Bank Math

PrepBank · পাতা ৬৬ / ১৬১ · ৬,৫০১–৬,৬০০ / ১৬,১২৪

৬,৫০১.

The ratio of total surface area to curved surface area of a cone whose radius is 7cm and height 24 cm, is -

ক
25 : 32
খ
24 : 25
গ
32 : 25
ঘ
35 : 25

ব্যাখ্যা

Question: The ratio of total surface area to curved surface area of a cone whose radius is 7cm and height 24 cm, is -

Solution:
the slant height of the cone is l = √(r² + h²)
l = √(7² + 24²)
l = 25
Total surface area : curved surface area
= (πrl + πr²) : πrl
= (l + r) : l
= (25 + 7) : 25
= 32 : 25

৬,৫০২.

A student's marks were wrongly entered as 75 instead of 55. Due to this mistake, the average marks for the class increased by 0.25. Find the number of students in the class.

ক
40
খ
80
গ
50
ঘ
60

ব্যাখ্যা

Question: A student's marks were wrongly entered as 75 instead of 55. Due to this mistake, the average marks for the class increased by 0.25. Find the number of students in the class.

Solution:
Let the number of students in the class be x.
Total increase in marks = x × 0.25 = x/4

According to the question
⇒ x/4 = (75 - 55)
⇒ x/4 = 20
⇒ x = 80.

∴The total number of students in the class is 80.

৬,৫০৩.

(3a + 5b)/(3a - 5b) = 5 then a : b is equal to?

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

ব্যাখ্যা

Question: (3a + 5b)/(3a - 5b) = 5 then a : b is equal to?

Solution:
(3a + 5b)/(3a - 5b) = 5
⇒ 3a + 5b = 15a - 25b
⇒ 12a = 30b
⇒ 2a = 5b
∴ a : b = 5 : 2

৬,৫০৪.

P, Q and R are three points on the circle. If PQ = PR = 6√2 cm and ∠QPR = 90° then the radius is -

ক
7 cm
খ
8 cm
গ
7.5 cm
ঘ
6 cm

ব্যাখ্যা

Question: P, Q and R are three points on the circle. If PQ = PR = 6√2 cm and ∠QPR = 90° then the radius is -

Solution:

Given that,

P, Q, R are points on the circle
PQ = PR = 6√2 cm
∠QPR = 90°

Using Pythagoras theorem in △PQR,
QR² = PQ² + PR² = (6√2)² + (6√2)² = 72 + 72
⇒ QR² = 144 = 12²
∴ QR = 12

∴ Radius r = QR/2 = 12/2 = 6 cm

৬,৫০৫.

X, Y, and Z invested Tk. 90000, Tk. 70000, Tk. 45000 respectively to start a business. At the end of 1 year, they earned a profit of Tk. 164000. What will be the Z’s share?

ক
ক) Tk. 3600
খ
খ) Tk. 5600
গ
গ) Tk. 7200
ঘ
ঘ) None of those.

ব্যাখ্যা

Question: X, Y, and Z invested Tk. 90000, Tk. 70000, Tk. 45000 respectively to start a business. At the end of 1 year, they earned a profit of Tk. 164000. What will be the Z’s share?

Solution:
Investment ration of X, Y & Z = 90000 : 70000 : 45000
= 18 : 14 : 9

Sum of the ration = (18 + 14 + 9)
= 41

∴ Z’s share = 164000 x (9/41)
= 36000

৬,৫০৬.

What percent of 8 is 10% of 5?

ক
7.5%
খ
6.5%
গ
6.25%
ঘ
5.76%

ব্যাখ্যা

Question: What percent of 8 is 10% of 5?

Solution:
10% of 5 = 5 × (10/100) = 0.5

0.5 is, {(0.5/8) × 100} = 6.25 percent of 8

∴ 6.25 percent of 8 is 10% of 5

৬,৫০৭.

A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

ক
3.6
খ
7.2
গ
8.4
ঘ
10
ঙ
None of these

ব্যাখ্যা

Question: A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

Solution:
Speed = 600/(5 × 60) m/sec
= 2 m/sec
= 2 × (18/5) km/hr
= 7.2 km/hr

৬,৫০৮.

The marked price of a radio is Tk. 480. The owner allows a discount of 10% and still earns the profit of 8%. If no discount is allowed, find his gain percent?

ক
25%
খ
12%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: The marked price of a radio is Tk. 480. The owner allows a discount of 10% and still earns the profit of 8%. If no discount is allowed, find his gain percent?

Solution:
Marked price= 480
The shopkeeper allows a discount of 10%,
so, the Selling price will be= (480 × 90)/100 = 432.

And the profit is 8%.
C.P = {100/(100 + p %)} × S.P
⇒ C.P = (100/108) × 432
∴ C.P = 400

If the discount is not allowed:
Let Profit = P%

S.P = Marked price = 480, and C.P = 400
Profit = S.P - C.P = 480 - 400 = 80

P% = (Profit/C.P) × 100
= (80/400) × 100
= 80/4
= 20%

৬,৫০৯.

A rectangle has a diagonal length of 14 meters and a width of 12meters. What is the area of the rectangle in square meters?

ক
52 square meters
খ
13√2 square meters
গ
24√13 square meters
ঘ
None

ব্যাখ্যা

Question: A rectangle has a diagonal length of 14 meters and a width of 12meters. What is the area of the rectangle in square meters?

Solution:
ধরি,

আয়তক্ষেত্র ABCD এর কর্ণের দৈর্ঘ্য AC = 14 মিটার এবং প্রস্থ AB = 12 মিটার
∴ দৈর্ঘ্য, BC = √(14² - 12²) মিটার
=√(196 - 144) মিটার
= √52 মিটার
= 2√13 মিটার

আয়তক্ষেত্রের ক্ষেত্রফল = (2√13 × 12) বর্গমিটার
= 24√13 বর্গমিটার

৬,৫১০.

The radius of a car wheel is 28 cm. How many revolutions will it make to cover a distance of 13.2 kilometers?

ক
8200
খ
10200
গ
6750
ঘ
11320
ঙ
7500

ব্যাখ্যা

Question: The radius of a car wheel is 28 cm. How many revolutions will it make to cover a distance of 13.2 kilometers?

Solution:
আমরা জানি,
চাকার পরিধি = 2πr
= 2 × (22/7) × 28
= 2 × 4 × 22
= 176 সে. মি.

মোট দূরত্ব = 13.2 কি. মি.
= 13.2 × 1000 × 100) সে. মি. [১ কি. মি. = 1000 মি., ১ মি = 100 সে. মি.]
= 1320000 সে. মি.

∴ ঘূর্ণন সংখ্যা = 1320000/176
= 7500 টি

৬,৫১১.

If 2A = 3B = 4C, Than, A : B : C is.

ক
2 : 3 : 4
খ
4 : 3 : 2
গ
6 : 4 : 3
ঘ
20 : 15 : 2

ব্যাখ্যা

Question: If 2A = 3B = 4C, Than, A : B : C is.

Solution:
Let
2A = 3B = 4C = x
2A = x
A = x/2

3B =x
B = x/3

4C = x
C = x/4

A : B : C = x/2 : x/3 : x/4
= (x/2) × 12 : (x/3) × 12 : (x/4) × 12
= 6 : 4 : 3

৬,৫১২.

In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A?

ক
50%
খ
53%
গ
54%
ঘ
55%
ঙ
57%

ব্যাখ্যা

Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A?

Solution:
Say there are total of 100 registered voters in that city.
Thus 60 are Democrats and 40 are Republicans.

60 × 0.75 = 45 Democrats are expected to vote for Candidate A;
40 × 0.20 = 8 Republicans are expected to vote for Candidate A.

Thus total of 45 + 8 = 53 registered voters are expected to vote for Candidate A,
which is 53% of the total number of registered voters.

৬,৫১৩.

log₅3 × log₃25 =?

ক
1
খ
2
গ
3
ঘ
5

ব্যাখ্যা

Question: log₅3 × log₃25 =?

Solution:
log₅3 × log₃25
= log₅3 × log₃5²
= log₅3 × 2log₃5
= 2 × log₅3 × log₃5
= 2 × log₅3 × (1/log₅3) [log_ab = 1/log_ba]
= 2

৬,৫১৪.

The average of a, b, c is 6 and a - b = 4, ab = 21, what is the value of c?

