/32 parts

1/32 parts work B can alone fill the tank in 1 hour
∴ 1 part work B can alone fill the tank in 1× (32/1) hours
= 32 hours

∴ B can alone fill the tank in 32 hours

১৪,৫২৯.

The distance between two parallel tangents of a circle is 20 cm, then the radius of the circle is-

ক
5 cm
খ
8 cm
গ
10 cm
ঘ
12 cm

ব্যাখ্যা

Question: The distance between two parallel tangents of a circle is 20 cm, then the radius of the circle is-

Solution:
Distance between two parallel tangents = 20 cm
That means, diameter = 20 cm
Therefore, the radius of the circle = 20/2
= 10 cm

১৪,৫৩০.

Which of the following inequalities is equivalent to 10 - 2x > 18?

ক
x > - 4
খ
x > 4
গ
x < 4
ঘ
x < - 4

ব্যাখ্যা

Question: Which of the following inequalities is equivalent to 10 - 2x > 18?

Solution:
10 - 2x > 18
⇒ - 2x > 18 - 10
⇒ - 2x > 8
⇒ - x > 4
∴ x < - 4

১৪,৫৩১.

How many prime numbers are there between 70 and 80?

ক
2
খ
5
গ
3
ঘ
4

ব্যাখ্যা

Question: How many prime numbers are there between 70 and 80?

Solution:
যে সংখ্যা ১ এবং সেই সংখ্যা ছাড়া অন্য কোনো সংখ্যা দ্বারা বিভাজ্য নয়, তাকে মৌলিক সংখ্যা বলে।

৭০ থেকে ৮০ এর মধ্যে সংখ্যাগুলো হলো:
৭১, ৭২, ৭৩, ৭৪, ৭৫, ৭৬, ৭৭, ৭৮, ৭৯

এদের মধ্যে মৌলিক সংখ্যা:
৭১, ৭৩, ৭৯

অতএব, মোট মৌলিক সংখ্যা = ৩টি

১৪,৫৩২.

If n is integer, then which of the following must be even?

ক
ক) n - 1
খ
খ) n + 1
গ
গ) 3n + 1
ঘ
ঘ) 2n + 2

ব্যাখ্যা

Question: If n is integer, then which of the following must be even?

Solution:
2n + 2
= 2 (n + 1)

একটি সংখ্যাকে ২ দ্বারা গুণ করলে, তা অবশ্যই জোড় সংখ্যা হবে।

n - 1, n + 1, 3n + 1; n এর বিভিন্ন মানের জন্য জোড় বা বিজোড় উভয়ই হতে পারে।

১৪,৫৩৩.

A thief is stopped by a policeman from a distance of 400 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 5 km/h and that of policeman as 9 km/h, how far the thief would have run, before he is over taken by the policeman?

ক
400 m
খ
450 m
গ
500 m
ঘ
535 m

ব্যাখ্যা

Question: A thief is stopped by a policeman from a distance of 400 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 5 km/h and that of policeman as 9 km/h, how far the thief would have run, before he is over taken by the policeman?

Solution:
Distance between thief and policeman = 400 metre
Relative speed of policeman with respect to thief
= (9 - 5) kmph = 4 kmph
= (4 × 5)/18 m./sec.
= 10/9 m./sec.

Now, Time taken in overtaking the thief = 400/(10/9) second
= (400 × 9)/10 second
= 360 s

∴ Distance covered by thief = Speed × Time
= {5 × 5 × (360/18)} m
= 500 m

১৪,৫৩৪.

The product of two positive numbers is p. If each of the number is increased by 2, the new product is how much greater than twice the sum of the two original number?

ক
ক) p times
খ
খ) 2p times
গ
গ) (p + 4) times
ঘ
ঘ) (2p + 3) times

ব্যাখ্যা

Question: The product of two positive numbers is p. If each of the number is increased by 2, the new product is how much greater than twice the sum of the two original number?

Solution:
let the two positive integers are x and y
so,
xy = p

hence,
(x + 2)(y + 2) - 2(x + y)
= xy + 2y + 2x + 4 - 2x - 2y
= xy + 4
= p + 4

১৪,৫৩৫.

If √a = √3 - √5 then the value of a² - 16a + 6 is?

ক
1
খ
2
গ
3
ঘ
4

ব্যাখ্যা

Question: If √a = √3 - √5 then the value of a² - 16a + 6 is?

Solution:
√a = √3 - √5
⇒ a = 3 + 5 - 2.√3.√5 (Squaring both sides)
⇒ a = 8 - 2√15
⇒ a - 8 = - 2√15
⇒ a²+ 64 - 16a = 60 (Squaring both sides)
⇒ a²+ 4 - 16a = 0
⇒ a² + 6 - 16a = 2
∴ a²- 16a + 6 = 2

১৪,৫৩৬.

If two-third of one-fourth of a number is 14, then three seventh of that number is?

ক
84
খ
72
গ
36
ঘ
24

ব্যাখ্যা

Question: If two-third of one-fourth of a number is 14, then three seventh of that number is?

Solution:

১৪,৫৩৭.

Radha’s salary is 50% more than Seeta’s salary. Radha got a raise of 40% on her salary while Seeta got a raise of 30% on her salary. By what percent is Radha’s salary more than Seeta’s?

ক
65.5%
খ
63.33%
গ
61.53%
ঘ
60.53%

ব্যাখ্যা

Question: Radha’s salary is 50% more than Seeta’s salary. Radha got a raise of 40% on her salary while Seeta got a raise of 30% on her salary. By what percent is Radha’s salary more than Seeta’s?

