Bank Math

PrepBank · পাতা ৫ / ১৬১ · ৪০১–৫০০ / ১৬,১২৪

৪০১.

729 ml of a mixture contains milk and water in ratio 7: 2. How much of the water is to be added to get a new mixture containing half milk and half water?

ক
ক) 405ml
খ
খ) 81ml
গ
গ) 72ml
ঘ
ঘ) 91ml
ঙ
ঙ) 95ml

সঠিক উত্তর: ক

ক) 405ml

উত্তর

সঠিক উত্তর: ক

ক) 405ml

ক

ব্যাখ্যা

Question: 729 ml of a mixture contains milk and water in ratio 7: 2. How much of the water is to be added to get a new mixture containing half milk and half water?

Solution:
The quantity of milk in mixture is (7/9) × 729 ml
= 567 ml
The quantity of water in mixture is (2/9) × 729 ml
= 162 ml

Let, we have to mix y ml water to to get a new mixture containing half milk and half water.

ATQ,
567/(162 + y) = 1/1
⇒ 567 = 162 + y
⇒ y = 567 - 162
∴ y = 405

৪০২.

Tk 12000 are to be distributed between B and A such that B gets Tk 4000 less than A. The ratio of the amount received by A to that received by B is -

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

সঠিক উত্তর: খ

খ) 2 : 1

উত্তর

সঠিক উত্তর: খ

খ) 2 : 1

খ

ব্যাখ্যা

Question: Tk 12000 are to be distributed between B and A such that B gets Tk 4000 less than A. The ratio of the amount received by A to that received by B is -

Solution:
A + B = 12000..........(i)
A - B = 4000...............(ii)

Now,
A + B + A - B = 12000 + 4000
⇒ 2A = 16000
⇒ A = 8000

So,
B gets = 12000 - 8000 = 4000

∴ A : B = 8000 : 4000 = 2 : 1

৪০৩.

A man spends one-quarter of his income on food. One-fifth of it on rent and remaining which is Tk. 517 on other commodities. What is his total income?

ক
ক) Tk. 890
খ
খ) Tk. 925
গ
গ) Tk. 940
ঘ
ঘ) Tk. 965

সঠিক উত্তর: গ

গ) Tk. 940

উত্তর

সঠিক উত্তর: গ

গ) Tk. 940

গ

ব্যাখ্যা

Question: A man spends one-quarter of his income on food. One-fifth of it on rent and remaining which is Tk. 517 on other commodities. What is his total income?

Solution:
Let the total income be Tk. x
Then remaining money,
x - {(x/4) + (x/5)}
= x - (9x/20)
= 11x/20

ATQ,
11x/20 = 517
⇒ x = (517 × 20)/11
⇒ x = 47 × 20
∴ x = 940

∴ His total income is Tk. 940

৪০৪.

The difference between two integers is 5. Their product is 500. Find the numbers.

ক
ক) 15, 20
খ
খ) 20, 25
গ
গ) 30, 25
ঘ
ঘ) 21, 26

সঠিক উত্তর: খ

খ) 20, 25

উত্তর

সঠিক উত্তর: খ

খ) 20, 25

খ

ব্যাখ্যা

Let the integers be x and (x + 5)
Then,
⇔x(x+5)=500
⇔x²+5x−500=0
⇔(x+25)(x−20)=0
⇔x=20
So, the numbers are 20 and 25

৪০৫.

The breadth of a rectangular field is increased by (r + 5)%, and the length decreased by r%. If the area of the field is unchanged, what is the value of r?

ক
ক) 20
খ
খ) 15
গ
গ) 8
ঘ
ঘ) 10

সঠিক উত্তর: ক

ক) 20

উত্তর

সঠিক উত্তর: ক

ক) 20

ক

ব্যাখ্যা

Question: The breadth of a rectangular field is increased by (r + 5)%, and the length decreased by r%. If the area of the field is unchanged, what is the value of r?

Solution:
ধরি,
আয়তক্ষেত্রের দৈর্ঘ্য = x
আয়তক্ষেত্রের প্রস্থ = y
আয়তক্ষেত্রের ক্ষেত্রফল = xy

নতুন ক্ষেত্রফল =[{(100 - r)/100} x] [{(105 + r)/100} y]
={(10500 - 5r - r²)/10000)} xy

প্রশ্নমতে,
{(10500 - 5r - r²)/10000)} xy = xy
⇒ r² + 5r - 500 = 0
⇒ r² + 25r - 20r - 500 = 0
⇒ (r + 25)(r - 20) = 0
∴ r =20

৪০৬.

One-third of one-fourth of a number is 12. Then the number is:

ক
72
খ
96
গ
144
ঘ
166

সঠিক উত্তর: গ

144

উত্তর

সঠিক উত্তর: গ

144

গ

ব্যাখ্যা

Question: One-third of one-fourth of a number is 12. Then the number is:

Solution:
Let the number be p.
We know that the term "of" indicates the sign of multiplication.

Now, it is given that one-third of one-fourth of p is 12, therefore, we have:

1/3 × 1/4 × p = 12
⇒ p/12 = 12
⇒ p = 12 × 12
⇒ p = 144

Hence, the number is 144.

৪০৭.

Three-eighth of 320 chairs was sold at a profit of Tk. 50 each and the rest for Tk. 33600. If the seller makes a profit of 20% on the whole transaction, what is the cost price of each of the chair?

ক
Tk. 150
খ
Tk. 175
গ
Tk. 120
ঘ
Tk. 125

সঠিক উত্তর: ক

Tk. 150

উত্তর

সঠিক উত্তর: ক

Tk. 150

ক

ব্যাখ্যা

Question: Three-eighth of 320 chairs was sold at a profit of Tk. 50 each and the rest for Tk. 33600. If the seller makes a profit of 20% on the whole transaction, what is the cost price of each of the chair?

Solution:
Three-eighth of 320 = (320 × 3)/8 = 120

120 chairs were sold at a profit of Tk. 50 each.
Profit on these 120 chairs = 6000.

S.P. of all 320 chairs = (C.P. of 120 chairs + Profit on 120 chairs) + S.P. of 200 chairs
= (120 × C.P) + 6000 + 33600
= (120 × C.P.) + 39600

But these 320 chairs were sold at a profit of 20%.
∴ S. P. of 320 chair is = (120/100) ×(320 × C.P.) = 1.2 × 320 × C.P. = 384 × C.P.

Now,
384 × C.P = 120 × C. P. + 39600
⇒ 384 C.P. = 120 C.P. + 39600
⇒ 264 C.P. = 39600
⇒ C. P. = 150.

৪০৮.

Rana was standing on comilla rail station which is 120 meters long. He finds that a train crosses the platform in 20 seconds and crosses him in 8 seconds . how fast was the train travelling?

ক
12 m/s
খ
8 m/s
গ
10 m/s
ঘ
9 m/s

সঠিক উত্তর: গ

10 m/s

উত্তর

সঠিক উত্তর: গ

10 m/s

গ

ব্যাখ্যা

Question: Rana was standing on comilla rail station which is 120 meters long. He finds that a train crosses the platform in 20 seconds and crosses him in 8 seconds . how fast was the train travelling?

Solution:
Let,
The length of the train = a meters.
It covers a meters in 8 sec and (a + 120) meters in 20 seconds.

So,
(a/8) = (a + 120)/20
⇒ 20a = 8(a + 120)
⇒ 20a = 8a + 960
⇒ 20a - 8a = 960
⇒ 12a = 960
∴ a = 80 meters

So, speed = a/8 = 80/8 = 10 m/s

৪০৯.

From a circular sheet of paper with a radius of 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

ক
4 : 3
খ
3 : 1
গ
3 : 4
ঘ
1 : 3

সঠিক উত্তর: খ

3 : 1

উত্তর

সঠিক উত্তর: খ

3 : 1

খ

ব্যাখ্যা

Question: From a circular sheet of paper with a radius of 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

Solution:
Area of the sheet of paper with a radius of 20 cm. = π(20)2 = 400π cm²
Area of 4 circles of radius 5 cm. = 4 × π(5)²=100π cm²
Area of remaining portion = 400π - 100π = 300π cm²
Therefore, the required ratio = 300π : 100π = 3 : 1

৪১০.

The average weight of 16 boys in a class is 50kg and that of the remaining 8 boys is 45kg. Find the average weight of all the boys in the class.

ক
ক) 48.33 kg
খ
খ) 42.73 kg
গ
গ) 41.43 kg
ঘ
ঘ) 49.25 kg

সঠিক উত্তর: ক

ক) 48.33 kg

উত্তর

সঠিক উত্তর: ক

ক) 48.33 kg

ক

ব্যাখ্যা

Question: The average weight of 16 boys in a class is 50kg and that of the remaining 8 boys is 45kg. Find the average weight of all the boys in the class.