ক
ক) 4
খ
খ) 16
গ
গ) 28
ঘ
ঘ) 4

ব্যাখ্যা

The average of a, b, c is 6
∴ (a + b + c)/3 = 6
⇒ a + b + c = 18
a - b = 4
and ab = 21
⇒ a = 21/b

Therefore,
a - b = 4
⇒ 21/b - b = 4
⇒ 21 - b² - 4b = 0
⇒ b² + 4b - 21 = 0
⇒ b² + 7b - 3b - 21 = 0
⇒ b(b + 7) - 3(b - 7) = 0
⇒ (b + 7)(b - 3) = 0
⇒ b = 3, - 7
Therefore,
(a + b + c) - (a - b) = 18 - 4
⇒ 2b + c = 14
⇒ c = 14 - 2b
⇒ c = 14 - 2 × 3 = 14 - 6 = 8 (when b = 3)
⇒ c = 14 - 2 × ( - 7) = 14 + 14 = 28 (when b = -7)
---------------------------------------------------------
a, b, c এর গড় 6 ও a - b = 4, ab = 21 হলে, c এর মান কত?

a, b, c এর গড় 6
∴ (a + b + c)/3 = 6
⇒ a + b + c = 18
a - b = 4
এবং ab = 21
⇒ a = 21/b
অতএব,
a - b = 4
⇒ 21/b - b = 4
⇒ 21 - b2 - 4b = 0
⇒ b² + 4b - 21 = 0
⇒ b² + 7b - 3b - 21 = 0
⇒ b(b + 7) - 3(b - 7) = 0
⇒ (b + 7)(b - 3) = 0
⇒ b = 3, - 7
অতএব,
(a + b + c) - (a - b) = 18 - 4
⇒ 2b + c = 14
⇒ c = 14 - 2b
⇒ c = 14 - 2 × 3 = 14 - 6 = 8 (যখন b = 3)
⇒ c = 14 - 2 × ( - 7) = 14 + 14 = 28 (যখন b = -7)

৬,৫১৫.

ক
9
খ
12
গ
15
ঘ
18

ব্যাখ্যা

Question:

Solution:

৬,৫১৬.

A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is:

ক
4 days
খ
6 days
গ
8 days
ঘ
18 days

ব্যাখ্যা

Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days

(A + B)'s 1 days work = (1/6) + (1/12) part
= (2 + 1)/12 part
= 3/12 part
= 1/4 part

So, (A + B) can complete the work in 4 days

৬,৫১৭.

A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of total time, to cover the remaining distance in the remaining time, his speed in kmph must be-

ক
ক) 10 kmph
খ
খ) 12 kmph
গ
গ) 14 kmph
ঘ
ঘ) 15 kmph

ব্যাখ্যা

Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of total time, to cover the remaining distance in the remaining time, his speed in kmph must be-

Solution:
Remaining distance = 6 - 3 = 3 km
remaining time = 1/3 × 45
= 15 min
= 15/60 hr
= 1/4 hr

Required speed = 3/(1/4) kmph
= 12 kmph

৬,৫১৮.

A man purchased a shirt at Taka 300 after availing a discount of 25%. What is the catalog price of the shirt?

ক
ক) Tk 400
খ
খ) Tk 225
গ
গ) Tk 375
ঘ
ঘ) Tk 500

ব্যাখ্যা

25% discount এ
তালিকা মূল্য 100 টাকা হলে ক্রয়মূল্য = 100 - 25 = 75 টাকা

75 টাকা ক্রয়মূল্য হলে তালিকামূল্য = 100 টাকা
1 টাকা ক্রয়মূল্য হলে তালিকামূল্য = 100/75 টাকা
300 টাকা ক্রয়মূল্য হলে তালিকামূল্য = (100 × 300)/75 টাকা
= 400 টাকা

৬,৫১৯.

A total profit of Tk. 3,600 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of C in the profit is:

ক
ক) 1,200
খ
খ) 1,500
গ
গ) 1,650
ঘ
ঘ) 1,700

ব্যাখ্যা

A Total Profit = Tk 3600
Profit ratio,
A : B = 5 : 4
B : C = 8 : 9
As B is common in both ratio, we make B equal in both ratio by multiplying One B in another.
A : B = 5 : 4 × 8
B : C = 8 × 4 : 9
So, ratio of
A : B : C = 40 : 32 : 36 = 10 : 8 : 9
Now,
C shares in profit = (3600×9)/27
= Tk 1200

৬,৫২০.

Find the area of an isosceles triangle given the length of the base is 10 cm and height is 15 cm.

ক
ক) 65 cm²
খ
খ) 75 cm²
গ
গ) 85 cm²
ঘ
ঘ) 95 cm²

ব্যাখ্যা

প্রশ্ন: Find the area of an isosceles triangle given the length of the base is 10 cm and height is 15 cm.

সমাধান:
Base of the triangle (b) = 10 cm
Height of the triangle (h) = 15 cm

Area of Isosceles Triangle = (1/2) × b × h
= (1/2) × 10 × 15
= 5 × 15
= 75 cm²

৬,৫২১.

A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?

ক
1 day
খ
2 days
গ
3 days
ঘ
5 days

ব্যাখ্যা

Question: A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?

Solution:
১ টি কেরিয়ার ১.৫ টন মাল বহন করতে সময় নেয় ১ দিন
২ টি কেরিয়ার ৩ টন মাল বহন করতে সময় নেয় = (১.৫ × ২)/৩ = ১ দিন

৬,৫২২.

Problem Solving, Analytical & Financial aptitude
The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. The series of successive discount is equivalent to a single discount of -

ক
20
খ
19
গ
18
ঘ
21
ঙ
None of these

ব্যাখ্যা

Question: The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. The series of successive discount is equivalent to a single discount of -

Solution:
Let,
The initial price is Tk. 100

After 1st 10% discount,
The price = 100 - 10% of 100 = 100 - 10 = 90

After 2nd 10% discount,
The price = 90 - 10% of 90 = 90 - 9 = 81

∴ equivalent single discount = 100 - 81 = 19

৬,৫২৩.

If (p² - q²) × (p - q)^-1 = 9, what is the value of p + q?

ক
ক) 3
খ
খ) 4
গ
গ) 9
ঘ
ঘ) 1/9

ব্যাখ্যা

Question: If (p² - q²) × (p - q)^-1 = 9, what is the value of p + q?

Solution:
(p² - q²) × (p - q)^-1 = 9
⇒ (p² - q²)/(p - q) = 9
⇒ (p + q) (p - q)/(p - q) = 9
∴ p + q = 9

৬,৫২৪.

A, B, and C invest in a business in the ratio 2 : 1 : 3. If the total profit is Tk 30,000, how much more did C get than A?

ক
1000 Tk
খ
2000 Tk
গ
6000 Tk
ঘ
5000 Tk

ব্যাখ্যা

Question: A, B, and C invest in a business in the ratio 2 : 1 : 3. If the total profit is Tk 30,000, how much more did C get than A?

Solution:
Let the invested shares ratio = 2x : x : 3x

Now
2x + x + 3x = 30000
Or, 6x = 30,000
∴ x = 5,000

∴ A’s share = 2 × 5,000 = 10,000
∴ C’s share = 3 × 5,000 = 15,000
∴ Difference = 15,000 - 10,000
= Tk 5,000

∴ C gets 5000 Tk more than A.

৬,৫২৫.

What is the sum of the following sequence: 5, 12, 19, 26, ... , 54?

ক
262
খ
248
গ
238
ঘ
236
ঙ
252

ব্যাখ্যা

Question: What is the sum of the following sequence: 5, 12, 19, 26, ... , 54?

Solution:
এটি একটি সমান্তর ধারা (arithmetic series)।
প্রথম পদ, a = 5
সাধারণ অন্তর, d = 12 - 5 = 7
শেষ পদ= 54

আমরা জানি,
n তম পদ = a + (n - 1)d
⇒ 54 = 5 + (n - 1)7
⇒ 49 = 7(n - 1)
⇒ n - 1 = 7
⇒ n = 8

সমষ্টি, S_n = n/2{2a + (n - 1)d}
∴ S₈ = (8/2){2(5) + (8 - 1)7}
= 4{10 + (7 × 7)}
= 4{10 + 49}
= 4 × 59
= 236

অতএব, প্রদত্ত ধারাটির সমষ্টি হলো 236

৬,৫২৬.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
ক) 20%
খ
খ) 25%
গ
গ) 35%
ঘ
ঘ) 15%

ব্যাখ্যা

ধরি,
বই এর দাম = 100 টাকা
কলম এর দাম= 100 + 25 = 125 টাকা
কলম হোল্ডার এর দাম = 100 + 50 = 150 টাকা

কলম থেকে কলম হোল্ডার এর দাম বেশি = 150 -125 টাকা
= 25 টাকা

কলম থেকে কলম হোল্ডার শতকরা বেশি = (25 x 100)/125
= 20%

৬,৫২৭.