Solution:
Let Seeta’s salary = Tk. 100
Then Radha’s salary = 100 × 50% + 100 = 150

Radha got a raise of 40% then 150 × 40% + 150 = 210
Seeta got a raise of 30% then 100 × 30% + 100 = 130

Now Radha salary more than Seeta salary by 210 - 130 = 80
Percent = (80/130) × 100 = 61.53%

১৪,৫৩৮.

If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is-

ক
50°
খ
60°
গ
70°
ঘ
80°
ঙ
90°

ব্যাখ্যা

Question: If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is-

Solution:
Since, ΔABC and ΔPQR are similar triangles.
then, ∠B = ∠Q = 83°
Thus, in ΔABC,
∠C = 180° - (∠A + ∠ B)
⇒ ∠C = 180° - (47° + 83°)
∴ ∠C = 50°

১৪,৫৩৯.

Find the smallest 5-digit number that is exactly divisible by 24, 36, and 60

ক
10080
খ
99980
গ
10980
ঘ
99720

ব্যাখ্যা

Question: Find the smallest 5-digit number that is exactly divisible by 24, 36, and 60

Solution:
Required smallest number must be divisible by the L.C.M. of 24, 36, and 60
L.C.M. of 24, 36, and 60
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
60 = 2 × 2 × 3 × 5

L.C.M. = 2 × 2 × 2 × 3 × 3 × 5
= 360

Now divide 10000 by 360 we get,
10000 ÷ 360 = 27.78

Take the ceiling of 27.78, which is 28
we get,
28 × 360 = 10080
10080 is the smallest 5-digit number which is divisible by 24, 36, and 60.

১৪,৫৪০.

A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:

ক
ক) 12 minutes
খ
খ) 18 minutes
গ
গ) 24 minutes
ঘ
ঘ) 16 minutes

ব্যাখ্যা

Question: A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:

Solution:
Ratio of the speed of A, B and C = 6 : 3 : 1
Then, ratio of time taken;
= 1/6 : 1/3 : 1 = 1 : 2 : 6

Hence, time taken by A = 72/6
= 12 minutes.

১৪,৫৪১.

If the average of two numbers is M and the larger number is L, what is the other number?

ক
M - L
খ
L - M
গ
2M - L
ঘ
L - 2M
ঙ
None of these

ব্যাখ্যা

Question: If the average of two numbers is M and the larger number is L, what is the other number?

Solution:
The average of two numbers is M
∴ The total of two numbers is 2M

The larger number is L
∴ The other number is 2M - L

১৪,৫৪২.

A person spends Tk. 8625 in buying some tables at Tk. 875 each and some chairs at Tk.125 each. The ratio of number of chairs to that of tables when the maximum number of tables is purchased -

ক
ক) 1 : 4
খ
খ) 2 : 3
গ
গ) 3 : 5
ঘ
ঘ) 4 : 3

ব্যাখ্যা

Question: A person spends Tk. 8625 in buying some tables at Tk. 875 each and some chairs at Tk.125 each. The ratio of number of chairs to that of tables when the maximum number of tables is purchased -

Solution:
Maximum possible number of tables = 9 [875 × 9 = 7875]
Number of chairs purchased = (8625 - 7875)/125 = 6

Hence, required ratio = 6 : 9 = 2 : 3

১৪,৫৪৩.

Two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 33 seconds. The ratio of their speeds is:

ক
ক) 3 : 2
খ
খ) 3 : 1
গ
গ) 4 : 3
ঘ
ঘ) 5 : 4

ব্যাখ্যা

Question: Two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 33 seconds. The ratio of their speeds is:

Solution:
Let,
The speed of the 1st train be x m/sec
The speed of the 2nd train be y m/sec

∴ Length of the 1st train = 37x metres
∴ Length of the 2nd train = 27y metres

ATQ,
(37x + 27y)/(x + y) = 33 [ time = distance/speed]
⇒ 37x + 27y = 33x + 33y
⇒ 37x - 33x = 33y - 27y
⇒ 4x = 6y
⇒ 2x = 3y
⇒ x/y = 3/2
∴ x : y = 3 : 2

১৪,৫৪৪.

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

ক
4/17
খ
5/18
গ
5/21
ঘ
None of the above

ব্যাখ্যা

Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

Solution:
Number of ways of (selecting at least two couples among five people selected) =⁵C₂ × ⁶C₁
As remaining person can be any one among three couples left.
∴ Required probability = (⁵C₂ × ⁶C¹)/¹⁰C₅
= (10 × 6)/252
= 60/252
= 5/21

১৪,৫৪৫.

The difference between the present age of Rifat and Rakib is 14 years. Seven years ago, the ratio of their ages was 5 : 7 respectively. What is Rakib's present age?

ক
49 years
খ
47 years
গ
42 years
ঘ
56 years

ব্যাখ্যা

Question: The difference between the present age of Rifat and Rakib is 14 years. Seven years ago, the ratio of their ages was 5 : 7 respectively. What is Rakib's present age?

Solution:
Let, 7 years ago,
Rifat's age was = 5x
Rakib's age = 7x

ATQ,
7x + 7 - 5x - 7 = 14
2x = 14
x = 7

Rakib's present age = (7 × 7) + 7 = 56 years

১৪,৫৪৬.

How much would I have to pay for a book which cost Tk. 70 to produce, if the printing company sold it to a book seller at 20% profit and the book seller sold it to me at a profit of 25%?

ক
ক) Tk. 90
খ
খ) Tk. 95
গ
গ) Tk. 105
ঘ
ঘ) Tk. 110

ব্যাখ্যা

Question: How much would I have to pay for a book which cost Tk. 70 to produce, if the printing company sold it to a book seller at 20% profit and the book seller sold it to me at a profit of 25%?