Solution:
Required average = (50 × 16 + 45× 8)/(16 + 8)
= (800 + 360)/24
= 1160/24
= 48.33

৪১১.

132 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

ক
336 m
খ
178 m
গ
1680 m
ঘ
168 m

সঠিক উত্তর: ঘ

168 m

উত্তর

সঠিক উত্তর: ঘ

168 m

ঘ

ব্যাখ্যা

Question: 132 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Solution:
Let, the length of the wire be h
Radius = 1/2 mm = 1/20 cm

ATQ,
πr²h = 132
⇒ (22/7) × (1/20)² × h = 132
⇒ h = (132 × 7 × 20 × 20)/22
⇒ h = 16800 cm
⇒ h = 16800/100 m
∴ h = 168 m

৪১২.

The L.C.M. of (6x² - x - 1), (3x² + 7x + 2) and (2x² + 3x - 2) is

ক
ক) (2x - 1) (3x + 1) (3x + 2)
খ
খ) (2x - 1) (3x + 1) (x - 2)
গ
গ) (2x + 1) (3x - 1) (x + 2)
ঘ
ঘ) (2x - 1) (3x + 1) (x + 2)

সঠিক উত্তর: ঘ

ঘ) (2x - 1) (3x + 1) (x + 2)

উত্তর

সঠিক উত্তর: ঘ

ঘ) (2x - 1) (3x + 1) (x + 2)

ঘ

ব্যাখ্যা

6x² - x - 1 = 6x² - 3x + 2x - 1
= 3x(2x - 1) + 1(2x - 1)
= (2x - 1) (3x + 1)

(3x²+ 7x + 2) = 3x² + 6x + x + 2
= 3x(x + 2) + 1(x + 2)
= (x + 2)(3x + 1)

(2x² + 3x - 2) = 2x² + 4x - x - 2
= 2x(x + 2) - 1(x + 2)
= (x + 2) (2x - 1)

∴ Required L.C.M. is = (2x - 1) (3x + 1) (x + 2)

৪১৩.

A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-

ক
8 hours
খ
10 hours
গ
11 hours
ঘ
12 hours

সঠিক উত্তর: খ

10 hours

উত্তর

সঠিক উত্তর: খ

10 hours

খ

ব্যাখ্যা

Question: A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-

Solution:
Let, A alone can fill the reservoir in x hours
B can fill in x + 5 hours

Both complete in 1 hour = (1/x) + (1/ x + 5)
= (2x + 5)/(x² + 5x)

In 6 hour Both together fill the full part or 1
In 1 hour Both together fill 1/6 part

Now
(2x + 5)/(x² + 5x) = 1/6
⇒ x² + 5x = 12x + 30
⇒ x² - 7x - 30 = 0
⇒ x² - 10x + 3x - 30 = 0
⇒ x(x - 10) + 3(x - 10) = 0
⇒ (x - 10) (x + 3) = 0
∴ x = 10 or, x = - 3 , negative value not possible

A alone can fill the reservoir in 10 hours

৪১৪.

A car travels first half distance between two places with a speed of 40 km/hr and rest of the half distance with a speed of 60 km/hr. The average speed of the car is-

ক
ক) 48 km/hr
খ
খ) 37 km/hr
গ
গ) 44 km/hr
ঘ
ঘ) 45 km/hr

সঠিক উত্তর: ক

ক) 48 km/hr

উত্তর

সঠিক উত্তর: ক

ক) 48 km/hr

ক

ব্যাখ্যা

Here, 2xy/(x+y) = (2×40×60)/(40+60) = 48

৪১৫.

In a zoo, there are deer and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of ducks in the zoo?

ক
120
খ
136
গ
150
ঘ
160

সঠিক উত্তর: খ

136

উত্তর

সঠিক উত্তর: খ

136

খ

ব্যাখ্যা

Question: In a zoo, there are deer and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of ducks in the zoo?

Solution:
ধরি, হাঁসের সংখ্যা x টি ও হরিণের সংখ্যা y টি

x + y = 180
⇒ 4x + 4y = 720

2x + 4y = 448

4x + 4y - 2x - 4y = 720 - 448
⇒ 2x = 272
∴ x = 136

হাঁসের সংখ্যা ১৩৬ টি

৪১৬.

If b is one-fourth of a, then what is the value of

ক
1/4
খ
1/3
গ
1
ঘ
2/3
ঙ
5/2

সঠিক উত্তর: ঙ

5/2

উত্তর

সঠিক উত্তর: ঙ

5/2

ঙ

ব্যাখ্যা

Question: If b is one-fourth of a, then what is the value of

Solution:
Given, b = 1/4 of a = a/4

Now,

৪১৭.

Rahim is saving for a new bike which will cost Tk. 48000. Rahim earns Tk. 150000 per month. Rahim spends his money on bills, food and extras in the ratio 8 : 3 : 4. Of the money he spends on extras, he spends 80% and puts 20% into his savings account. How long will it take Rahim to save for his new bike?

ক
1 month
খ
3 months
গ
5 months
ঘ
6 months

সঠিক উত্তর: ঘ

6 months

উত্তর

সঠিক উত্তর: ঘ

6 months

ঘ

ব্যাখ্যা

Question: Rahim is saving for a new bike which will cost Tk. 48000. Rahim earns Tk. 150000 per month. Rahim spends his money on bills, food and extras in the ratio 8 : 3 : 4. Of the money he spends on extras, he spends 80% and puts 20% into his savings account. How long will it take Rahim to save for his new bike?

Solution:
Rahim’s earnings of Tk. 150000 are divided in the ratio of 8 : 3 : 4.

The total number of shares is 8 + 3 + 4 = 15.

Each share is worth Tk. 150000 ÷ 15 = 10000

Rahim spends 4 shares on extras so 4 × 10000 = 40000

20% of 40000 = 8000

The number of months it will take Rahim is 48000 ÷ 8000 = 6

৪১৮.

Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

ক
Tk. 15435
খ
Tk. 15400
গ
Tk. 1455
ঘ
Tk. 1400
ঙ
Tk. 1435

সঠিক উত্তর: ঙ

Tk. 1435

উত্তর

সঠিক উত্তর: ঙ

Tk. 1435

ঙ

ব্যাখ্যা

Question: Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

Solution:
Let the sum P = 14000.
Rate of interest = 5%
Period = 2 years

Hence, compound interest = 14000(1 + 5/100)² - 14000
= 14000(1.05)² - 14000
= 14000 × 1.05 × 1.05 - 14000
= 15435 - 14000
= 1435

৪১৯.

If the total payroll expense of a certain business in year Y was Tk. 84000, which was 20 percent more than in year X, what was the total payroll expense in year X?

ক
Tk. 70000
খ
Tk. 68320
গ
Tk. 64000
ঘ
Tk. 60000
ঙ
Tk. 52320

সঠিক উত্তর: ক

Tk. 70000

উত্তর

সঠিক উত্তর: ক

Tk. 70000

ক

ব্যাখ্যা

Question: If the total payroll expense of a certain business in year Y was Tk. 84000, which was 20 percent more than in year X, what was the total payroll expense in year X?

Solution:
Total payroll expense in year Y was Tk. 84000, that is 20% more than year X = 120% of X

∴ 120% of X = 84000
⇒ (120/100) × X = 84000
⇒ X = (84000 × 100)/120
∴ X = 70000

৪২০.

Solution set of the inequality,
2x + 3 > 5x - 6 is-

ক
(∞, 6)
খ
(- ∞, 3)
গ
[- ∞, - 3)
ঘ
(- ∞, - 3]

সঠিক উত্তর: খ

(- ∞, 3)

উত্তর

সঠিক উত্তর: খ

(- ∞, 3)

খ

ব্যাখ্যা

Question: Solution set of the inequality,
2x + 3 > 5x - 6 is-

Solution:
2x + 3 > 5x - 6
⇒ 3 > 5x - 2x - 6
⇒ 3 + 6 > 3x
⇒ 9 > 3x
⇒ 3 > x
⇒ x < 3

∴ নির্ণেয় সমাধান সেট: (- ∞, 3)

৪২১.

A sum of money at simple interest amount to tk. 2,800 in 2 years and to tk. 3,250 in 5 years at a rate of:

ক
4%
খ
6%
গ
3%
ঘ
5%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A sum of money at simple interest amount to tk. 2,800 in 2 years and to tk. 3,250 in 5 years at a rate of:

Solution:
Simple interest for 3 years = (3250 - 2800) Tk.
= Tk. 450
∴ Simple Interest for 3 years = Tk. 450
∴ Simple Interest for 5 years = Tk. (450 × 5/3)
= Tk. 750

∴ Principal = 3250 - 750 = Tk. 2500

We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (750 × 100)/(2500 × 5)
∴ r = 6%

৪২২.

The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Tk. 6000. By what percent is the salary of C more than that of A?