An amount of Tk. 6000 lent 5% per annum compounded interest for 2 years will become?

ক
Tk. 6610
খ
Tk. 6615
গ
Tk. 4610
ঘ
Tk 5615

ব্যাখ্যা

Question: An amount of Tk. 6000 lent 5% per annum compounded interest for 2 years will become?

Solution:
Here,
Principal, P = Tk. 6000
Rate of interest, r = 5% = 5/100 = 1/20
Time, n = 2 years.

We know,
C = P (1 + r)ⁿ
= 6000 × {1+ (1/20)}²
= 6000 × {(21/20) × (21/20)}
= 6000 × (441/400)
= 6615

∴ Compound Interest Tk. 6615.

৬,৫২৮.

The difference between the numerator and the denominator of a fraction is 5. If 5 is added to the denominator the fraction is decreased by 5/4 then the value of the fraction will be equal to:

ক
1/4
খ
3/4
গ
9/4
ঘ
11/4

ব্যাখ্যা

Question: The difference between the numerator and the denominator of a fraction is 5. If 5 is added to the denominator the fraction is decreased by 5/4 then the value of the fraction will be equal to:

Solution:
ধরি,
ভগ্নাংশটির হর = x
ভগ্নাংশটির লব = x + 5

∴ ভগ্নাংশটি = (x + 5)/x

প্রশ্নমতে,
{(x + 5)/x} - {(x + 5)/(x + 5)} = 5/4
⇒ {(x + 5)/x} - 1 = 5/4
⇒ {(x + 5)/x} = (5/4) + 1
∴ {(x + 5)/x} = 9/4

∴ ভগ্নাংশটি = 9/4

৬,৫২৯.

In how many ways can a group of 2 teachers and 5 students be formed from 5 teachers and 8 students?

ক
320
খ
560
গ
720
ঘ
120

ব্যাখ্যা

Question: In how many ways can a group of 2 teachers and 5 students be formed from 5 teachers and 8 students?

Solution:
We have 5 teachers and 8 students.
We need to choose 2 teachers from 5 and 5 students from 8.

∴ Number of ways = ⁵C₂ × ⁸C₅= {5!/(2!(5 - 2)!)} × {8!/(5!(8 - 5)!)}
= {5!/(2!×3!)} × {8!/(5!×3!)}
= {(5×4)/(2×1)} × {(8×7×6)/(3×2×1)}
= 10 × 56
= 560 ways

৬,৫৩০.

If each side of a rectangle is increased by 50%, its area will increase by -

ক
ক) 200%
খ
খ) 125%
গ
গ) 150%
ঘ
ঘ) 50%

ব্যাখ্যা

ধরি, আয়তক্ষেত্রটির দৈর্ঘ্য x একক এবং প্রস্থ y একক
সুতরাং ক্ষেত্রফল = xy বর্গ একক
৫০% বৃদ্ধিতে নতুন দৈর্ঘ্য = x + (xএর৫০%) = x + x/2 = ৩x/2
৫০% বৃদ্ধিতে নতুন প্রস্থ = y + (yএর ৫০%) = y + y/2 = ৩y/2
নতুন ক্ষেত্রফল = (৩x/2) × (৩y/2) = ৯xy/৪
ক্ষেত্রফল বৃদ্ধি পেয়েছে = ৯xy/৪ - xy = ৫xy/৪
∴ ক্ষেত্রফল শতকরা বৃদ্ধি পেয়েছে = (৫xy × ১০০)/৪xy = ১২৫%

শর্টকাটঃ ক্ষেত্রফল বৃদ্ধি পাবে = [50 + 50 + (50×50 / 100)] % = 125%

৬,৫৩১.

A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 9 meter². The area of the whole room is 25 meter². What is the length of the one side of the carpet?

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

ব্যাখ্যা

Question: A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 9 meter². The area of the whole room is 25 meter². What is the length of the one side of the carpet?

Solution:
মনে করি,
কার্পেটের এক বাহুর দৈর্ঘ্য x মিটার

প্রশ্নমতে,
25 - 9 = x²
⇒ 16 = x²
⇒ 4² = x²
∴ x = 4

৬,৫৩২.

If then find the value of x.

ক
2
খ
√2
গ
2√2
ঘ
1

ব্যাখ্যা

Question: If then find the value of x.

Solution:

৬,৫৩৩.

X can complete a work in 12 days, and Y alone can do it in 18 days. They work together for 6 days, and Z completes the remaining work in 3 days. If the total payment for the work is Tk. 600, how much should Z get?

ক
Tk. 75
খ
Tk. 90
গ
Tk. 100
ঘ
Tk. 120

ব্যাখ্যা

Question: X can complete a work in 12 days, and Y alone can do it in 18 days. They work together for 6 days, and Z completes the remaining work in 3 days. If the total payment for the work is Tk. 600, how much should Z get?

সমাধান:
X-এর একদিনের কাজ = 1/12
Y-এর একদিনের কাজ = 1/18

X ও Y একসাথে ৬ দিন কাজ করে:
= 6 × (1/12 + 1/18)
= 6 × {(3 + 2)/36} = 6 × (5/36) = 30/36 = 5/6

∴ বাকি কাজ = 1 − 5/6 = 1/6

Z এই 1/6 কাজ ৩ দিনে করেছে, অর্থাৎ Z-এর কাজ = 1/6

X-এর কাজ = 6 × 1/12 = 1/2
Y-এর কাজ = 6 × 1/18 = 1/3
Z-এর কাজ = 1/6

তাহলে অনুপাত = 1/2 : 1/3 : 1/6
= 3 : 2 : 1

মোট টাকা = 600
Z-এর অংশ = 1/(3+2+1) = 1/6
∴ Z পাবে = 600 × (1/6) = 100 টাকা

৬,৫৩৪.

On reducing the entry fee by 25% in a park, the number of people coming to the park increased by 20%, then the percent increase or decrease in the income from the entry fee is -

ক
ক) 8% increase
খ
খ) 7% decrease
গ
গ) 10% decrease
ঘ
ঘ) 9% increase

ব্যাখ্যা

Let
The entry fee = Tk. 100 per head and number of people coming to the park = 100.
So income = Tk. (100 × 100) = Tk.10000.

Further entry fee is Tk.(100 - 25) = Tk. 75 and number of people coming to the park = 100 + 20 = Tk.120.
Hence income = Tk. (75 × 120) = Tk. 9000.

So decrease in income = Tk. (10000 - 9000) = Tk. 1000.

The percent decrease in the income = (1000/10000) ×100 = 10%

৬,৫৩৫.

How many kg of custard powder costing Tk. 42 per kg must be mixed with 16 kg of custard powder costing Tk. 60 per kg so that 20 % may be gained by selling the mixture at Tk. 60 per kg?

ক
11 kg
খ
14 kg
গ
12 kg
ঘ
20 kg

ব্যাখ্যা

Question: How many kg of custard powder costing Tk. 42 per kg must be mixed with 16 kg of custard powder costing Tk. 60 per kg so that 20 % may be gained by selling the mixture at Tk. 60 per kg?

Solution:
SP = 60.
Gain= 20%.
CP = (100/120) × 60.
∴ CP = 50.

Ratio between the 2 varieties of custard powder = 60 - 50 : 50 - 42 = 10 : 8.

∴ if x is the required quantity then 10 : 8 = x : 16
⇒ x = 20 kg.

৬,৫৩৬.

Piyal can complete a work in 10 days working 8 hours a day. Sajid can complete the same work in 8 days working 10 hours a day. If both piyal and sajid work together,working 8 hours a day,in how many days can they complete the work?

ক
ক) 3 days
খ
খ) 4 days
গ
গ) 5 days
ঘ
ঘ) 6 days

ব্যাখ্যা

Question: Piyal can complete a work in 10 days working 8 hours a day. Sajid can complete the same work in 8 days working 10 hours a day. If both piyal and sajid work together,working 8 hours a day,in how many days can they complete the work?