Solution:
উৎপাদন খরচ = 70 টাকা

20% লাভে
উৎপাদন খরচ 100 টাকা হলে বিক্রয়মূল্য = 100 + 20 বা 120 টাকা
উৎপাদন খরচ 1 টাকা হলে বিক্রয়মূল্য = 120/100 টাকা
উৎপাদন খরচ 70 টাকা হলে বিক্রয়মূল্য = (120 × 70)/100 টাকা
= 84 টাকা

company এর বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য

খুচরা বিক্রেতার 25% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 100 + 25 বা 125 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য = 125/100 টাকা
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (125 × 84)/100 টাকা
= 105 টাকা

১৪,৫৪৭.

A swimming pool 9 m wide and 12 m long and 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:

ক
140 m³
খ
170 m³
গ
270 m³
ঘ
340 m³

ব্যাখ্যা

Question: A swimming pool 9 m wide and 12 m long and 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is:

Solution:
Given, length width of the swimming pool is 9 m and 12 m respectively.

The volume of the swimming pool
= 9 × 12 × {(1 + 4)/2}
= 9 × 12 × (5/2)
= 270 m³

১৪,৫৪৮.

If (2 + √x) > 2√x, which of the following must be true?

ক
x < 1
খ
x < 2
গ
x < 3
ঘ
x < 4
ঙ
none of these

ব্যাখ্যা

Question: If (2 + √x) > 2√x, which of the following must be true?

Solution:
2 + √x > 2√x
⇒ 2 > 2√x - √x
⇒ 2 > √x
⇒ 4 > x
∴ x < 4

১৪,৫৪৯.

Ruma is as much older than Jui as she is younger than Lima. If the sum of the ages of Jui and Lima is 50 years, and Jui is 20 years old, then what is the difference between Ruma and Jui's age?

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

ব্যাখ্যা

Question: Ruma is as much older than Jui as she is younger than Lima. If the sum of the ages of Jui and Lima is 50 years, and Jui is 20 years old, then what is the difference between Ruma and Jui's age?

Solution:
Given,
Jui's age is 20 years
the sum of the ages of Jui and Lima is 50 years
∴ The age of Lima is = 50 - 20 year
= 30 years

let,
the age of Ruma is x years

ATQ,
x - 20 = 30 - x
⇒ 2x = 50
∴ x = 25

So, the difference between Ruma and Jui's age is = (25 - 20) years
= 5 years

১৪,৫৫০.

The average of x and y is 7, and z = 3x + 2. What is the average of y and z?

ক
ক) 2x + 8
খ
খ) 2x - 8
গ
গ) 2x + 16
ঘ
ঘ) x + 8

ব্যাখ্যা

Question: The average of x and y is 7, and z = 3x + 2. What is the average of y and z?
Solution:
x এবং y এর গড় = 7
x + y = 7 × 2
x + y = 14
y = 14 - x

(y + z)/2 = (14 - x + 3x + 2)/2
= (16 + 2x)/2
= 2(8 + x)/2
= 8 + x

১৪,৫৫১.

A jar contains a mixture of oil and water in the ratio 22: 3. 50 liters of the mixture was taken out and 25 liters of water was added to it. If water was 34% in the resultant mixture, what was the initial quantity of the mixture (in liters) in the jar?

ক
ক) 175
খ
খ) 150
গ
গ) 75
ঘ
ঘ) 125

ব্যাখ্যা

Question: A jar contains a mixture of oil and water in the ratio 22 : 3. 50 liters of the mixture was taken out and 25 liters of water was added to it. If water was 34% in the resultant mixture, what was the initial quantity of the mixture (in liters) in the jar?

Solution:
ধরি
মিশ্রণে তেলের পরিমাণ = 22x লিটার
মিশ্রণে পানির পরিমাণ = 3x লিটার

মিশ্রণে মোট পরিমাণ = 22x + 3x = 25x

50 লিটার মিশ্রণে পানির পরিমাণ = 50 × 3/(22 + 3) = 6 লিটার

প্রশ্নমতে
3x - 6 + 25 = (25x - 50 + 25) × (34/100)
3x + 19 = (25x - 25)× (34/100)
3x + 19 = 17(x - 1)/2
6x + 38 = 17x - 17
6x - 17x = - 17 - 38
- 11x = - 55
x = 5

মিশ্রণের মোট পরিমাণ = 25x = 25 × 5 = 125 লিটার

১৪,৫৫২.

If p and q are positive integers with qp = 36, then p/q cannot be ____

ক
1/4
খ
4/9
গ
1/2
ঘ
None of these

ব্যাখ্যা

Question: If p and q are positive integers with qp = 36, then p/q cannot be ____

Solution:
দেওয়া আছে
qp = 36

36 এর উৎপাদকগুলো হলো: 1, 2, 3, 4, 6, 9, 12, 18, 36

এখন
p/q = 3/12 = 1/4
p/q = 4/9
p/q = 2/18 = 1/9
p/q = 1/36
p/q = 6/6 = 1

p/q = 1/2 কোনভাবেই হতে পারে না।

১৪,৫৫৩.

{2√(27) - √(75) +√(12)} is equal to-

ক
ক) 4√3
খ
খ) √3
গ
গ) 2√3
ঘ
ঘ) 3√3

ব্যাখ্যা

Question: {2√(27) - √(75) +√(12)} is equal to-

Solution:
(2√27- √75+√12)
= √108 - √75 + √12
= √(36 × 3) - √(25 × 3) + √(4 × 3)
= 6√3 - 5√3 + 2√3
= 3√3

১৪,৫৫৪.