ক
ক) 100%
খ
খ) 200%
গ
গ) 300%
ঘ
ঘ) 600%
ঙ
ঙ) 350%

সঠিক উত্তর: খ

খ) 200%

উত্তর

সঠিক উত্তর: খ

খ) 200%

খ

ব্যাখ্যা

Let the salaries of A, B, C be x, 2x and 3x respectively.
Then, 2x + 3x = 6000
=> x = 1200.
A's salary = TK. 1200, B's salary = TK. 2400, and Cs salary TK. 3600.
Excess of C's salary over A's = [(2400/1200) x 100]
= 200%.

৪২৩.

If a train of length 120 meters, crosses a tree in 6 seconds, then the time taken to covers 24 km by the train is: (in minutes)

ক
12
খ
20
গ
11
ঘ
14

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Length of the train = 120 m
Time taken to cross the tree = 6 seconds.
According to the question,
The time taken by the train to cover 120 m is 6 seconds.
Speed of the train = distance/time
= 120/6 m/s.
= 20 m/s.
Time taken to cover 24 km (24000 m) = 24000/20 seconds
= 1200 seconds
Since, 60 seconds = 1 minute
Then,
1200 seconds = 1200/60 minutes.
= 20 minutes.
Hence, the answer is 20 minutes.

৪২৪.

Two trains of equal length are running on parallel lines in the same direction at 65 km/hr and 80 km/hr. The faster train passes the slower train in 48 seconds. The length of each train is:

ক
80 m
খ
100 m
গ
120 m
ঘ
150 m

সঠিক উত্তর: খ

100 m

উত্তর

সঠিক উত্তর: খ

100 m

খ

ব্যাখ্যা

Question: Two trains of equal length are running on parallel lines in the same direction at 65 km/hr and 80 km/hr. The faster train passes the slower train in 48 seconds. The length of each train is:

Solution:
যেহেতু ট্রেন দুটি একই দিকে চলছে, তাই তাদের আপেক্ষিক গতিবেগ হবে তাদের গতিবেগের পার্থক্য।
আপেক্ষিক গতিবেগ = (80 - 65) কিমি/ঘন্টা
= 15 কিমি/ঘন্টা
= 15 × (5/18) মিটার/সেকেন্ড
= 75/18 মিটার/সেকেন্ড
= 25/6 মিটার/সেকেন্ড

ধরি, প্রতিটি ট্রেনের দৈর্ঘ্য x মিটার।
যখন দ্রুতগামী ট্রেনটি ধীরগামী ট্রেনটিকে অতিক্রম করে, তখন মোট অতিক্রান্ত দূরত্ব হয় উভয় ট্রেনের দৈর্ঘ্যের যোগফল।
∴ মোট অতিক্রান্ত দূরত্ব = (x + x) মিটার = 2x মিটার

এখন,
দূরত্ব = গতিবেগ × সময়
2x = (25/6) × 48
2x = 25 × 8
2x = 200
x = 100 মিটার

সুতরাং, প্রতিটি ট্রেনের দৈর্ঘ্য হলো 100 মিটার।

৪২৫.

A shopkeeper sold one item at a 15% profit and another item at a 5% loss. If the cost price of both items is the same, find the overall profit percent.

ক
6.5%
খ
6%
গ
8.2%
ঘ
5%

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: A shopkeeper sold one item at a 15% profit and another item at a 5% loss. If the cost price of both items is the same, find the overall profit percent.

Solution:
ধরি,
প্রতিটি দ্রব্যের ক্রয়মূল্য = x টাকা

15% লাভে,
একটি দ্রব্যের বিক্রয়মূল্য = x + 15% of x
= x + (15x/100)
= x + (3x/20)
= 23x/20 টাকা

5% ক্ষতিতে,
অপর দ্রব্যের বিক্রয়মূল্য = x - 5% of x
= x - (5x/100)
= x - (x/20)
= 19x/20 টাকা

মোট ক্রয়মূল্য = x + x = 2x টাকা
মোট বিক্রয়মূল্য = (23x/20 + 19x/20) টাকা
= 42x/20
= 21x/10 টাকা

∴ মোট লাভ = বিক্রয়মূল্য - ক্রয়মূল্য
= (21x/10) - 2x
= x/10 টাকা

∴ শতকরা লাভ = (লাভ/ক্রয়মূল্য) × 100%
= (x/10 ÷ 2x) × 100%
= (1/20) × 100%
= 5%

৪২৬.

3 workers can do a job in 12 days. Two of the workers work twice as fast as the third. How long it will take if one of the faster workers do the job himself?

ক
ক) 12 minutes
খ
খ) 15 minutes
গ
গ) 18 minutes
ঘ
ঘ) None of these

সঠিক উত্তর: ঘ

ঘ) None of these

উত্তর

সঠিক উত্তর: ঘ

ঘ) None of these

ঘ

ব্যাখ্যা

৩ জন শ্রমিক একটি কাজ ১২ দিনে করতে পারে।
এই ৩ জনের মধ্যে ২ জন ৩য় জনের তুলনায় দ্বিগুণ কাজ করতে পারে।
প্রথম দুজনের ১ জন শ্রমিকের কাজ = ২ × ৩য় শ্রমিকের কাজ।
সুতরাং ৩ জন শ্রমিকের কাজ = ৫ × ৩য় শ্রমিকের কাজ।
৫ × ৩য় শ্রমিক কাজটি করতে পারে = ১২ দিনে
৩য় শ্রমিক কাজটি করতে পারে = ৫ × ১২ দিনে = ৬০ দিনে।
২ × ৩য় শ্রমিক কাজটি করতে পারে = ৬০/২ দিনে = ৩০ দিনে
নির্ণেয় সময় = ৩০ দিন

৪২৭.

A dice is thrown randomly. What is the probability that the number shown on the dice is not divisible by 3?

ক
1/3
খ
1/2
গ
3/4
ঘ
2/3

সঠিক উত্তর: ঘ

2/3

উত্তর

সঠিক উত্তর: ঘ

2/3

ঘ

ব্যাখ্যা

Question: A dice is thrown randomly. What is the probability that the number shown on the dice is not divisible by 3?

Solution:
Numbers on dice are {1, 2, 3, 4, 5, 6}
Numbers on dice not divisible by 3 are {1, 2, 4, 5}
Number of favorable outcomes = 4
Total possible outcomes = 6

∴ The probability that the number shown on the dice is not divisible by 3 is 4/6 = 2/3

৪২৮.

A is 6 times greater than B then by what percent is B smaller than A?

ক
83.33%
খ
85%
গ
89.33%
ঘ
72%
ঙ
None

সঠিক উত্তর: ঙ

None

উত্তর

সঠিক উত্তর: ঙ

None

ঙ

ব্যাখ্যা

Question: A is 6 times greater than B then by what percent is B smaller than A?

Solution:

Let B = 10

Then, A = 10 + 60 = 70

∴ A - B = 70 - 10 = 60

B is 60 less than A.

∴ B, % less than A = (60/70) × 100 = 85.71%

৪২৯.

A man can row 6 km/hr in still water. It the speed of the current is 2 km/hr, it takes 3 hrs more in upstream than in the downstream for the same distance. The distance is _____

ক
ক) 30 km
খ
খ) 24 km
গ
গ) 20 km
ঘ
ঘ) 32 km

সঠিক উত্তর: খ

খ) 24 km

উত্তর

সঠিক উত্তর: খ

খ) 24 km

খ

ব্যাখ্যা

Question: A man can row 6 km/hr in still water. It the speed of the current is 2 km/hr, it takes 3 hrs more in upstream than in the downstream for the same distance. The distance is _____

Solution:
ধরি,
দূরত্ব = x কি.মি.

প্রশ্নমতে,
x/(6 - 2) - x/(6 + 2) = 3
⇒ x/4 - x/8 = 3
⇒ (2x - x)/8 = 3
⇒ x/8 = 3
∴ x = 24

∴ নির্ণেয় দূরত্ব 24 কি.মি.

৪৩০.

Solve: x⁴ - 5x² + 4 = 0

ক
± 1, ± 5
খ
± 3, ± 2
গ
± 1, ± 2
ঘ
± 4, ± 1

সঠিক উত্তর: গ

± 1, ± 2

উত্তর

সঠিক উত্তর: গ

± 1, ± 2

গ

ব্যাখ্যা

Question: Solve: x⁴ - 5x² + 4 = 0

Solution:
Given,
x⁴ - 5x² + 4 = 0
(x²)² - 5x² + 4 = 0
Let
x² = a

∴ a² - 5a + 4 = 0
⇒ a² - 4a - a + 4 = 0
⇒ a(a - 4) - 1(a - 4) = 0
⇒ (a - 4)(a - 1) = 0

∴ a - 4 = 0
⇒ a = 4
⇒ x² = 4
∴ x = ± 2

and,
a - 1 = 0
⇒ a = 1
⇒ x² = 1
∴ x = ± 1

∴ x = ± 1, ± 2

৪৩১.