Solution:
পিয়াল প্রতিদিন ৮ ঘণ্টা করে কাজ করে, ১০ দিনে একটি কাজ করতে পারে।
মোট ঘণ্টা = ১০ × ৮ ঘণ্টা
= ৮০ ঘণ্টা

সাজিদ প্রতিদিন ১০ ঘণ্টা করে ৮ দিনে একটি কাজ করতে পারে।
মোট ঘণ্টা = ১০ × ৮ ঘণ্টা
= ৮০ ঘণ্টা

দুইজন একসাথে এক ঘণ্টায় করতে পারে = (১/৮০) + (১/৮০) অংশ
= ২/৮০ অংশ
= ১/৪০ অংশ

সম্পূর্ণ অংশ করতে সময় লাগে = ৪০ ঘণ্টা

দৈনিক ৮ ঘণাট করে কাজ করলে, সময় লাগে = ৪০/৮ দিন
= ৫ দিন

৬,৫৩৭.

A person incurs a loss of 5% by selling a watch for Tk.1330. At what price should the watch be sold to earn 5% profit ?

ক
ক) Tk.1450
খ
খ) Tk.1470
গ
গ) Tk.1460
ঘ
ঘ) Tk.1430

ব্যাখ্যা

Question: A person incurs a loss of 5% by selling a watch for Tk.1330. At what price should the watch be sold to earn 5% profit ?

Solution:
5% ক্ষতিতে
বিক্রয়মূল্য 95 টাকা হলে ক্রয়মূল্য 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/95 টাকা
বিক্রয়মূল্য 1330 টাকা হলে ক্রয়মূল্য (100 × 1330)/95 টাকা
= 1400 টাকা

5% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 105 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য 105/100 টাকা
ক্রয়মূল্য 1400 টাকা হলে বিক্রয়মূল্য (105 × 1400)/100 টাকা
= 1470 টাকা

৬,৫৩৮.

Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the field?

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

ব্যাখ্যা

Question: Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the field?

Solution:
সুমিত একদিনে করে ১/৬ অংশ কাজ

আমিত একদিনে করে (১/৪) - (১/৬)
= ১/১২ অংশ কাজ

সম্পূর্ণ কাজটি করতে অমিতের সময় লাগবে = ১২ দিন

৬,৫৩৯.

Jenny notices a consistent, increasing pattern in the number of geese she sees flying over her house each day. If she sees 5 geese on Monday, 8 geese on Tuesday, 11 geese on Wednesday and 14 geese on Thursday and the next week starts on Sunday, on which of the following day of the next week will she see a prime number of geese if the pattern continues?

ক
ক) Sunday
খ
খ) Monday
গ
গ) Thursday
ঘ
ঘ) Friday

ব্যাখ্যা

Question: Jenny notices a consistent, increasing pattern in the number of geese she sees flying over her house each day. If she sees 5 geese on Monday, 8 geese on Tuesday, 11 geese on Wednesday and 14 geese on Thursday and the next week starts on Sunday, on which of the following day of the next week will she see a prime number of geese if the pattern continues?

Solution:

সোমবার, মঙ্গলবার, বুধবার এবং বৃহস্পতিবারে যথাক্রমে ৫টি, ৮টি, ১১টি এবং ১৪টি পাখি উড়ে যায়।

অতএব, প্যাটার্ন অনুসারে, শুত্রুবার, শনিবার, রবিবারে যথাক্রমে ১৭টি, ২০টি, ২৩টি পাখি উড়ে যাবে।

অতএব, জেনি পরবর্তী সপ্তাহের রবিবারে মৌলিক সংখ্যায় পাখিগুলো দেখবে।

৬,৫৪০.

The number of number-pairs lying between 40 and 100 with their HCF as 15 is -

ক
4
খ
6
গ
10
ঘ
8

ব্যাখ্যা

Question: The number of number-pairs lying between 40 and 100 with their HCF as 15 is -

Solution:
গ.সা.গু ১৫ এমন প্রতিটি সংখ্যার উৎপাদক ১৫।
৪০ থেকে ১০০ এর মধ্যে ১৫ এর গুণিতক ৪৫, ৬০, ৭৫, ৯০

সংখ্যা জোড়: (৪৫, ৬০), (৪৫, ৭৫), (৪৫, ৯০), (৬০, ৭৫), (৬০, ৯০), (৭৫, ৯০)
কিন্তু এখানে (৪৫, ৯০) এর গ.সা.গু হলো ৪৫ এবং (৬০, ৯০) এর গ.সা.গু হলো ৩০।

তাই ৪ টি সংখ্যাজোড় আছে যাদের গ.সা.গু ১৫।

৬,৫৪১.

At what rate of compound interest per annum will a sum of Tk. 1200 become Tk. 1348.32 in 2 years?

ক
ক) 7.5%
খ
খ) 6.5%
গ
গ) 7%
ঘ
ঘ) 6%

ব্যাখ্যা

Given amount = Tk. 1348.32
Principle = Tk. 1200
And time = 2 years

According to the law,
A = P(1 + R/100)ⁿ
1348.32 = 1200(1 + R/100)²
1348.32/1200 = (1 + R/100)²
11236/10000 = (1 + R/100)²
(106/100)² = (1 + R/100)²
(1 + 6/100)² = (1 + R/100)²
R = 6% per annum.

৬,৫৪২.

One of the diagonals of a rhombus is double the other diagonal. Its area is 36 sq. cm. The sum of the diagonal is?

ক
15
খ
18
গ
20
ঘ
22

ব্যাখ্যা

Question: One of the diagonals of a rhombus is double the other diagonal. Its area is 36 sq. cm. The sum of the diagonal is?

Solution:
let, one diagonal is x m
other is 2x

0.5 × x × 2x = 36
⇒ x² = 36
⇒ x = 6

sum of diagonals = x + 2x
= 3x
= 3 × 6
= 18

৬,৫৪৩.

ক
0
খ
1/2
গ
1
ঘ
2

ব্যাখ্যা

Question:

Solution:

৬,৫৪৪.

A speed of 65 m/sec is the same as:

ক
ক) 224 km/hr
খ
খ) 210 km/hr
গ
গ) 234 km/hr
ঘ
ঘ) 220 km/hr

ব্যাখ্যা

Question: A speed of 65 m/sec is the same as:

Solution:
65 m/sec = 65 × (18/5 )
= 234 km/hr. [meter × 18/5]

৬,৫৪৫.

A³ is odd, which if the following is true?

ক
ক) A is odd only
খ
খ) A² is odd only
গ
গ) A² is even
ঘ
ঘ) Both A and A² are odd

ব্যাখ্যা

Let, A³ = 27 = 3³
So, A = 3
and, A² = 9

৬,৫৪৬.

Let the ratio of x to y be a/b : - b/a, and if (x - y) = (a/b + b/a), it follows that x is equal to:

ক
- a/b
খ
a/b
গ
(a - b)/a
ঘ
None of the above

ব্যাখ্যা

Question: Let the ratio of x to y be a/b : - b/a, and if (x - y) = (a/b + b/a), it follows that x is equal to:

Solution:
Given,
⇒ x/y =(a/b)/(-b/a)
⇒ x/y = - a²/b²
⇒ y =(−b²/a²)x

Now,
x - y = a/b + b/a
⇒ x + (b²/a²)x = (a² + b²)/ab
⇒ x(a² + b²)/a² = (a²+b²)/ab
⇒ x = a²/ab
⇒ x = a/b

৬,৫৪৭.

The sides of a triangular field are 13 m, 14 m, and 15 m respectively. What is its area?

ক
90 square meters
খ
72 square meters
গ
84 square meters
ঘ
96 square meters
ঙ
100 square meters

ব্যাখ্যা

Question: The sides of a triangular field are 13 m, 14 m, and 15 m respectively. What is its area?

Solution:
Let the sides of the triangle are,
a = 13 m, b = 14 m, c = 15 m

We know,
Semi-perimeter, s = (a + b + c)/2
= (13 + 14 + 15)/2
= 42/2
= 21 m

We know the formula for the area of a triangle,
Area = √[s(s - a)(s - b)(s - c)]
= √[21(21 - 13)(21 - 14)(21 - 15)]
= √[21 × 8 × 7 × 6]
= √[21 × 8 × 42]
= √7056
= 84

Therefore, the area of the triangular field is 84 square meters.

৬,৫৪৮.

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
8 seconds
খ
11 seconds
গ
15 seconds
ঘ
22 seconds

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.

৬,৫৪৯.

If x = 20%, by what percent is x larger than x²?