A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 854 in 4 years. The sum is-

ক
Tk. 522
খ
Tk. 426
গ
Tk. 336
ঘ
Tk. 322
ঙ
None

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 721)
= Tk. 133

∴ Simple interest for 3 years = Tk.(133 × 3)
= Tk. 399

∴ Sum = (721 - 399)
= Tk. 322

১৪,৫৫৫.

If 10 circles, all with different radii, are positioned in the same plane, what is the maximum possible number of distinct points where 2 or more of the circles intersect?

ক
45
খ
40
গ
90
ঘ
80

ব্যাখ্যা

Question: If 10 circles, all with different radii, are positioned in the same plane, what is the maximum possible number of distinct points where 2 or more of the circles intersect?

Solution:
From 10 circles, the number of pairs that be formed = ¹⁰C₂ = 95
ince each of these 45 pairs may intersect in at most two points, the maximum possible number of intersections = 45 × 2 = 90

১৪,৫৫৬.

The next number in the sequence 8, 13, 21, 34, 55, 89, ____ is -

ক
142
খ
144
গ
148
ঘ
176

ব্যাখ্যা

আমরা জানি,
Fibonacci সংখ্যা = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... পরপর দুটি সংখ্যার যােগফল পরবর্তী সংখ্যার সমান।
সুতরাং, এই ধারার পরবর্তী সংখ্যা হবে = 55 + 89 = 144

১৪,৫৫৭.

How many times is the area of the square constructed on a straight line greater than the area of the square constructed on one-third of that line?

ক
3
খ
6
গ
12
ঘ
9
ঙ
None of these

ব্যাখ্যা

Question: How many times is the area of the square constructed on a straight line greater than the area of the square constructed on one-third of that line?

Solution:
Let the length of the straight line be a units.
∴ Area of the square built on the whole line = a²

And, one-third of the line = a/3
∴ Area of the square built on one-third of the line = (a/3)² = a²/9

∴ Ratio = (square on whole line)/(square on one-third)
= a²/(a²/9)
= a² × (9/a²)
= 9

So the square on the whole line is 9 times the square on one-third of the line.

১৪,৫৫৮.

A train takes 18 seconds to pass completely through a station 162m long and 15 seconds through another station 120m long. The length of the train is-

ক
100 m
খ
90 m
গ
80 m
ঘ
70 m

ব্যাখ্যা

Question: A train takes 18 seconds to pass completely through a station 162m long and 15 seconds through another station 120m long. The length of the train is-

Solution:
ট্রেনটি 18 সেকেন্ডে অতিক্রম করে 162 মিটার + ট্রেনের দৈর্ঘ্য
ট্রেনটি 15 সেকেন্ডে অতিক্রম করে 120 মিটার + ট্রেনের দৈর্ঘ্য
ট্রেনটি 3 সেকেন্ডে অতিক্রম করে = 42 মিটার
ট্রেনটি 1 সেকেন্ডে অতিক্রম করে = 42/3 মিটার
ট্রেনটি 15 সেকেন্ডে অতিক্রম করে = (42 × 15)/3 মিটার
= 210 মিটার

∴ ট্রেনটির দৈর্ঘ্য = (210 - 120) মিটার = 90 মিটার।

১৪,৫৫৯.

There is 24% sugar in the 300 mm mixture. If 300 mm water is added to it, then what percentage of sugar is there in the new mixture?

ক
12%
খ
7.2%
গ
6%
ঘ
10%

ব্যাখ্যা

In 300 mm mixture, amount of sugar = 24% of 300 = 72 mm
If 200 mm water is added to it, total mixture = 300 + 300 = 600 mm
Therefore, amount of sugar percentage = 72/600 × 100% = 12%

১৪,৫৬০.

If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio

ক
3 : 13
খ
36 : 13
গ
13 : 9
ঘ
9 : 13

ব্যাখ্যা

Question: If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio

Solution:
A/B × B/C = 3/4 × 12/13 = 36/52 = 9/13
A : C = 9 : 13

১৪,৫৬১.

ক
secA + tanA
খ
secA - tanA
গ
secA + cotA
ঘ
cosA + tanA

ব্যাখ্যা

Question:

Solution:

১৪,৫৬২.

A boy was asked to multiply a number by 25 but by mistake he multiplied by 45 and the answer was 200 more than the correct answer. What was the number?

ক
7
খ
8
গ
10
ঘ
12

ব্যাখ্যা

Question: A boy was asked to multiply a number by 25 but by mistake he multiplied by 45 and the answer was 200 more than the correct answer. What was the number?

Solution:
Let,
The number be x

ATQ,
45x - 200 = 25x
⇒ 45x - 25x = 200
⇒ 20x = 200
∴ x = 10

১৪,৫৬৩.

In a market survey 20% respondents opted for product A whereas 60% opted for product B, the remaining individuals were not certain. If the difference in number between those who opted for product B and those who were uncertain was 720, how many individuals were covered in the survey ?

ক
ক) 1,440
খ
খ) 1,800
গ
গ) 3,600
ঘ
ঘ) None

ব্যাখ্যা

Question: In a market survey 20% respondents opted for product A whereas 60% opted for product B, the remaining individuals were not certain. If the difference in number between those who opted for product B and those who were uncertain was 720, how many individuals were covered in the survey?

Solution:
Percentage of uncertain individuals
=[100 - (20 + 60)]%
= 20%

Now
60% of x - 20% of x = 720
40% of x = 720
40x/100 = 720
40x = 720 × 100
x = (720 × 100)/40
x = 1800

১৪,৫৬৪.

What is the H.C.F. of 9/20, 15/28, and 21/35?

ক
2/75
খ
1/28
গ
3/140
ঘ
6/35

ব্যাখ্যা

Question: What is the H.C.F. of 9/20, 15/28, and 21/35?