Raktim sold a book at a loss of 30%. If he has sold it for Tk. 140 more, he would have made a profit of 40%. The cost price of the book is =?

ক
Tk. 180
খ
Tk. 200
গ
Tk. 220
ঘ
Tk. 250

সঠিক উত্তর: খ

Tk. 200

উত্তর

সঠিক উত্তর: খ

Tk. 200

খ

ব্যাখ্যা

Question: Raktim sold a book at a loss of 30%. If he has sold it for Tk. 140 more, he would have made a profit of 40%. The cost price of the book is =?

Solution:
let, cost price of the book is x taka

selling price = 0.7x taka

ATQ,
.7x + 140 = 1.4x
⇒ 0.7x = 140
⇒ x = 140/0.7
= Tk. 200

৪৩২.

If p, q, r are non-zero numbers and p + q = r, which of the following is equal to 1?

ক
ক) (p - q)/r
খ
খ) (p - r)/q
গ
গ) (q - r)/p
ঘ
ঘ) (r - q)/p

সঠিক উত্তর: ঘ

ঘ) (r - q)/p

উত্তর

সঠিক উত্তর: ঘ

ঘ) (r - q)/p

ঘ

ব্যাখ্যা

Question: If p, q, r are non-zero numbers and p + q = r, which of the following is equal to 1?

Solution:
p + q = r
⇒ p = r - q

(r - q)/p
= p/p
= 1

৪৩৩.

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 3 women?

ক
3/5
খ
3/8
গ
1/7
ঘ
3/7

সঠিক উত্তর: ঘ

3/7

উত্তর

সঠিক উত্তর: ঘ

3/7

ঘ

ব্যাখ্যা

Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 3 women?

Solution:
A small company employs 3 men and 5 women.
Total people = 8

ways of selecting 4 people from 8 = ⁸C₄
= 70

ways of selecting 3 women from 5 = ⁵C3
ways of selecting 1 men from 3 = ³C₁

∴ probability = (⁵C₃× ³C₁)/ 70
= (10 × 3)/70
= 3/7

৪৩৪.

The product of two numbers is 2028 and their HCF is 13. The number of such pairs is =?

ক
4
খ
3
গ
2
ঘ
1

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: The product of two numbers is 2028 and their HCF is 13. The number of such pairs is =?

Solution:
Let the two numbers be x and y respectively.

It is given that the product of the two numbers is 2028, therefore,
xy = 2028

Also, 13 is their HCF, thus both numbers must be divisible by 13.

So, let x = 13a and y = 13b, then,
13a × 13b = 2028
⇒ 169ab = 2028
⇒ ab = 2028
∴ ab = 12

Therefore, the required possible pair of values of x and y which are prime to each other are (1, 12) and (3, 4).
Thus, the required numbers are (12, 156) and (39, 52).

Hence, the number of possible pairs is 2.

৪৩৫.

Today Al is 3 times as old as Pat. In 13 years, Al will be one year less than twice as old as Pat will be then. How many years old is Al today?

ক
12
খ
33
গ
36
ঘ
42
ঙ
49

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Today Al is 3 times as old as Pat. In 13 years, Al will be one year less than twice as old as Pat will be then. How many years old is Al today?

Solution:
Let,
Age of Al is A
Age of Pat is P
∴ A = 3P

ATQ,
A + 13 = 2(P + 13) - 1
⇒ 3P + 13 = 2P + 26 -1
∴ P = 12

∴ Age of Al is = 3 × 12 = 36 years old

৪৩৬.

A school has only 3 classes having 20, 30 and 40 students respectively. The percentages of students passed are 30%, 50% and 60% respectively. Find the percentage of passed students of the entire school.

ক
ক) 40
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 30

সঠিক উত্তর: খ

খ) 50

উত্তর

সঠিক উত্তর: খ

খ) 50

খ

ব্যাখ্যা

Number of students (passed) = 20×30% + 30×50% + 40×60%
= 6 + 15 + 24
= 45
Percentage of passed students of the entire school = 45/90 × 100 = 50%

৪৩৭.

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%

সঠিক উত্তর: ঘ

20%

উত্তর

সঠিক উত্তর: ঘ

20%

ঘ

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%.
Apply formula:
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

Now, apply formula:
P% = (Profit/C.P) × 100

So, gain % = ((480 - 400)/400) × 100
= 80/4
= 20%

৪৩৮.

If ABC is a right triangle, what is the value of ∠CAB?

ক
45°
খ
65°
গ
55°
ঘ
35°

সঠিক উত্তর: গ

55°

উত্তর

সঠিক উত্তর: গ

55°

গ

ব্যাখ্যা

Question: If ABC is a right triangle, what is the value of ∠CAB?

Solution:
∠C = 360° - 325° = 35°

∠A = 180° - 90° - ∠C
= 180° - 90° - 35°
= 55°

৪৩৯.

The 180 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows except-

ক
4
খ
20
গ
30
ঘ
40

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: The 180 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows except-

Solution:
Obviously the number of rows must be a factor of 180. The only option which is not a factor of 180 is D (40).
180/4=45
180/20=9
180/30=6
180/40=4.50

৪৪০.

The speed of a boat in still water is 5 km/hr. If the speed of the boat against the stream is 3 km/hr, what is the speed of the stream?

ক
1.5 km/hr
খ
2 km/hr
গ
2.5 km/hr
ঘ
1 km/hr

সঠিক উত্তর: খ

2 km/hr

উত্তর

সঠিক উত্তর: খ

2 km/hr

খ

ব্যাখ্যা

Question: The speed of a boat in still water is 5 km/hr. If the speed of the boat against the stream is 3 km/hr, what is the speed of the stream?

Solution:
Let the speed of stream = X km/hr

Speed of boat = 5 km/hr
Speed upstream = 3km/hr

Apply formula:
Speed upstream = speed of boat - speed of stream
3 = 5 - X
∴ X = 5 - 3 = 2 km/hr

৪৪১.

The ratio between the speeds of two trains is 8 : 9. If the second train runs 432 km in 4 hours, then the speed of the first train is:

ক
ক) 84 km/hr.
খ
খ) 72 km/hr.
গ
গ) 96 km/hr.
ঘ
ঘ) 92 km/hr.

সঠিক উত্তর: গ

গ) 96 km/hr.

উত্তর

সঠিক উত্তর: গ

গ) 96 km/hr.

গ

ব্যাখ্যা

Let the speed of two trains be 8x and 9x km/hr.
It is given that the second train runs 432 km in 4 hours,

We have,
9x = 432/4
9x= 108
x = 108/9
x = 12

The speed of the first train is = 8 × 12 = 96 km/hr.

৪৪২.

The electricity bill of a certain establishement is partially fixed and partially varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Tk. 1800. In another month 620 units are consumed are the bill is Tk. 2040. In yet another month if 1000 units are consumed what would be the bill (in Tk.) for the month?

ক
2180 tk
খ
2450 tk
গ
2840 tk
ঘ
None of the above

সঠিক উত্তর: ঘ

None of the above

উত্তর

সঠিক উত্তর: ঘ

None of the above

ঘ

ব্যাখ্যা

Question: The electricity bill of a certain establishement is partially fixed and partially varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Tk. 1800. In another month 620 units are consumed are the bill is Tk. 2040. In yet another month if 1000 units are consumed what would be the bill (in Tk.) for the month?

Solution:
620 Unit এর বিল = 2040 টাকা
540 Unit এর বিল = 1800 টাকা

80 Unit এর বিল = (2040 - 1800) টাকা
= 240 টাকা
1 Unit এর বিল =240/80 = 3 টাকা

540 Unit এর বিল =3 × 540 = 1620 টাকা

540 Unit এ fixed বিলের পরিমাণ = 1800 - 1620 টাকা
= 180 টাকা

1000 Unit এর বিল = 180 + (1000 × 3)টাকা
= 3180 টাকা

৪৪৩.

The average salary of all the workers in a workshop is Tk. 6000. The average salary of 7 technicians is Tk. 12000 and the average salary of the rest is Tk. 5000. How many workers are there?

ক
40
খ
45
গ
49
ঘ
55

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: The average salary of all the workers in a workshop is Tk. 6000. The average salary of 7 technicians is Tk. 12000 and the average salary of the rest is Tk. 5000. How many workers are there?

Solution:
let, there are x number of workers
The average salary of all the workers in a workshop is Rs. 6000
∴ total salary = 6000 × x = 6000x

The average salary of 7 technicians is Tk. 12000
∴ salary of 7 technicians is = (12000 × 7) = 84000 tk

the average salary of the rest is Tk. 5000
∴ salary of the rest = 5000 × (x - 7) tk

5000 × (x - 7) + 84000 = 6000x
⇒ 5000x - 35000 + 84000 = 6000x

⇒ 1000x = 49000
∴ x = 49

so, there are 49 workers.