ক
25%
খ
400 %
গ
120%
ঘ
240%

ব্যাখ্যা

x = 20%
⇒ x
= 20/100
= 1/5

⇒ x²
= 1/25
= 1/25 × 100%
= 4%

x is larger than x² (in percentage)
= (20% - 4%)
= 16%

x is larger than x² (in percentage)
= 16/4 ×100%
= 400%

৬,৫৫০.

A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

ক
Tk. 22500
খ
Tk. 23400
গ
Tk. 25000
ঘ
Tk. 21650

ব্যাখ্যা

Question: A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি, কর্মীর পূর্বের বেতন = x টাকা।

6% বৃদ্ধিতে বেতন = x + x এর 6%
= x + (6x/100) = 106x/100

বোনাস হিসেবে 450 টাকা যোগ করলে মোট বেতন = (106x/100) + 450

8% বৃদ্ধিতে বেতন = x + x এর 8%
= x + (8x/100) = (108x/100)

প্রশ্নমতে,
(106x/100) + 450 = (108x/100)
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = (2x/100)
⇒ x = (450 × 100)/2
∴ x = 22500

অর্থাৎ, কর্মীর পূর্ববর্তী বেতন ছিল 22500 টাকা।

৬,৫৫১.

The LCM of two numbers is 1890 and their HCF is 30. If one of them is 270, the other will be -

ক
200
খ
210
গ
230
ঘ
250

ব্যাখ্যা

Question: The LCM of two numbers is 1890 and their HCF is 30. If one of them is 270, the other will be -

Solution:
HCF of the numbers × LCM of the numbers = Multiplication of the numbers
⇒ 30 × 1890 = 270 × N
⇒ N = (30×1890)/270
⇒ N = 210

৬,৫৫২.

If the volume of a sphere is 288π cm³, what is the surface area of the sphere?

ক
108π cm²
খ
144π cm²
গ
72π cm²
ঘ
36π cm²

ব্যাখ্যা

Question: If the volume of a sphere is 288π cm³, what is the surface area of the sphere?

Solution:
Given that the volume, V = 288π cm³
or, (4/3)πr³ = 288π
or, r³ = 216
∴ r = 6 cm

Surface area of a sphere, A = 4πr²
= 4π(6)²
= 144π cm²

৬,৫৫৩.

If the ratio of cost price and selling price is of an article be 20 : 21, the percentage of profit is-

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

ব্যাখ্যা

Let cost price 20x
selling price 21x
profit = 21x - 20x = x
Percentage of profit is ={(x/20x)× 100}%
= 5%

৬,৫৫৪.

Given that x² is an odd number, determine the nature of x² − x.

ক
Odd
খ
Even
গ
Negative
ঘ
Positive

ব্যাখ্যা

Question: Given that x² is an odd number, determine the nature of x² − x.

Solution:
যেহেতু x² বিজোড় তাই x ও বিজোড়
এখন,
x² - x
= x(x - 1)
= (x - 1)x

(x - 1) এবং x দুইটি ক্রমিক সংখ্যা।

x বিজোড় সংখ্যা হলে (x - 1) অবশ্যই জোড় সংখ্যা হবে।
কারণ দুইটি ক্রমিক সংখ্যার মধ্যে একটি বিজোড় হলে অন্যটি জোড় হবে।

সুতরাং, x ও (x - 1) এর গুনফল = x² - x একটি জোড় সংখ্যা। [ জোড় × বিজোড় = জোড় ]

৬,৫৫৫.

In a class of 100 students, 55 are taking Biology, 35 are taking Chemistry and 10 are taking both courses. How many students are not enrolled in either course?

ক
10
খ
15
গ
20
ঘ
24

ব্যাখ্যা

Question: In a class of 100 students, 55 are taking Biology, 35 are taking Chemistry and 10 are taking both courses. How many students are not enrolled in either course?

Solution:
দেওয়া আছে,
মোট শিক্ষার্থীর সংখ্যা, n(U) = 100
জীববিজ্ঞান নেওয়া শিক্ষার্থীর সংখ্যা, n(B) = 55
রসায়ন নেওয়া শিক্ষার্থীর সংখ্যা, n(C) = 35
উভয় বিষয় নেওয়া শিক্ষার্থীর সংখ্যা, n(B ∩ C) = 10

কমপক্ষে একটি বিষয় নেওয়া শিক্ষার্থীর সংখ্যা, n(B ∪ C) = n(B) + n(C) - n(B ∩ C)
⇒ n(B ∪ C) = 55 + 35 - 10
⇒ n(B ∪ C) = 90 - 10
⇒ n(B ∪ C) = 80

কোনোটিই নেয়নি এমন শিক্ষার্থীর সংখ্যা = n(U) - n(B ∪ C)
= 100 - 80
= 20

সুতরাং, 20 জন শিক্ষার্থী কোনো কোর্সই গ্রহণ করেনি।

৬,৫৫৬.

Find the greatest number that will divide 39, 87, and 179 and leave the same remainder.

ক
7
খ
9
গ
4
ঘ
12

ব্যাখ্যা

Question: Find the greatest number that will divide 39, 87, and 179 and leave the same remainder.

Solution:
the number is the H.C.F of (87 - 39), (179 - 87) and (179 - 39)
= H.C.F of 48, 92 and 140
= 4

৬,৫৫৭.

If a² + b² + c² = 1, what is the maximum value of abc?

ক
1/3
খ
2/√3
গ
1/3√3
ঘ
1

ব্যাখ্যা

So the maximum value of a² b² c² = (1/3 × 1/3 × 1/3) = 1/27
( When the sum of the three positive quantities is fixed, the product will be maximum when the quantities are equal)
Hence, the maximum value of ABC = 1/√27
= 1/(3√3)

৬,৫৫৮.

Tickets for all but 100 seats in a 10000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of Tk. 2. What was the total revenue from ticket sales?

ক
Tk. 15840
খ
Tk. 17820
গ
Tk. 18000
ঘ
Tk. 19800
ঙ
Tk. 21780

ব্যাখ্যা

Question: Tickets for all but 100 seats in a 10000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of Tk. 2. What was the total revenue from ticket sales?

Solution:
100 are not sold from 10000
So seats sold = 9900

20% of 9900 is = (20/100) × 9900 = 1980
and remaining 80% is 9900 - 1980 = 7920.

each ticket cost Tk. 2 and 1980 seats cost Tk. 1

So, total revenue = 2 × 7920 + 1980 = 17820

৬,৫৫৯.

A starts 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
Tk. 7500
খ
Tk. 8000
গ
Tk. 8500
ঘ
Tk. 9000

ব্যাখ্যা

Question: A starts 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.
Then,
(3500 × 12)/7x = 2/3
⇒ 14x = 126000
∴ x = 9000.

৬,৫৬০.

The highest common factor (HCF) of x² - 1, x⁴ - 1 and x⁴ - x³ + x - 1 is

ক
x⁶ - 1
খ
x³ + 1
গ
x² - 1
ঘ
x³ - 1

ব্যাখ্যা

Question: The highest common factor (HCF) of x² - 1, x⁴ - 1 and x⁴ - x³ + x - 1 is-

Solution:
১ম রাশি = x² - 1 = (x + 1)(x - 1)

২য় রাশি = x⁴ - 1 = (x² - 1)(x² + 1) = (x² + 1) (x + 1)(x - 1)

৩য় রাশি = x⁴ - x³ + x - 1 = (x⁴ - x³) + (x - 1)
= x³(x - 1) + 1(x - 1)
= (x³ + 1)(x - 1)
= (x + 1)(x² - x + 1)(x - 1)
= (x - 1)(x + 1)(x² - x + 1)

∴ নির্ণয়ে গ.সা.গু = (x + 1)(x - 1) = x² - 1

৬,৫৬১.

If log_x125 = 3 then x = ?

ক
ক) √5
খ
খ) 5
গ
গ) 7
ঘ
ঘ) 9

ব্যাখ্যা

log_x125 = 3
Or, x³ = 125 = 5³
Or, x = 5

৬,৫৬২.

In how many years will the profit of Tk. 10,000 be Tk. 4,800 at the rate of 12% profit?

ক
4 years
খ
5 years
গ
6.5 years
ঘ
7 years

ব্যাখ্যা

Question: In how many years will the profit of Tk. 10,000 be Tk. 4,800 at the rate of 12% profit?

Solution:
Given,
P = Tk. 10000
I = Tk. 4800
r = 12% = 12/100

We know,
n = I/Pr
= 4800/(10000 × 12/100)
= (4800 × 100)/(10000 × 12)
= 4 years

৬,৫৬৩.

Which of the following years is not a leap year?