Solution:
We know, H.C.F. of fractions = (H.C.F. of numerators) / (L.C.M. of denominators)
H.C.F of numerators: H.C.F of 9, 15 and 21
9 = 3 × 3
15 = 3 × 5
21 = 3 × 7
H.C.F = 3

L.C.M of denominators: L.C.M of 20, 28 and 35
20 = 2² × 5
28 = 2² × 7
35 = 5 × 7
L.C.M = 2² × 5 × 7 = 140

∴ Required H.C.F. = 3/140

১৪,৫৬৫.

The ratio of the present ages of two friends is 3 : 5. After 7 years, the ratio becomes 2 : 3. What will be the ratio of their ages after 10 years?

ক
31 : 45
খ
15 : 22
গ
29 : 43
ঘ
None of these

ব্যাখ্যা

Question: The ratio of the present ages of two friends is 3 : 5. After 7 years, the ratio becomes 2 : 3. What will be the ratio of their ages after 10 years?

Solution:
Let
The present age of the friend₁ = 3x
The present age of the friend₂ = 5x

After 7 years, their ages will be,
⇒ (3x + 7)/(5x + 7) = 2/3
⇒ 10x + 14 = 9x + 21
⇒ 10x - 9x = 21 - 14
∴ x = 7

Present age of friend₁= 3x = 21 years
Present age of friend₂= 5x = 35 years

Now, after 10 years,
friend₁ age = 21 + 10 = 31 years
friend₂ age = 35 + 10 = 45 years

∴ The ratio of their ages after 10 years,
= 31 : 45

১৪,৫৬৬.

The ratio between the ages of Nila and Shila is 5 : 6 respectively. If the ratio between the one-third age of Nila and half of Shila's age is 5 : 9, then what is Shila's age = ?

ক
ক) 25 years
খ
খ) 30 years
গ
গ) 36 years
ঘ
ঘ) Cannot be determined
ঙ
ঙ) None of these

ব্যাখ্যা

Let Nila's age be 5x years and
Shila's age be 6x years

((1/3)×5x):((1/2)×6x) = 5:9
⇒ 5x/(3×3x) = 5/9

Thus, Shila's age cannot be determined

১৪,৫৬৭.

By selling an article for Tk 2800, a seller gains 12%. If the profit is reduced to 10% then the selling price will be -

ক
ক) 2600
খ
খ) 2650
গ
গ) 2700
ঘ
ঘ) 2750

ব্যাখ্যা

Question: By selling an article for Tk 2800, a seller gains 12%. If the profit is reduced to 10% then the selling price will be -

Solution:
let, the cost price = x

now,
112% of x = Tk 2800
∴ 1% of x = Tk 2800/112
∴ 110% of x = Tk (2800 × 110)/112
= Tk 2750

১৪,৫৬৮.

In an exam, the average marks for 80 students of Class V is 35. The average of marks in section A of the class is 55 while the average of marks in section B is 30. Find the number of students in Class V B.

ক
45
খ
50
গ
64
ঘ
70

ব্যাখ্যা

Total students i.e. Section A + Section B = 80
Section A = 80 - Section B = 80 - B

∴ 80 x 35 = B x 30 + (80 - B) x 55
⇒ 2800 = 30B + 4400 - 55B
⇒ 1600 = 25 B
⇒ B = 64

∴ B = 64 = Number of students in Class V B.

১৪,৫৬৯.

ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

ক
12
খ
9
গ
12√2
ঘ
18

ব্যাখ্যা

Question: ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

Solution:
চিত্রানুসারে, O হলো বৃত্তের কেন্দ্র এবং OA ও OB হলো বৃত্তের ব্যাসার্ধ, যার দৈর্ঘ্য 3।
AOB একটি সমকোণী ত্রিভুজ, যেখানে ∠AOB = 90° এবং অতিভুজ = AB

পিথাগোরাসের উপপাদ্য অনুসারে,
AB² = OA² + OB²
AB² = 3² + 3²
AB² = 9 + 9
AB² = 18

আমরা জানি, বর্গক্ষেত্রের ক্ষেত্রফল = বাহুর দৈর্ঘ্য^২
যেহেতু ABCD একটি বর্গ, তাই এর ক্ষেত্রফল হলো AB²
সুতরাং, বর্গটির ক্ষেত্রফল হলো 18

১৪,৫৭০.

The ratio of two numbers is 2 : 3. The sum of the numbers is 100. The difference between the two numbers is:

ক
ক) 15
খ
খ) 40
গ
গ) 25
ঘ
ঘ) 20

ব্যাখ্যা

ধরি,
ছোট সংখ্যাটি 2x
বড় সংখ্যাটি 3x

প্রশ্নমতে,
2x + 3x = 100
5x = 100
x = 100/5
x = 20

ছোট সংখ্যাটি 2x = 2 × 20 = 40
বড় সংখ্যাটি 3x = 3 × 20 = 60

সংখ্যা দুইটির পার্থক্য 60 - 40 = 20

১৪,৫৭১.

How much sugar, costing Tk. 95 per kg, should be mixed with 17 kg of tea priced at Tk. 200 per kg to get a blend worth Tk. 130 per kg?

ক
34 kg
খ
30 kg
গ
28 kg
ঘ
26 kg
ঙ
None of the above

ব্যাখ্যা

Question: How much sugar, costing Tk. 95 per kg, should be mixed with 17 kg of tea priced at Tk. 200 per kg to get a blend worth Tk. 130 per kg?

Solution:
Ratio in which tea and sugar should be mixed
= 200 - 130 : 130 - 95
= 70 : 35
= 10 : 5
= 2 : 1

Let x be the quantity at 95/kg.