৪৪৪.

The salaries of Salman and Parimal are in the ratio of 4:5. If the salary of each is increased by Tk. 3000, the new ratio becomes 25:31. What is Parimal's new salary?

ক
65000 tk
খ
76000 tk
গ
89000 tk
ঘ
93000 tk

সঠিক উত্তর: ঘ

93000 tk

উত্তর

সঠিক উত্তর: ঘ

93000 tk

ঘ

ব্যাখ্যা

Question: The salaries of Salman and Parimal are in the ratio of 4:5. If the salary of each is increased by Tk. 3000, the new ratio becomes 25:31. What is Parimal's new salary?

Solution:
Let the original salaries of Salman and Parimal be 4x and 5x respectively.

So,
(4x + 3000)/(5x + 3000) = 25/31
⇒ 124x + 93000 = 125x + 75000
⇒ 125x - 124x = 93000 - 75000
⇒ x = 18000

Parimal's original salary = 5 × 18000 = 90000 tk
So, Parimal's new salary = 90000 + 3000 = 93000 tk

৪৪৫.

The area of a square inscribed in a circle is 70 cm². What is the area of the circle?

ক
110 cm²
খ
120 cm²
গ
220 cm²
ঘ
150 cm²

সঠিক উত্তর: ক

110 cm²

উত্তর

সঠিক উত্তর: ক

110 cm²

ক

ব্যাখ্যা

Question: The area of a square inscribed in a circle is 70 cm². What is the area of the circle?

Solution:
The area of a square inscribed in a circle is 70 cm²
side of square = √70 cm
diagonal of the square = √2 × √70
= 2√70 cm

diameter of circle = √140 cm
= 2√35 cm

radius of the circle = √35 cm

∴ area of the circle = π (√35)² cm²
= (22/7) × 35 cm²
= 110 cm²

৪৪৬.

Find the least number which will leave the remainder 7 when divided by 8, 12, 16, and 20.

ক
237
খ
243
গ
267
ঘ
247

সঠিক উত্তর: ঘ

247

উত্তর

সঠিক উত্তর: ঘ

247

ঘ

ব্যাখ্যা

Question: Find the least number which will leave the remainder 7 when divided by 8, 12, 16, and 20.

Solution:
8 = 2 × 2 × 2;
12 = 2 × 2 × 3;
16 = 2 × 2 × 2 × 2;
20 = 2 × 2 × 5;
LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240;
This is the least number that is exactly divisible by 8, 12, 16, and 20
Thus,
The required number which leaves the remaining 7 is,
240 + 7 = 247

৪৪৭.

Chaman has two big cans of wine and water mixture. Chaman mixes the contents of both the cans in a big container. The new mixture has half water and half wine. In what quantity did Chaman mix contents of Can 1 and 2 if Can 2 has wine to water ratio of 2 : 3 and Can 1 has wine to water ratio 5 : 3?

ক
3 : 4
খ
4 : 5
গ
5 : 6
ঘ
6 : 7

সঠিক উত্তর: খ

4 : 5

উত্তর

সঠিক উত্তর: খ

4 : 5

খ

ব্যাখ্যা

Question: Chaman has two big cans of wine and water mixture. Chaman mixes the contents of both the cans in a big container. The new mixture has half water and half wine. In what quantity did Chaman mix contents of Can 1 and 2 if Can 2 has wine to water ratio of 2 : 3 and Can 1 has wine to water ratio 5 : 3?

Solution:
Let,
Amount taken from Can 1 = x parts
Amount taken from Can 2 = y parts

In Can 1:
Wine = 5x/(8x) of total = 5x/8
Water = 3x/(8x) of total = 3x/8

In Can 2:
Wine = 2y/(5y) of total = 2y/5
Water = 3y/(5y) of total = 3y/5

In final mixture (Wine:Water = 1 : 1)
So, Total Wine = Total Water
⇒ (5x/8) + (2y/5) = (3x/8) + (3y/5)
⇒ (25x + 16y)/40 = (15x + 24y)/40
⇒ 25x + 16y = 15x + 24y
⇒ 25x - 15x = 24y - 16y
⇒ 10x = 8y
∴ x : y = 4 : 5

Therefore, Chaman should mix contents of Can 1 and Can 2 in the ratio 4 : 5.

৪৪৮.

If the length of a rectangle is increased by 20% and width is decreased by 20%, what is the change in area of the rectangle?

ক
unchanged
খ
decreased by 4%
গ
increases by 4%
ঘ
increases by 5%

সঠিক উত্তর: খ

decreased by 4%

উত্তর

সঠিক উত্তর: খ

decreased by 4%

খ

ব্যাখ্যা

Question: If the length of a rectangle is increased by 20% and width is decreased by 20%, what is the change in area of the rectangle?

Solution:
Let,
length of rectangle = 20 and width = 10
so, area = 20 × 10 = 200

Now new length = 20 + 20 × 20%
= 20 + 4
= 24

New Width = 10 - 10 × 20%
= 10 - 2
= 8

So, New area = 24 × 8 = 192

And area decreased by (200 - 192) = 8

In percent = (8/200) × 100 = 4%
So, 4% decreased

৪৪৯.

According to a recent survey of students at a public university, 65% are skilled in Mathematics and 45% are skilled in Statistics. How many students are proficient in both Mathematics and Statistics?

ক
10%
খ
15%
গ
20%
ঘ
25%

সঠিক উত্তর: ক

10%

উত্তর

সঠিক উত্তর: ক

10%

ক

ব্যাখ্যা

Question: According to a recent survey of students at a public university, 65% are skilled in Mathematics and 45% are skilled in Statistics. How many students are proficient in both Mathematics and Statistics?

Solution:
Good at Mathematics n(M) = 65
Good at Statistics n(S) = 45
good in both Mathematics and Statistics n(M ∩ S)

We know that
n(M ∪ S) = n(M) + n(S) - n(M ∩ S)
⇒ n(M ∩ S) = n(M) + n(S) - n(M ∪ S) = 65 + 45 - 100 = 110 - 100 = 10

৪৫০.

40 workers can build 40 engines working 6 hours a day. How many workers need to be appointed extra to boost the production to double if they work 8 hours a days?

ক
20 workers
খ
22 workers
গ
25 workers
ঘ
30 workers
ঙ
32 workers

সঠিক উত্তর: ক

20 workers

উত্তর

সঠিক উত্তর: ক

20 workers

ক

ব্যাখ্যা

Question: 40 workers can build 40 engines working 6 hours a day. How many workers need to be appointed extra to boost the production to double if they work 8 hours a days?

Solution:
6 hours to build 40 engines by 40 workers
1 hour to build 1 engine by = (40 × 6)/40 workers
8 hours to build 80 engine by = (6 × 80)/8 workers
= 60 workers

∴ extra workers = (60 - 40) = 20 workers

৪৫১.

A man on tour travels first 180 km at 96 km/hr and the next 180 km at 80 km/hr. The average speed for the first 360 km of the tour is:

ক
ক) 970/11 km/hr.
খ
খ) 950/11 km/hr.
গ
গ) 810/11 km/hr.
ঘ
ঘ) 960/11 km/hr.

সঠিক উত্তর: ঘ

ঘ) 960/11 km/hr.

উত্তর

সঠিক উত্তর: ঘ

ঘ) 960/11 km/hr.

ঘ

ব্যাখ্যা

Question: A man on tour travels first 180 km at 96 km/hr and the next 180 km at 80 km/hr. The average speed for the first 360 km of the tour is:

Solution:
Total time taken = (180/96) + (180/80)
= (900 + 1080)/480
= 1980/480
= 99/24

Average speed = 360/(99/24) km/hr.
= (360 × 24)/99
= 960/11 km/hr.

৪৫২.

A team of 10 workers can complete a task in 6 days by working 4 hours per day. If the same task is assigned to 15 workers, how many hours per day should they work in order to finish it in 2 days?

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

সঠিক উত্তর: খ

8 hours per day

উত্তর

সঠিক উত্তর: খ

8 hours per day

খ

ব্যাখ্যা

Question: A team of 10 workers can complete a task in 6 days by working 4 hours per day. If the same task is assigned to 15 workers, how many hours per day should they work in order to finish it in 2 days?

Solution:
10 persons can do the work in 6 days by working 4 hours a day
∴ Total man-hours = 10 × 6 × 4 = 240 hours

Let the required hours per day for 15 persons to finish in 2 days = x hours
∴ Total man-hours = 15 × 2 × x = 30x

Equating total work:
30x = 240
⇒ x = 240/30
⇒ x = 8

∴ 15 persons need to work 8 hours per day to complete the work in 2 days.

৪৫৩.

A, B, C enter into partnership, A invests 3 times as much as B invests and B invests two third of what C invests. At the end of the year, profit earned is Tk. 6,600. What is the share of B?