ক
1600
খ
800
গ
700
ঘ
2000

ব্যাখ্যা

Question: Which of the following years is not a leap year?

Solution:
A century divisible by 400 is a leap year.
The years 800, 1600 and 2000 are divisible by 400, so they are leap years.

The year 700 is not divisible by 400, so it is not a leap year.

৬,৫৬৪.

If 61% of Bangladeshi people like coffee and 74% like tea, how many like both?

ক
ক) 13%
খ
খ) 16%
গ
গ) 26%
ঘ
ঘ) 35%

ব্যাখ্যা

n(C ∩ T) = 61% + 74% - 100% = 35%

৬,৫৬৫.

If (3x + 2y) = 7 and (2x - 2y) = - 2, then find the value of (4y - 3x).

ক
- 2
খ
11
গ
5
ঘ
2

ব্যাখ্যা

Question: If (3x + 2y) = 7 and (2x - 2y) = - 2, then find the value of (4y - 3x).

Solution:
3x + 2y = 7........(1)
(2x - 2y) = - 2
⇒ 2(x - y) = - 2
⇒ x - y = - 1
∴ x = y - 1 ..............(2)

x এর মান (1) নং এ বসিয়ে পাই
3x + 2y = 7
⇒ 3(y - 1) + 2y = 7
⇒ 3y - 3 +2y = 7
⇒ 5y = 7 + 3
⇒ 5y = 10
∴ y = 2

y এর মান (2) নং এ বসিয়ে পাই
x = y - 1
⇒ x = 2 - 1
∴ x = 1

∴ 4y - 3x = 4 × 2 - 3 × 1 = 8 - 3 = 5

৬,৫৬৬.

30 men can complete a road construction project in 20 days, working 8 hours a day. How many men need to be appointed extra to complete the same work in 12 days, working 10 hours a day?

ক
8
খ
9
গ
10
ঘ
15

ব্যাখ্যা

Question: 30 men can complete a road construction project in 20 days, working 8 hours a day. How many men need to be appointed extra to complete the same work in 12 days, working 10 hours a day?

Solution:
দৈনিক ৮ ঘণ্টা করে কাজ করে ২০ দিনে শেষ করতে লোক লাগে ৩০ জন
∴ দৈনিক ১ ঘণ্টা করে কাজ করে ১ দিনে শেষ করতে লোক লাগে (৩০ × ৮ × ২০) জন
∴ দৈনিক ১০ ঘণ্টা করে কাজ করে ১২ দিনে শেষ করতে লোক লাগে (৩০ × ৮ × ২০)/(১০ × ১২) জন
= ৪০ জন

∴ অতিরিক্ত লোক লাগবে = (৪০ - ৩০) = ১০ জন

৬,৫৬৭.

An association of mathematics teachers has 1260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?

ক
75%
খ
58%
গ
42%
ঘ
34%
ঙ
25%

ব্যাখ্যা

Question: An association of mathematics teachers has 1260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?

Solution:
Total number of members = 1260
Number of members that cast votes = 525
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100) × 525 = 315

Percent of total membership that voted for winning candidate = (315/1260) × 100 = 25%

৬,৫৬৮.

Mr. Masum usually makes 45% profit on every Mobile phone he sells. During a sale, he reduces his margin of profit to 40%, while his sales increase by 10%, What is the ratio of his new profit to his usual profit?

ক
44 : 47
খ
11 : 35
গ
34 : 45
ঘ
44 : 45

ব্যাখ্যা

Question: Mr. Masum usually makes 45% profit on every Mobile phone he sells. During a sale, he reduces his margin of profit to 40%, while his sales increase by 10%, What is the ratio of his new profit to his usual profit?

Solution:
প্রথমে Mobile বিক্রয় করেন = x টি

45% লাভে মোট লাভ = 45x/100
10% বিক্রি বৃদ্ধিতে নতুন বিক্রির পরিমাণ = x + x এর 10%
= x + 10x/100
= 1.1x

নতুন লাভ = 1.1x × 40/100
= 44x/100

নতুন লাভ : পুরাতন লাভ = 44x/100 : 45x/100
= 44 : 45

৬,৫৬৯.

A square field is surrounded by a path of uniform width 4 meters. If the area of the path is 192 square meters, find the side length of the field.

ক
6 meters
খ
8 meters
গ
10 meters
ঘ
12 meters

ব্যাখ্যা

Question: A square field is surrounded by a path of uniform width 4 meters. If the area of the path is 192 square meters, find the side length of the field.

Solution:
Let the side of the field = x meters.
Then, the side of the field including the path = x + (2 × 4)
= x + 8 meters.

Area of path = Area of field with path - Area of field
⇒ 192 = (x + 8)² - x²
⇒ 192 = x² + 16x + 64 - x²
⇒ 192 = 16x + 64
⇒ 16x = 192 - 64
⇒ 16x = 128
⇒ x = 128/16
⇒ x = 8 meters

∴ Therefore, the side length of the field is 8 meters.

৬,৫৭০.

Jamal is now four times older than Arif. In 30 years, he will be 18 years older than Arif. What is Jamal's age now in years?

ক
24
খ
28
গ
32
ঘ
none

ব্যাখ্যা

Question: Jamal is now four times older than Arif. In 30 years, he will be 18 years older than Arif. What is Jamal's age now in years?

Solution:
Let,
Age of Arif = x
Age of Jamal = 4x

ATQ,
4x + 30 = (x + 30) + 18
⇒ 3x = 18
∴ x = 6

∴ Jamal's age = 4 × 6 = 24 years

৬,৫৭১.

ক
4
খ
8
গ
2ⁿ
ঘ
2^{n + 1}

ব্যাখ্যা

Question:

Solution:

৬,৫৭২.

A watch which gains 5 seconds in 3 minutes was set at 7 am. In the afternoon of the same day when the true time is 1 pm, the watch will indicate -

ক
ক) 1 : 05 pm
খ
খ) 1 : 10 pm
গ
গ) 1 : 12 pm
ঘ
ঘ) 12 : 55 pm

ব্যাখ্যা

প্রশ্ন: A watch which gains 5 seconds in 3 minutes was set at 7 am. In the afternoon of the same day when the true time is 1 pm, the watch will indicate -

সমাধান:
একটি ঘড়ি ৭ টায় চালু করা হয়েছে। ঘড়িটি প্রতি ৩ মিনিটে ৫ সেকেন্ড লাভ করে।

1 p.m - 7 a.m. = ৬ ঘণ্টা
= (৬ × ৬০) মিনিট
= ৩৬০ মিনিট

৩ মিনিটে লাভ করে ৫ সেকেন্ড
১ মিনিটে লাভ করে ৫/৩ সেকেন্ড
∴ ৩৬০ মিনিটে লাভ করে (৫ × ৩৬০)/৩ সেকেন্ড
= ৬০০ সেকেন্ড
= ৬০০/৬০ মিনিট
= ১০ মিনিট

অর্থাৎ, ঘড়িটি প্রকৃত সময় থেকে ১০ মিনিট বেশী দেখাবে।
∴ প্রকৃত সময় যখন দুপুর ১ টা, ঘড়ি দেখাবে ১ টা ১০ মিনিট।

৬,৫৭৩.

How many rotations will the short hand of a clock complete in 72 hours?

ক
6
খ
8
গ
10
ঘ
16

ব্যাখ্যা

Question: How many rotations will the short hand of a clock complete in 72 hours?

Solution:

Here,
Short hand = Hour hand

The short hand rotates a full rotation in 12 hours.

Number of rotations
= 72/12
= 6

৬,৫৭৪.

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
3 : 1
খ
3 : 2
গ
7 : 2
ঘ
5 : 3

ব্যাখ্যা

Question: 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:

Solution:
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

৬,৫৭৫.

A seller sold his articles in two types such that three fourth at a profit of 10% and the remaining at loss of 2%. If the total profit was Tk. 1500, what was the total value of the articles?

ক
Tk. 20409.25
খ
Tk. 21009.48
গ
Tk. 21428.57
ঘ
Tk. 21400

ব্যাখ্যা

Let the total value be Tk. X.
The value of 3/4 th = Tk. 3X/4 then the value of 1/4 th = Tk. X/4
Since he made a profit of 10% on 3X/4 and loss 2% on X/4
Selling price = Tk. [110% of 3X/4] + [98% of X/4]
= Tk. 330X/400 + 98X/400
= Tk. 428X/400
Since the total cost price is Tk. X and the total profit is Tk. 1500 then
Tk. {(428X /400) - X} = Tk. 1500
⇒ {(428X - 400X)/400} = 1500
⇒ 28X = 1500 x 400
⇒ 28X = Tk. 6,00,000
⇒ X = 6,00,000/28 = Tk. 21428.57
= Tk. 21428.57
Hence the answer is Tk. 21428.57

৬,৫৭৬.