∴ 2 : 1 = x : 17
⇒ 2/1 = x/17
⇒ x = 34

Hence x = 34 kg.

১৪,৫৭২.

If A's income is 25% less than that of B, then how much percent is B's income more than that of A?

ক
33.33%
খ
35%
গ
25%
ঘ
30.33%

ব্যাখ্যা

Question: If A's income is 25% less than that of B, then how much percent is B's income more than that of A?

Solution:
Let B's income 100
So, A’s income = 75
So, B’s income more than A in % = (25×100)/75
= 100/3
= 33.33%

১৪,৫৭৩.

A certain sum amounts to Tk. 7350 in 2 years and to Tk. 8575 in 3 years. Find the sum and rate percent :

ক
5400 Tk
খ
6800 Tk
গ
5600 Tk
ঘ
7200 Tk

ব্যাখ্যা

Interest for 1 year is the same whether it's simple interest or compound interest.
Now interest of third-year = 8575 - 7350 = 1225;
means principal for this interest is 7350 if compound interest is taken 7350 is the principal interest = 1225

if 100 is the principal interest = (1225/7350) × 100 = 50/3%
When a thing increases for two successive times the overall increase on initial amount = a + b + (a × b)/100

Therefore overall interest for two years = 50/3 + 50/3 + [(50/3) × (50/3)]/100 = 325/9 %
Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount principal =100
if 7350 is the amount principal =(900/1225) × 7350 =5400

So sum = 5400

১৪,৫৭৪.

The cost of cultivating a square field at the rate of Tk. 685 per hectare is Tk. 6165. The cost of putting a fence around it at the rate of Tk. 48.75 per meter would be -

ক
Tk. 23400
খ
Tk. 52650
গ
Tk. 58500
ঘ
Tk. 117000

ব্যাখ্যা

Question: The cost of cultivating a square field at the rate of Tk. 685 per hectare is Tk. 6165. The cost of putting a fence around it at the rate of Tk. 48.75 per meter would be -

Solution:
Area of the field = 6165/685 hectare
= 9 hectare
= (9 × 10000) m²
= 90000 m²

∴ Side of the field = √90000 m
= 300 m

Perimeter of the field = (300 × 4) m
= 1200 m.

Cost of fencing = Tk. (1200 × 48.75)
= Tk. 58500

১৪,৫৭৫.

The current of a stream runs at the rate of 2 km per hr. A motorboat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motorboat -

ক
ক) 16 km/hr
খ
খ) 20 km/hr
গ
গ) 12 km/hr
ঘ
ঘ) 22 km/hr

ব্যাখ্যা

Let the speed of the boat in still water=x km/hr
Speed of the current = 2 km/hr
Then, speed downstream = (x + 2) km/hr
speed upstream = (x - 2) km/hr
Total time taken to travel 10 km upstream and back = 55 minutes
= (55/60) hr
= 11/12 hr.
According to question,
10/(x - 2) + 10/(x + 2) = 11/12
⇒ 120(x+2)+120(x−2) = 11(x² - 4)
⇒ 240x = 11x² - 44
⇒ 11x² - 240x - 44 = 0
⇒ 11x(x -22) + 2(x - 22) = 0
⇒ (x -22) (11x + 2) = 0
Since x cannot be negative.
So, x = 22 km/hr.
Hence, the Speed of the motorboat is 22 km/hr.

১৪,৫৭৬.

With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. Find the length of the total journey?

ক
70 kms
খ
60 kms
গ
45 kms
ঘ
30 kms

ব্যাখ্যা

Question: With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. Find the length of the total journey?

Solution:
Let the time taken by train be 't' hrs.
Then,
40t = 35(t + 15/60)
⇒ 40t = 35t + 35/4
∴ t = 7/4 hrs

Therefore, Required length of the total journey d = v × t
= 40 × 7/4
= 70 kms.

১৪,৫৭৭.

Find the greatest possible distance, which can be used to measure the distances 5 m, 3 m, 12 cm, 9 m and 76 cm exactly.

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

ব্যাখ্যা

প্রশ্ন : Find the greatest possible distance, which can be used to measure the distances 5 m, 3 m, 12 cm, 9 m and 76 cm exactly.
সমাধান :
The greatest possible distance which can measure 5 m, 3 m, 12 cm, 9 m and 76 cm = HCF of (5 m, 3 m, 12 cm, 9 m and 76 cm)

⇒ HCF of (500 cm, 300 Cm, 12 cm, 900 cm and 76 cm)
500 cm = 4 × 5 × 5 × 5
300 cm = 3 × 4 × 5 × 5
12 cm = 3 × 4
900 cm = 3 × 3 × 4 × 5 × 5
76 cm = 4 × 19

The required HCF = 4 cm

∴ The greatest possible distance is 4 cm.

১৪,৫৭৮.

The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

ক
ক) 8 : 7
খ
খ) 7 : 6
গ
গ) 9 : 8
ঘ
ঘ) 3 : 4

ব্যাখ্যা

Question: The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

Solution:
A এর বয়স = 44 × (6/11) বছর = 24 বছর
B এর বয়স = (44 - 24) বছর = 20 বছর
8 বছর পর তাদের বয়সের অনুপাত = (24 + 8)/(20 + 8)
= 32/28
= 8/7
= 8 : 7

১৪,৫৭৯.

What will be simple interest for 1 year and 4 months on a sum of Tk. 25,800 at the rate of 14% per annum?

ক
ক) Tk. 4,816
খ
খ) Tk. 2,580
গ
গ) Tk. 4,815
ঘ
ঘ) None of these

ব্যাখ্যা

এখানে,
আসল P = 25,800 টাকা
সুদের হার r = 14%
সময় n = 1 বছর 4 মাস = 1 + 1/3 =4/3 বছর
মুনাফা I = ?