ক
ক) 1,100
খ
খ) 1,150
গ
গ) 1,175
ঘ
ঘ) 1,200

সঠিক উত্তর: ঘ

ঘ) 1,200

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1,200

ঘ

ব্যাখ্যা

ধরি,
C বিনিয়োগ করে x টাকা
B বিনিয়োগ করে (x এর 2/3) টাকা
= 2x/3 টাকা
A বিনিয়োগ করে {3 × (2x/3)} টাকা
=2x টাকা

A , B এবং C এর বিনিয়োগের অনুপাত = 2x : (2x/3) : x
= 2 : (2/3) : 1
= 6 : 2 : 3
বিনিয়োগের অনুপাতের যোগফল = 6 + 2 + 3 = 11

B লাভ পাবে = (6,600 এর 2/11) = 1200 টাকা

৪৫৪.

Asif and Rasel take 9 days to do a particular job. Asif takes 18 days to do the job alone. In how many days can Rasel do the job alone?

ক
ক) 12 days
খ
খ) 15 days
গ
গ) 18 days
ঘ
ঘ) 20 days

সঠিক উত্তর: গ

গ) 18 days

উত্তর

সঠিক উত্তর: গ

গ) 18 days

গ

ব্যাখ্যা

Question: Asif and Rasel take 9 days to do a particular job. Asif takes 18 days to do the job alone. In how many days can Rasel do the job alone?

Solution:
১৮ দিনে আসিফ করে সম্পূর্ণ বা ১ অংশ
∴ ১ দিনে আসিফ করে ১/১৮ অংশ
∴ ৯ দিনে আসিফ করে ৯/১৮ অংশ = ১/২ অংশ

∴ রাসেল ৯ দিনে করে (১ - ১/২) অংশ = ১/২ অংশ

রাসেল ১/২ অংশ করে ৯ দিনে
∴ রাসেল ১ বা সম্পূর্ণ অংশ করে (৯ × ২) দিনে = ১৮ দিনে

৪৫৫.

A and B together have Tk 2250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

ক
Tk. 900
খ
Tk. 1660
গ
Tk. 1350
ঘ
Tk. 1050

সঠিক উত্তর: গ

Tk. 1350

উত্তর

সঠিক উত্তর: গ

Tk. 1350

গ

ব্যাখ্যা

Question: A and B together have Tk 2250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

Solution:
ATQ,
4A/15 = 2B/5
⇒ A = (2B × 15)/(5 × 4)
⇒ A = 3B/2
⇒ A/B = 3/2
⇒ A/B = 3/2

∴ A's share = 2250(3/5) = Tk. 1350

৪৫৬.

Find the LCM of the fractions 2/3, 5/9, 1/3.

ক
10/3
খ
10/9
গ
1/3
ঘ
1/9

সঠিক উত্তর: ক

10/3

উত্তর

সঠিক উত্তর: ক

10/3

ক

ব্যাখ্যা

Question: Find the LCM of the fractions 2/3, 5/9, 1/3.

Solution:
Given,
the fractions are 2/3, 5/9 and 1/3

We know,
LCM of the fraction = LCM of numerator/HCF of denominator

LCM of numerators = LCM of (2, 5, 1) = 2 × 5 × 1 = 10
HCF of denominators = HCF of ( 3, 9, 3) = 3

∴ LCM of fraction = 10/3

৪৫৭.

Working alone, Anik can complete a task in ‘a’ days and Bijoy in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If Anik starts they finish the task in exactly 10 days. If Bijjoy starts, they take half a day more. How long does it take to complete the task if they both work together?

ক
54/11 days
খ
210/41 days
গ
36/7 days
ঘ
None of these

সঠিক উত্তর: গ

36/7 days

উত্তর

সঠিক উত্তর: গ

36/7 days

গ

ব্যাখ্যা

Question: Working alone, Anik can complete a task in ‘a’ days and Bijoy in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If Anik starts they finish the task in exactly 10 days. If Bijjoy starts, they take half a day more. How long does it take to complete the task if they both work together?

Solution:
Let, Anik can complete work in x days and Bijoy can do in y days

If Anik starts,
(6/x) + (4/y) = 1
⇒ 4x + 6y = xy

If Bijoy starts,
(6/y) + (4.5/x) = 1
⇒ 4.5y + 6x = xy

24x + 36y - 18y - 24x = 6xy - 4xy
⇒ 18y = 2xy
⇒ x = 9

36 + 6y = 9y
⇒ 3y = 36
⇒ y = 12

both do one day = (1/9) + (1/12)
= (4 + 3)/36
= 7/36

if they both work together days needed = 36/7 days

৪৫৮.

A moneylender charges Tk. 180 as simple interest on a sum of Tk. 600 for four months. What is the rate of interest per annum?

ক
80%
খ
85%
গ
90%
ঘ
95%

সঠিক উত্তর: গ

90%

উত্তর

সঠিক উত্তর: গ

90%

গ

ব্যাখ্যা

Question: A moneylender charges Tk. 180 as simple interest on a sum of Tk. 600 for four months. What is the rate of interest per annum?

Solution:
Principal = Tk. 600
Interest = Tk. 180
Time = 4 months = 4/12 = 1/3 years
Rate of interest =R

Applying formula: Rate of Interest = (I × 100)/(P × t)
R = (180 × 100)/(600 × 1/3)
= (180 × 100)/200
= 90%

৪৫৯.

1 year ago the ratio between A’s salary and B’s Salary was 3 : 4.Ratios of their individual salaries between last year’s and present year’s are 4 : 5 & 2 : 3 respectively. At present the total of their salary is Tk 4160. The salary of A now is:

ক
ক) 1040
খ
খ) 1600
গ
গ) 2560
ঘ
ঘ) 3120
ঙ
ঙ) None of the above

সঠিক উত্তর: খ

খ) 1600

উত্তর

সঠিক উত্তর: খ

খ) 1600

খ

ব্যাখ্যা

Present ratio of A & B
A : B
3 × (5/4) : 4 × (3/2)
= 15/4 : 12/4
= 15 : 24
= 5 : 8

A’s present salary = ( 4160 of 5/13) = 1600

৪৬০.

Which of the following fractions is smaller than 7/8 and greater than 3/7?

ক
11/12
খ
5/9
গ
4/11
ঘ
1/3

সঠিক উত্তর: খ

5/9

উত্তর

সঠিক উত্তর: খ

5/9

খ

ব্যাখ্যা

Question: Which of the following fractions is smaller than 7/8 and greater than 3/7?

Solution:
7/8 = 0.875
3/7 = 0.4286

ক) 11/12 = 0.917 (> 0.875)
খ) 5/9 = 0.5556 (satisfies the condition)
গ) 4/11 = 0.3636 (< 0.4286)
ঘ) 1/3 = 0.3333 (< 0.4286))

∴ অপশন (খ) সঠিক উত্তর।

৪৬১.

log₃(x⁴ - x³) - log₃(x - 1) = 3 then x is equal to-

ক
1
খ
3
গ
2
ঘ
4

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: log₃(x⁴ - x³) - log₃(x - 1) = 3 then x is equal to-

Solution:
Given that,
⇒ log₃(x⁴ - x³) - log₃(x - 1) = 3
⇒ log₃{(x⁴ - x³)/(x - 1)} = 3
⇒ log₃{x³(x - 1)/(x - 1)} = 3
⇒ log₃x³ = 3
⇒ 3log₃x = 3
⇒ log₃x = 1
⇒ x = 3¹
∴ x = 3

৪৬২.

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

ক
Tuesday
খ
Monday
গ
Friday
ঘ
None of the above

সঠিক উত্তর: ক

Tuesday

উত্তর

সঠিক উত্তর: ক

Tuesday

ক

ব্যাখ্যা

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

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

∴ 16th March, 2004 is Tuesday.

৪৬৩.

The percentage profit earned by selling an article for Tk. 1,920 is equal to the percentage loss incurred by selling the same article for Tk. 1,280. At what price should the article be sold to make 25% profit?

ক
ক) Tk. 2,000
খ
খ) Tk. 2,200
গ
গ) Tk. 2,400
ঘ
ঘ) Data inadequate

সঠিক উত্তর: ক

ক) Tk. 2,000

উত্তর

সঠিক উত্তর: ক

ক) Tk. 2,000

ক

ব্যাখ্যা

Let, the cost price be Tk. x
Now, according to the question
19,20 - x = x - 1,280
⇒ x + x = 19,20 + 1,280
⇒ 2x = 3,200
⇒ x = 3,200 /2
∴ x = 1,600

The cost price of the article is Tk. 1,600.

Now at 25% profit , the selling price will be = {1600 + (1600×25)/100}
= (1600 + 400) Tk.
= 2000 Tk.

৪৬৪.

What would be the mirror image of the clock when the time is 01 : 40?