The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is-

ক
654
খ
548
গ
580
ঘ
476

ব্যাখ্যা

Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is-

Solution:
The number leaves a remainder 8 when divided by 12, 15, 20 and 54.
So the required number = LCM(12, 15, 20, 54) + 8

Now,
12 = 2 × 2 × 3
15 = 3 × 5
20 = 2 × 2 × 5
54 = 2 × 3 × 3 × 3

∴ LCM(12, 15, 20, 54) = 540

∴ Required Number = 540 + 8 = 548

৬,৫৭৭.

When 40% of the first number is added to the second number, the second number becomes 7/5 times the first number. What is the ratio of the first number to the second number?

ক
1 : 1
খ
2 : 3
গ
3 : 4
ঘ
3 : 8

ব্যাখ্যা

Question: When 40% of the first number is added to the second number, the second number becomes 7/5 times the first number. What is the ratio of the first number to the second number?

Solution:
Let the first number = x
and the second number = y.

According to the question,
y + 40% of x = (7/5)x
⇒ y + (40/100) x = (7/5)x
⇒ y + (4/10)x = (7/5)x
⇒ y = (7/5)x - (4/10)x
⇒ y = (14 - 4)x/10
⇒ y = 10x/10
⇒ y = x

Therefore, x : y = x : x = 1 : 1

৬,৫৭৮.

Working 5 hours a day, A can complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:

ক
ক) 3 days
খ
খ) 4 days
গ
গ) 4.5 days
ঘ
ঘ) 5.4 days

ব্যাখ্যা

Working 5 hours a day, A can complete the work in 8 days i.e.
= 5 × 8 = 40 hours
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6 × 10 = 60 hours
(A + B)'s 1 hour's work,
= 1/40 + 1/60 = (3+2)/ 120
= 5/120
= 1/24
Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.

৬,৫৭৯.

A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

ক
Tk.175
খ
Tk. 200
গ
Tk. 225
ঘ
Tk. 250

ব্যাখ্যা

Question: A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

Solution:
Let, cost price of the machine is x taka

Selling price = 1.1x taka

ATQ,
1.1x - 40 = 0.9x
⇒ 1.1x - 0.9x = 40
⇒ 0.2x = 40
⇒ x = 40/.2
= Tk. 200

৬,৫৮০.

In a selection process, the ratio of applicants who were selected to those who were rejected is 10 : 4. If 420 applicants were rejected, what was the total number of applicants?

ক
1400
খ
1520
গ
1620
ঘ
1470

ব্যাখ্যা

Question: In a selection process, the ratio of applicants who were selected to those who were rejected is 10 : 4. If 420 applicants were rejected, what was the total number of applicants?

Solution:
Given ratio,
Selected : Rejected = 10 : 4
This means for every 10 selected applicants, 4 are rejected.

Let, Number of selected applicants = 10k
Number of rejected applicants = 4k

According to the question,
Rejected applicants = 420
So, 4k = 420
⇒ k = 420/4
∴ k = 105

∴ Selected applicants = 10k = 10 × 105 = 1050
∴ Rejected applicants = 4k = 420 (given)

∴ Total number of applicants = Selected + Rejected
= 1050 + 420
= 1470

So the total number of applicants was 1470.

৬,৫৮১.

The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is -

ক
490
খ
90
গ
46
ঘ
10

ব্যাখ্যা

Question: The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is

Solution:
let, the numbers are 5x, 5y

5xy = 495
⇒ xy = 495/5
⇒ xy = 99

5(x + y) = 100
⇒ x + y = 20
⇒ x + 99/x = 20
⇒ x² - 20x + 99 = 0
⇒ x² - 11x - 9x + 99 = 0
⇒ x (x - 11) - 9 (x - 11) = 0
⇒ (x - 9) (x - 11) = 0
⇒ x = 9 or, x = 11

if x = 9, y = 11
if x = 11, y = 9

difference = 5 (11 - 9) = 5 × 2 = 10

৬,৫৮২.

What is the value of 0.001/(0.1×0.1)?

ক
ক) 0.01
খ
খ) 0.1
গ
গ) 1.1
ঘ
ঘ) 0.001

ব্যাখ্যা

0.001/(0.1×0.1)
= 0.001/0.01
= 100/1000
= 0.1

৬,৫৮৩.

A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Taka 855, the total profit is?

ক
Tk. 2250
খ
Tk. 1500
গ
Tk. 2500
ঘ
Tk. 1800

ব্যাখ্যা

Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's
share is Taka 855, the total profit is?

Solution:
Given that,
A and B invest in a business in the ratio = 3 : 2
5% of the total profit goes to charity
A’s share of the remaining profit = Tk. 855
Now,
Let the total profit = Tk. x
5% of x goes to charity, so the remaining profit = 95% of x = 95x/100
A’s share = (3/5)(95x/100) = 57x/100

ATQ,
⇒ 57x/100 = 855
⇒ x = (855 × 100)/57
⇒ x = 15 × 100
∴ x = 1500

∴ Total profit = Tk. 1500

৬,৫৮৪.

10 men survive 24 days on 15 cans of food. How many cans are needed for 8 men to survive 36 days?

ক
15
খ
16
গ
17
ঘ
18

ব্যাখ্যা

Question: 10 men survive 24 days on 15 cans of food. How many cans are needed for 8 men ot survive 36 days?

Solution:
10 জন মানুষের 24 দিনে প্রয়োজন 15 ক্যানস
10 জন মানুষের 1 দিনে প্রয়োজন 15/24 ক্যানস
10 জন মানুষের 36 দিনে প্রয়োজন ( 15 × 36)/24
1 জন মানুষের 36 দিনে প্রয়োজন ( 15 × 36)/(24 × 10) ক্যানস
8 জন মানুষের 36 দিনে প্রয়োজন = (15 × 36 × 8)/(24 × 10)
= 18 ক্যানস

৬,৫৮৫.

The average weight of three friends is 35 kg. None of the friends weighs less than 33 kg. What can be the maximum weight of any of the three friends?

ক
37 kg
খ
39 kg
গ
40 kg
ঘ
41 kg

ব্যাখ্যা

Question: The average weight of three friends is 35 kg. None of the friends weighs less than 33 kg. What can be the maximum weight of any of the three friends?

Solution:
Here,
The average weight of three friends is 35 kg

∴ Total weight of three friends = (35 × 3) kg
= 105 kg

Minimum weight of two friends (33 × 2) kg
= 66 kg

∴ The maximum weight of any three friends is (105 - 66) kg
= 39 kg

৬,৫৮৬.

Though Zaman was a rich man, he preferred humility in his interactions. (Make it compound)

ক
Zaman was a rich man and prefer humility in his interactions.
খ
Zaman was a rich man yet preferred humility in his interactions.
গ
Zaman was a rich man yet he prefer humility in his interactions.
ঘ
Zaman is a rich man yet he preferred humility in his interactions.

ব্যাখ্যা

♦ Complex sentence to compound sentence:

• Though/Although যুক্ত complex sentence কে compound sentence- এ পরিবর্তন করতে but/yet coordinate marker ব্যবহার করতে হয়।

- অর্থাৎ দুইটা sentence- এর অর্থ যদি পরস্পর বিপরীত হয় তাহলে but/yet দ্বারা compound sentence করতে হয়।

Example:
• Complex: Though Zaman was a rich man, he preferred humility in his interactions.
• Compound: Zaman was a rich man yet preferred humility in his interactions.

৬,৫৮৭.

A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

ক
75
খ
133
গ
80
ঘ
120

ব্যাখ্যা

Question: A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

Solution:
এখানে ৪% লাভ দেয়া স্টকটি বর্তমানে ৫% লাভ দেয়।

অর্থাৎ,
বর্তমানে ৫ টাকা লাভ করতে বিনিয়োগ করতে হবে ১০০ টাকা
বর্তমানে ১ টাকা লাভ করতে বিনিয়োগ করতে হবে ১০০/৫ টাকা
বর্তমানে ৪ টাকা লাভ করতে বিনিয়োগ করতে হবে (১০০ × ৪)/৫ টাকা
= ৮০ টাকা

∴ স্টকটির বাজারমূল্য ৮০ টাকা।

৬,৫৮৮.