আমরা জানি
I = Pnr
= 25800 × (4/3) × (14/100)
= 4,816

১৪,৫৮০.

Two numbers are in the ratio 4 : 5 and their greatest common divisor (GCD) is 14. Find their least common multiple (LCM).

ক
280
খ
196
গ
320
ঘ
224

ব্যাখ্যা

Question: Two numbers are in the ratio 4 : 5 and their greatest common divisor (GCD) is 14. Find their least common multiple (LCM).

Solution:
Let the two numbers are,
First number = 4k
Second number = 5k
Since the numbers are in the ratio 4 : 5, and 4 and 5 are co-prime gcd(4,5) = 1,
the HCF of the two numbers is exactly k.

Given that, HCF = 14
Therefore, k = 14

So the actual numbers are:
First number = 4 × 14 = 56
Second number = 5 × 14 = 70

We know,
HCF × LCM = Product of the two numbers
⇒ 14 × LCM = 56 × 70
⇒ LCM = (56 × 70)/14
∴ LCM = 4 × 70 = 280

So the least common multiple (LCM) of the two numbers is 280.

১৪,৫৮১.

ক
98
খ
35
গ
350
ঘ
None

ব্যাখ্যা

Question:

Solution:

১৪,৫৮২.

Nirob cuts a 4 cm cube into 1 cm cubes. What is the percentage increase in the surface area after cutting?

ক
200%
খ
250%
গ
300%
ঘ
340%

ব্যাখ্যা

Question: Nirob cuts a 4 cm cube into 1 cm cubes. What is the percentage increase in the surface area after cutting?

Solution:
শুরুতে পৃষ্ঠতলের ক্ষেত্রফল = 6 × 4²
= 6 × 16
= 96

ধরি, n সংখ্যক ঘনক তৈরি করা হলো।
n 1³ = 4³
n = 64

64 টি ঘনকের প্রত্যেকটির পৃষ্ঠতলের ক্ষেত্রফল = 6 × 1²
= 6 cm²

মোট পৃষ্ঠতলের ক্ষেত্রফল = 64 × 6
= 384 cm²

বৃদ্ধি = 384 - 96
= 288 cm²

∴ শতকরা বৃদ্ধি = (288/96) × 100%
= 300%

১৪,৫৮৩.

If 7¹²⁶ is divided by 48, find the reminder.

ক
ক) 7
খ
খ) 1
গ
গ) 39
ঘ
ঘ) 3

ব্যাখ্যা

Question: If 7¹²⁶ is divided by 48, find the reminder.

Solution:
7¹²⁶ = (7²)⁶³ = 49⁶³
we know that, (xⁿ - aⁿ) is divisible by (x - a) for all values of n.
so,
(49⁶³ - 1) is divisible by (49 - 1) or, 48.

∴ remainder when divided by 48 is 1

১৪,৫৮৪.

A cyclist moving on a circular track of radius 100 meters completes one revolution in 2 minutes. What is the average speed of a cyclist (approx.)?

ক
ক) 314 m/min
খ
খ) 200 m/min
গ
গ) 300 m/min
ঘ
ঘ) 900 m/min
ঙ
ঙ) 500 m/min

১৪,৫৮৫.

There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?

ক
55
খ
60
গ
25
ঘ
192

ব্যাখ্যা

Since, no order to the committee is mentioned, a combination instead of a permutation is used.
Let's sort out what we have and what we want.
Have: 5 women, 6 men.
Want: 3 women AND 1 man.
The word AND means multiply.
Woman and Men

⁵C₃× ⁶C₁
= 5!/(2! × 3!) × 6!/(5! × 1!)
= (5 × 2) × 6
= 60.

১৪,৫৮৬.

How many different ways can the letters of the word “BALLOON” be arranged?

ক
1320
খ
1260
গ
1180
ঘ
1050

ব্যাখ্যা

Question: How many different ways can the letters of the word “BALLOON” be arranged?

Solution:
The given word contains 7 letters, where L and O is taken 2 times.

∴ Required number of ways = 7!/(2! × 2!)
= 5040/4
= 1260

∴ 1260 distinct arrangements

১৪,৫৮৭.

From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is-

ক
120 m
খ
120√2 m
গ
200 m
ঘ
100√3 m

ব্যাখ্যা

Question: From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is-

Solution:

Given that,
Hight of tower, AB = 100 m
Angle of elevation from point P, ∠APB = 30°

We know,
tanθ = opposite/adjacent = AB/PA
⇒ tan30° = 100/PA
⇒ 1/√3 = 100/PA
∴ PA = 100√3 m

Thus, the distance from point P to the foot of the tower is 100√3 m.

১৪,৫৮৮.

If 9³ × 81² ÷ 27³ = 3^x then, what is the value of x?

ক
4
খ
5
গ
6
ঘ
3

ব্যাখ্যা

Question: If 9³ × 81² ÷ 27³ = 3^x then, what is the value of x?

Solution:
Given,
9³ × 81² ÷ 27³ = 3^x
⇒ 3^x = (3²)³ × (3⁴)² ÷ (3³)³
⇒ 3^x = 3⁶ × 3⁸ ÷ 3⁹
⇒ 3^x = 3⁽^{6 + 8 - 9)}
⇒ 3^x = 3⁵
∴ x = 5

১৪,৫৮৯.

How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

ক
36 Kg
খ
42 Kg
গ
54 Kg
ঘ
63 Kg

ব্যাখ্যা

Question: How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

Solution:
By the rule of alligation:
C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind

Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then,
7 : 3 = x : 27
or x = (7 × 27)/3 = 63 kg.