ক
10 : 20
খ
11 : 20
গ
4 : 10
ঘ
10 : 04

সঠিক উত্তর: ক

10 : 20

উত্তর

সঠিক উত্তর: ক

10 : 20

ক

ব্যাখ্যা

Question: What would be the mirror image of the clock when the time is 01 : 40?

Solution:
Hence,
11 : 60 - 01 : 40
= 10 : 20

∴ The mirror image of 1 : 40 would be 10 : 20.

৪৬৫.

The perimeter of a rectangular field is 104 meters. If the length of the field is 10 meters more than twice the width, what is the area of that field in square meters?

ক
530
খ
532
গ
580
ঘ
588

সঠিক উত্তর: খ

532

উত্তর

সঠিক উত্তর: খ

532

খ

ব্যাখ্যা

Question: The perimeter of a rectangular field is 104 meters. If the length of the field is 10 meters more than twice the width, what is the area of that field in square meters?

Solution:
Let,
The width of the rectangular field is x meter
∴ The length of the rectangular field is 2x + 10 meter

ATQ,
2(2x + 10 + x) = 104
⇒ 3x + 10 = 52
⇒ 3x = 42
∴ x = 14

∴ The area of that field is = (2x + 10) × x = (2 × 14 + 10) × 14 = (28 + 10) × 14 square meters
= 38 × 14 square meters
= 532 square meters

৪৬৬.

If X = 48 and BAT = 46, then MAT will be equal to-

ক
72
খ
68
গ
58
ঘ
54

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: If X = 48 and BAT = 46, then MAT will be equal to-

Solution:

Here,
The Position number of X is 24 which is re-write as 24 × 2 = 48.
Now,
BAT = (2 × 2) + (1 × 2) + (20 × 2)
= 4 + 2 + 40
= 46

Similarly,
MAT = (13 × 2) + (1 × 2) + (20 × 2)
= 26 + 2 + 40
= 68

৪৬৭.

In a class composed of x girls and y boys what part of the class is composed of girls?

ক
ক) y/(x + y)
খ
খ) x/(xy)
গ
গ) x/(x + y)
ঘ
ঘ) y/(xy)
ঙ
ঙ) None of these

সঠিক উত্তর: গ

গ) x/(x + y)

উত্তর

সঠিক উত্তর: গ

গ) x/(x + y)

গ

ব্যাখ্যা

Question: In a class composed of x girls and y boys what part of the class is composed of girls?

Solution:
The part of the class composed of girls can be calculated using the ratio of girls to the total number of students (girls + boys)

Total number of students = x + y

∴ The class is composed of girls = Number of girls / Total number of students
= x/(x + y)

৪৬৮.

Three persons stared a placement business with a capital of Tk. 3000. B invests Tk. 600 less than A and C invests Tk. 300 less than B. What is B's share in a profit of Tk. 886 ?

ক
ক) Tk. 255.50
খ
খ) Tk. 265.80
গ
গ) Tk. 245.70
ঘ
ঘ) Tk. 275.90

সঠিক উত্তর: খ

খ) Tk. 265.80

উত্তর

সঠিক উত্তর: খ

খ) Tk. 265.80

খ

ব্যাখ্যা

Let
A's capital = Tk. x
Then, B's capital = Tk. (x - 600)
C's capital = Tk.(x - 600) - 300 = Tk. (x - 900)
∴ x + (x - 600) + (x - 900) = 3000
⇒ 3x = 4500
⇒ x = 1500
A's capital = Tk. 1500
B's capital = Tk. (1500 - 600) = Tk.900
C's capital = Tk. (1500 - 900) = Tk.600

So, A : B : C=1500 : 900 : 600
=5 : 3 : 2

Hence, B's share= Tk.(886 × 3/10)
= Tk. 265.80

৪৬৯.

The average of 6 numbers is 25. If 3 more numbers, with an average of 22 are added to these numbers, what will be the average of the combined 9 numbers?

ক
24
খ
25
গ
26
ঘ
28

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The average of 6 numbers is 25. If 3 more numbers, with an average of 22 are added to these numbers, what will be the average of the combined 9 numbers?

Solution:
The average of 6 numbers is 25
∴ The total of 6 numbers is 25 × 6 = 150

The average of 3 numbers is 22
∴ The total of 3 numbers is 22 × 3 = 66

The sum of 9 numbers is = 150 + 66 = 216
∴ The average of 9 numbers is 216/9 = 24

৪৭০.

A boat goes 6 km upstream in 24 minutes. The speed of the stream is 3 km/hr. The speed of boat in still water is

ক
12 km/hr
খ
14 km/hr
গ
16 km/hr
ঘ
18 km/hr

সঠিক উত্তর: ঘ

18 km/hr

উত্তর

সঠিক উত্তর: ঘ

18 km/hr

ঘ

ব্যাখ্যা

Question: A boat goes 6 km upstream in 24 minutes. The speed of the stream is 3 km/hr. The speed of boat in still water is

Solution:
The speed upstream is 6/24 km/min
= (6 × 60)/24 km/hr
= 15 km/hr

Let,
The speed of boat in still water is x km/hr

Here, x - 3 = 15
⇒ x = 15 + 3
∴ x = 18

∴ The speed of the boat in still water is 18 km/hr

৪৭১.

A reduction is 25% of the price of an article enables a buyer to buy 50 kilograms more for tk 500. What is the reduced price per kilogram in Taka?

ক
2
খ
2.50
গ
3
ঘ
3.50

সঠিক উত্তর: খ

2.50

উত্তর

সঠিক উত্তর: খ

2.50

খ

ব্যাখ্যা

Question: A reduction is 25% of the price of an article enables a buyer to buy 50 kilograms more for tk 500. What is the reduced price per kilogram in Taka?

Solution:
25% মূল্য হ্রাসে
পূর্বের 100 টাকা দ্রব্য পাওয়া যায় 75 টাকায়

পূর্বের 1 টাকা দ্রব্য পাওয়া যায় 75/100 টাকায়
500 টাকা দ্রব্য পাওয়া যায় (75 × 500)/100
= 375 টাকায়

500 টাকায় এখন পূর্বাপেক্ষা 50 কেজি দ্রব্য বেশি পাওয়া যায়।

50 কেজির বর্তমান মূল্য 125 টাকা

50 কেজির বর্তমান মূল্য 125/50 টাকা

= 2.5 টাকা

৪৭২.

The speed of a boat in still water is 6 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

ক
1 km/h
খ
2 km/h
গ
3 km/h
ঘ
4 km/h

সঠিক উত্তর: খ

2 km/h

উত্তর

সঠিক উত্তর: খ

2 km/h

খ

ব্যাখ্যা

Question: The speed of a boat in still water is 6 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

Solution:
Let the speed of the current be = x km/h

Then,
Downstream speed = (6 + x) km/h
Upstream speed = (6 − x) km/h

According to the question:
(6 + x) = 2(6 − x)
⇒ 6 + x = 12 - 2x
⇒ 2x + x = 12 - 6
⇒ 3x = 6
⇒ x = 6/3
⇒ x = 2

∴ The speed of the current = 2 km/h

৪৭৩.

A booster pump can be used to fill as well as to empty the tank. The capacity of the tank is 1200 m³. The emptying capacity of the tank is 10 m³ per minute higher than its filling capacity and the pump requires 4 minutes less to vacant the tank than it requires to fill it. Calculate the filling capacity of the pump is-

ক
40 m³/min
খ
45 m³/min
গ
55 m³/min
ঘ
50 m³/min

সঠিক উত্তর: ঘ

50 m³/min

উত্তর

সঠিক উত্তর: ঘ

50 m³/min

ঘ

ব্যাখ্যা

Question: A booster pump can be used to fill as well as to empty the tank. The capacity of the tank is 1200 m³. The emptying capacity of the tank is 10 m³ per minute higher than its filling capacity and the pump requires 4 minutes less to vacant the tank than it requires to fill it. Calculate the filling capacity of the pump is-

Solution:
Let, the filling capacity of the pump = x m³/min

Given that,
Capacity of the tank = 1200 m³
Emptying rate is 10 m³/min more than filling rate
Emptying time is 4 minutes less than filling time

Then,
Filling time = 1200/x minutes
Emptying capacity = x+10 m³/min
Emptying time = 1200/(x + 10)

According to question,
(1200/x) - {1200/(x + 10)} = 4
(1/x) - {1/(x + 10)} = 1/300
(x + 10 - x)/x(x + 10) = 1/300
x2 + 10x - 3000 = 0
(x + 60) (x - 50) = 0

So, possible values is,
x = 50 And x = - 60 [not valid]

So, the filling capacity of the pump is 50 m³/min

৪৭৪.

In a simultaneous throw of a pair of dice, what is the probability of getting a total more than 9?

ক
1/6
খ
2/9
গ
5/18
ঘ
1/36

সঠিক উত্তর: ক

1/6

উত্তর

সঠিক উত্তর: ক

1/6

ক

ব্যাখ্যা

Question: In a simultaneous throw of a pair of dice, what is the probability of getting a total more than 9?