ক
13/8
খ
15/8
গ
17/8
ঘ
18/7

ব্যাখ্যা

Question:

Solution:

৬,৫৮৯.

Which number will complete the series:
155, 151, 147, 143, 139, ........?

ক
132
খ
136
গ
135
ঘ
134

ব্যাখ্যা

Question: Which number will complete the series:
155, 151, 147, 143, 139, ........?

Solution:
The pattern is followed by
155 - 4 = 151
151 - 4 = 147
147 - 4 = 143
143 - 4 = 139
139 - 4 = 135

Hence the number= 135.

৬,৫৯০.

The ratio between the speed of two cars is 7:8. If the 2 nd car runs 200 km in 5 hr, then find the speed of the first car-

ক
ক) 25 Km/hr
খ
খ) 28 Km/hr
গ
গ) 40 Km/hr
ঘ
ঘ) 35 Km/hr
ঙ
ঙ) 37 km/hr

ব্যাখ্যা

Let the speed of first car = 7x
2nd car = 8x.

According to the question
8x = 200/5 = 40 [using speed = distance time]
x = 40/8 = 5

Speed of first car = 7x = 7 X 5 = 35 Km/hr

৬,৫৯১.

Altaf saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent he save in the transaction?

ক
(120/11)%
খ
(100/11)%
গ
(91/11)%
ঘ
10%

ব্যাখ্যা

Question: Altaf saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent he save in the transaction?

Solution:
cost price = 25 + 2.5 = 27.5 taka

Approximate save = (2.5/27.5) × 100%
= (100/11)%

৬,৫৯২.

The diagonal of a rectangle is √41 cm and its area is 20cm². What is the perimeter of the rectangle?

ক
ক) 16cm
খ
খ) 17cm
গ
গ) 20cm
ঘ
ঘ) 18cm

ব্যাখ্যা

Let, Length = a, width = b
So, area, ab = 20

ATQ,
diagonal = √(a² + b²) = √41
⇒ a² + b²= 41
⇒ (a + b)² – 2ab = 41
⇒ (a + b)² – 2×20 = 41
⇒ (a + b)² = 41 + 40 = 81
⇒ a + b = 9
∴ Perimeter = 2(a + b) = 2×9 = 18 cm

৬,৫৯৩.

Three angles of a triangle are in proportion 5 : 6 : 7. Then what is the difference in degrees between he biggest and the smallest angles?

ক
ক) 20°
খ
খ) 10°
গ
গ) 30°
ঘ
ঘ) 25°

ব্যাখ্যা

Question: Three angles of a triangle are in proportion 5 : 6 : 7. Then what is the difference in degrees between he biggest and the smallest angles?

Solution:
অনুপাতগুলোর যোগফল = 18
তিন কোণের সমষ্টি = 180°

∴ বৃহত্তম কোণের পরিমাণ = (7 × 180)/18
= 70°

ক্ষুদ্রতম কোণের পরিমাণ = (5 × 180)/18
= 50°

∴ বৃহত্তম কোণ ও ক্ষুদ্রতম কোণের পার্থক্য = (70° - 50°)
= 20°

৬,৫৯৪.

To find the difference between the compound interest (compounded annually) and the simple interest on Tk. 17700 deposited at a 4% annual interest rate for 2 years.

ক
Tk. 32.32
খ
Tk. 26
গ
Tk. 28.32
ঘ
Tk. 32
ঙ
None of these

ব্যাখ্যা

Question: To find the difference between the compound interest (compounded annually) and the simple interest on Tk. 17700 deposited at a 4% annual interest rate for 2 years.

Solution:
Given that,
Principal, P = Tk. 17700
Rate of Interest, r = 4% per annum
Time, n = 2 years

We know,
Simple Interest(SI) = (P × r × n)/100
SI = (17700 × 4 × 2)/100
= (141600)/100
= Tk. 1,416

Compound Interest (CI),
CI = 17700 × (1 + 4/100)² - 17700
= {17700 × (104/100)²} - 17700
= {17700 × (104/100) × (104/100)} - 17700
= {(177 × 10816)/100} - 17700
= 19144.32 - 17700
= Tk. 1,444.32

∴ Difference = CI - SI = 1444.32 - 1416 = 28.32

৬,৫৯৫.

what is the angle between the hour and minute hands of a clock when it is 3 : 20?

ক
25°
খ
35°
গ
20°
ঘ
30°

ব্যাখ্যা

Question: what is the angle between the hour and minute hands of a clock when it is 3 : 20?

Solution:
3 টা 20 মিনিট = 3 + (20/60) ঘণ্টা
= 3 + 1/3 = 10/3 ঘণ্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে
ঘণ্টার কাঁটা 1 ঘণ্টায় = 360°/12 = 30°
ঘণ্টার কাঁটা 10/3 ঘণ্টায় = 30° × 10/3 = 100° ঘোরে

আবার,
মিনিটের কাঁটা 60 মিনিটে ঘোরে 360°
মিনিটের কাঁটা 1 মিনিটে ঘোরে 360°/60 = 6°
মিনিটের কাঁটা 20 মিনিটে ঘোরে (6 × 20) = 120° ঘোরে

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |120° - 100°| = 20°

৬,৫৯৬.

The area of a rhombus is 96 sq.cm and the length of one of the diagonals is 16 cm. The length of the other diagonal is -

ক
ক) 18
খ
খ) 12
গ
গ) 9
ঘ
ঘ) 6

ব্যাখ্যা

আমরা জানি,
রম্বসের ক্ষেত্রফল = 1/2 × কর্ণদ্বয়ের গুণফল ।
অর্থ্যাৎ 1/2 × 16 × অপর কর্ণ = 96
⇒ অপর কর্ণ = (96 × 2 )/16 c.m.
⇒ অপর কর্ণ = 12 c.m.
Answer: অপর কর্ণের দৈর্ঘ্য 12 c.m.

৬,৫৯৭.

Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 48. Then the average mark obtained by the girls is:

ক
32
খ
35
গ
36
ঘ
38

ব্যাখ্যা

Question: Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 48. Then the average mark obtained by the girls is:

Solution:
Average mark of 40 students is 45
Total mark of 40 students is (45 × 40)
= 1800

Average mark of all the 30 boys is 48
Total mark of all the 30 boys is (48 × 30)
= 1440

∴ Total marks of all the 10 girls is (1800 - 1440) = 360
The average mark of all the 10 girls is 360/10 = 36

৬,৫৯৮.

An alloy contains Copper, Zinc and Nickel in the ratio of 5 : 3 : 2. The quantity of Nickel that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is-

ক
10 kg
খ
14 kg
গ
16 kg
ঘ
20 kg

ব্যাখ্যা

Question: An alloy contains Copper, Zinc and Nickel in the ratio of 5 : 3 : 2. The quantity of Nickel that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is-

Solution:
Given that,
An alloy contains Copper : Zinc : Nickel = 5 : 3 : 2
Total weight = 100 kg

Now, Sum of the ratio, 5 + 3 + 2 = 10
Copper = (

kg
Zinc = (3/10)

kg
Nickel = (2/10)

kg

Now, Let the amount of Nickel to be added be x kg
Then, new quantity of Nickel =

Nickel that must be added 10 kg.

৬,৫৯৯.

In the picture area of the square ABCD is 196 square miles, O is the center of the circle. What will be the area of the circle in square miles?

ক
ক) 100π
খ
খ) 49π
গ
গ) 144π
ঘ
ঘ) 64π

ব্যাখ্যা

Question: In the picture area of the square ABCD is 196 square miles, O is the center of the circle. What will be the area of the circle in square miles?

Solution:
Area of the square ABCD is 196 square miles
Side of square = √196
= 14 miles

Diameter of circle = side of square
= 14 miles
Radius = 14/2 miles
= 7 miles

∴ Area of circle = π7²
= 49π square miles

৬,৬০০.

A bag contains 3 red, 4 green, and 3 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

ক
7/15
খ
2/21
গ
5/12
ঘ
7/12

ব্যাখ্যা

Question: A bag contains 3 red, 4 green, and 3 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 = (3 + 4 + 3)
= 10

Then, n(S) = Number of ways of drawing 2 balls out of 10
= ¹⁰C₂ = 45

Let, E = Event of 2 balls, none of which is blue
∴ n(E) = Number of ways of drawing 2 balls out of (3 + 4) balls
= ⁷C₂ = 21

∴ P(E) = n(E)/n(S)
= 21/45
= 7/15