১৪,৫৯০.

If a computer does five calculations in a nanosecond then how many calculations does it do in a second?

ক
20 million
খ
25 million
গ
20 billion
ঘ
5 billion
ঙ
15 billion

ব্যাখ্যা

We know, 1 nanosecond = 10^-9 seconds
then,
5/(10^-9) = x/1
x = 5 × 10⁹
x = 5,000,000,000
x = 5 billion

১৪,৫৯১.

Sawpon buys a car at 20% discount of the price and sells it at 20% higher price. His percentage gain is-

ক
ক) 40%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 50%

ব্যাখ্যা

Question: Sawpon buys a car at 20% discount of the price and sells it at 20% higher price. His percentage gain is-

Solution:
Let
The value of the car (M.P.) = Tk. 100
Then, C.P. = 80% of 100= Tk. 80
S.P. =120% of 100= Tk. 120
Profit = (120 - 80) Tk.

∴ Profit % = (40/80) × 100 = 50%

The profit percentage is 50%.

১৪,৫৯২.

If w is 20% less than m, and n is 20% less than z, than wn is what percent less than mz ?

ক
ক) 37%
খ
খ) 36%
গ
গ) 20%
ঘ
ঘ) 40%

ব্যাখ্যা

ধরি,
m = 100
w = 100 - 100 এর 20% = 100 - 20 = 80
আবার,
z = 100
n = 100 - 100 এর 30% = 100 - 20 = 80

wn = 80 × 80 = 6400
mz = 100 × 100 = 10000

wn , mz এর চেয়ে কম = 10000 - 6400 = 3600
wn , mz এর চেয়ে শতকরা কম ={(3600/10000) × 100}% = 36%

১৪,৫৯৩.

If (x + 3)² = 225, Which of the following can be the value of (x + 1)?

ক
11
খ
13
গ
15
ঘ
16

ব্যাখ্যা

Question: If (x + 3)² = 225, Which of the following can be the value of (x + 1)?

Solution:
Given,
(x + 3)² = 225
⇒ (x + 3)² = (15)²
∴ x + 3 = ± 15

When, x + 3 = 15
⇒ x = 15 - 3
∴ x = 12

∴ x + 1 = 12 + 1 = 13

১৪,৫৯৪.

The average weight of 18 boys was recorded as 60 kg. If the weight of the teacher was added, the average increased by 2 kg. What was the teacher's weight?

ক
75
খ
86
গ
98
ঘ
105

ব্যাখ্যা

Question: The average weight of 18 boys was recorded as 60 kg. If the weight of the teacher was added, the average increased by 2 kg. What was the teacher's weight?

Solution:
Average weights of 18 boys = 60 kg
Total weights of 18 boys = 18 × 60 kg = 1080 kg

The weight of the teacher was added then average increase by 2 kg
So, new average weight is 62 kg
Total people including teacher = 19

∴ total weight including teacher
= 62 × 19 kg
= 1178 kg

∴ Weight of teacher = 1178 – 1080 = 98 kg

১৪,৫৯৫.

Asad went to the market to buy 12 oranges. But he found that he had the money to buy only 10 oranges. He calculated that if the price per piece of orange was tk. 3 less, he could have bought 12 oranges. How much did Asad have?

ক
ক) 150
খ
খ) 160
গ
গ) 175
ঘ
ঘ) 180

ব্যাখ্যা

Let, Asad have X taka
ATQ,
X/10 - X/12 = 3
⇒ 6X - 5X = 60×3
⇒ X = 180

১৪,৫৯৬.

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

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

ব্যাখ্যা

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

১৪,৫৯৭.

A is travelling at 54 km per hour on a highway while B is traveling at a speed of 20 meters per second. what is the difference in their speeds in meters per second?

ক
ক) 3 m/sec
খ
খ) 4 m/sec
গ
গ) 5 m/sec
ঘ
ঘ) 10 m/sec

ব্যাখ্যা

A's speed :
= 54 km/hr.
= (54 × 1000)/3600
= 15 m/sec

B's speed = 20 m/sec
Difference :
= (20 - 15) m/sec
= 5 m/sec

১৪,৫৯৮.

A train takes 50 seconds to cross the 204 m long bridge. If the same train takes 20 seconds to cross a board, then tell the length of the train. (In meters)

ক
ক) 136 m
খ
খ) 106 m
গ
গ) 126 m
ঘ
ঘ) 146 m

ব্যাখ্যা

Let the length of the train be x m.
Length of the bridge = 204 m

Now
⇒ (x + 204)/50 = x/20
(x + 204)/5 = x/2
⇒ 2x + 408 = 5x
5x - 2x = 408
3x = 408
x = 136

∴ Length of the train is 136 m

১৪,৫৯৯.

Five people want to rent the last two copies of a movie. How many ways can these five people rent the two movies?

ক
ক) 10
খ
খ) 9
গ
গ) 8
ঘ
ঘ) 7

ব্যাখ্যা

Question: Five people want to rent the last two copies of a movie. How many ways can these five people rent the two movies?
Solution:
5 জন লোক 2টি মুভি ভাড়া নিতে পারে = ⁵C₂ = 10

১৪,৬০০.

The number of parallellograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is -

ক
ক) 6
খ
খ) 9
গ
গ) 12
ঘ
ঘ) 18

ব্যাখ্যা

আমরা দেখতে পাচ্ছি যে চারটি পরস্পর সমান্তরাল রেখাকে তিনটি পরস্পর সমান্তরাল রেখা ছেদ করলে মোট আয়তক্ষেত্রের সংখ্যা হবেঃ
6 + 5 + 4 + 3 + 2 + 2 + 1 = 18