Solution:
When two fair six-sided dice are thrown together. Then we get,
Total outcomes = 6 × 6 = 36

And, Count outcomes with sum > 9

We want sum > 9 ⇒ sums = 10, 11, 12
Sum 10 = (4, 6), (5, 5), (6, 4) ⇒ 3 outcomes
Sum 11 = (5, 6), (6, 5) ⇒ 2 outcomes
Sum 12 = (6, 6) ⇒ 1 outcome

∴ Total favorable outcomes = 3 + 2 + 1 = 6

∴ Probability(sum > 9) = favorable outcomes/total outcomes
= 6/36
= 1/6

So the probability of getting a total more than 9 is 1/6.

৪৭৫.

If a man estimates his loss as 20% of the selling price, then his loss percent is = ?

ক
ক) 20/3%
খ
খ) 25/3%
গ
গ) 40/3%
ঘ
ঘ) 50/3 %

সঠিক উত্তর: ঘ

ঘ) 50/3 %

উত্তর

সঠিক উত্তর: ঘ

ঘ) 50/3 %

ঘ

ব্যাখ্যা

According to the question,
Loss = 20% Selling price
i.e.
Loss/ Selling price = 1/5
∴ Cost price = Selling price + Loss
= 5 + 1
= 6
∴Loss%=1/6 ×100=50/3%

৪৭৬.

The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.

ক
ক) 50%
খ
খ) 40%
গ
গ) 30%
ঘ
ঘ) 20%

সঠিক উত্তর: ক

ক) 50%

উত্তর

সঠিক উত্তর: ক

ক) 50%

ক

ব্যাখ্যা

Question: The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed?

Solution:
ধরি,
আয়তাকার বস্তুর, দৈর্ঘ্য = a
প্রস্থ = b
উচ্চতা = h
∴ আয়তন V = abh
আয়তন ৫০% বাড়ালে নতুন আয়তন = 1.5 abh

নতুন উচ্চতা যদি H হয় তাহলে = abH = 1.5abh
H = 1.5h
∴ উচ্চতার পরিবর্তন = 1.5h - h = 0.5h

শতকরা পরিবর্তন = (0.5h/h)100% = 50%

৪৭৭.

Passing marks in an examination are 40%. If a candidate gets 65 marks and fails by 15 marks, the maximum marks in the examination are-

ক
250
খ
220
গ
200
ঘ
180

সঠিক উত্তর: গ

200

উত্তর

সঠিক উত্তর: গ

200

গ

ব্যাখ্যা

Question: Passing marks in an examination are 40%. If a candidate gets 65 marks and fails by 15 marks, the maximum marks in the examination are-

Solution:
Let,
The maximum marks be x
passing marks be 40% of x = (40/100)x = (2x)/5

ATQ,
65 + 15 = (2x)/5
⇒ 80 = (2x)/5
⇒ 2x = 400
∴ x = 200

৪৭৮.

Father is aged 3 times more than his son and after 8 years he will be 2.5 times, Now, what is the age of the son?

ক
24
খ
48
গ
72
ঘ
32

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Father is aged 3 times more than his son and after 8 years he will be 2.5 times, Now, what is the age of the son?

Solution:
মনে করি,
ছেলের বর্তমান বয়স x বছর
যদি বাবার বর্তমান বয়স ছেলের বর্তমান বয়স অপেক্ষা 3 গুণ বেশি হয়
তাহলে, বাবার বর্তমান বয়স = 3x বছর

8 বছর পর,
ছেলের বয়স হবে (x + 8) বছর
বাবার বয়স হবে (3x + 8) বছর

প্রশ্নমতে,
(3x + 8) = 2.5(x + 8)
⇒ (3x + 8) = 2.5x + 20
⇒ 3x - 2.5x = 20 - 8
⇒ 0.5x = 12
⇒ x = 12/0.5
∴ x = 24

∴ ছেলের বর্তমান বয়স 24 বছর।

৪৭৯.

If x/y = 5/3 then (8x - 5y) : (8x + 5y) =

ক
5 : 11
খ
6 : 5
গ
5 : 6
ঘ
3 : 8

সঠিক উত্তর: ক

5 : 11

উত্তর

সঠিক উত্তর: ক

5 : 11

ক

ব্যাখ্যা

Question: If x/y = 5/3 then (8x - 5y) : (8x + 5y) =

Solution:
x : y = 5 : 3
⇒ x/y = 5/3
⇒ 8x/5y = (5 × 8)/(3 × 5) [ 8/5 দ্বারা গুণ করে ]
⇒ 8x/5y = 8/3
⇒ (8x - 5y)/(8x + 5y) = (8 - 3)/(8 + 3) [বিয়োজন - যোজন করে]
⇒ (8x - 5y)/(8x + 5y) = (8 - 3)/(8 + 3)
∴ (8x - 5y) : (8x + 5y) = 5 : 11

৪৮০.

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

ক
704
খ
504
গ
604
ঘ
800

সঠিক উত্তর: ক

704

উত্তর

সঠিক উত্তর: ক

704

ক

ব্যাখ্যা

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

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

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

৪৮১.

A metal sphere weighing 120 kilograms is melted and recast into 6000 identical nails. Calculate the weight of each nail in grams.

ক
20 grams
খ
18 grams
গ
22 grams
ঘ
21 grams

সঠিক উত্তর: ক

20 grams

উত্তর

সঠিক উত্তর: ক

20 grams

ক

ব্যাখ্যা

Question: A metal sphere weighing 120 kilograms is melted and recast into 6000 identical nails. Calculate the weight of each nail in grams.

Solution:
দেওয়া আছে,
ধাতুর বলের ওজন = 120 = 120 × 1000 = 120000 গ্রাম
পেরেকের সংখ্যা = 6000 টি

এখন,
6000 পেরেকের ওজন = 120000 গ্রাম
∴ 1 টি পেরেকের ওজন = (120000/6000) = 20 গ্রাম

৪৮২.

What is the value of x in the equation log_x(1/81) = 4

ক
ক) 1/3
খ
খ) 1/2
গ
গ) 3
ঘ
ঘ) 2

সঠিক উত্তর: ক

ক) 1/3

উত্তর

সঠিক উত্তর: ক

ক) 1/3

ক

ব্যাখ্যা

log_x(1/81) = 4
⇒ x⁴ = 1/81
⇒ x⁴ = (1/3)⁴
∴ x = 1/3

৪৮৩.

A man completes 1/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?

ক
50
খ
70
গ
40
ঘ
30

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A man completes 1/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?

Solution:
Work done = 1/8
Balance work = 1 - (1/8) = 7/8

A man completes 1/8 of a job in 10 days
A man completes 1 part of a job in 10 × 8 days
= 80 days

∴ More days required = 80 - 10
= 70 days.

৪৮৪.

Two dice are tossed at once. What is the probability that their combined total is no less than 10?

ক
1/6
খ
1/2
গ
1/4
ঘ
1/12
ঙ
1/3

সঠিক উত্তর: ক

1/6

উত্তর

সঠিক উত্তর: ক

1/6

ক

ব্যাখ্যা

Question: Two dice are tossed at once. What is the probability that their combined total is no less than 10?

solution:
When two fair six-sided dice are tossed, the total number of possible outcomes = 6 × 6 = 36.
We want the probability that the sum is ≥ 10 (i.e., 10, 11, or 12).

List all favorable outcomes,
Sum = 10: (4, 6), (5, 5), (6, 4) = 3 ways
Sum = 11: (5, 6), (6, 5) = 2 ways
And Sum = 12: (6,6) = 1 way

∴ Total favorable outcomes = 3 + 2 + 1 = 6

∴ Probability = favorable outcomes/total outcomes
= 6/36
= 1/6

So the probability is 1/6.

৪৮৫.

The speed of a boat in standing water is 9 kmph, and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is-

ক
10 h
খ
14 h
গ
18 h
ঘ
24 h
ঙ
25 h

সঠিক উত্তর: ঘ

24 h

উত্তর

সঠিক উত্তর: ঘ

24 h

ঘ

ব্যাখ্যা

Question: The speed of a boat in standing water is 9 kmph, and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is-

Solution:
Speed upstream = (9 - 1.5) kmph
= 7.5 kmph
Speed downstream = (9 + 1.5) kmph
=10.5 kmph
∴ Total time taken = (105/7.5) + (105/10.5)
= 14 + 10
= 24 h

৪৮৬.

Complete the series: 2u, 7o, 31i, 127e, _______

ক
254u
খ
322o
গ
486l
ঘ
511a
ঙ
None

সঠিক উত্তর: ঘ

511a

উত্তর

সঠিক উত্তর: ঘ

511a

ঘ

ব্যাখ্যা

Question: Complete the series: 2u, 7o, 31i, 127e, _______

Solution:
এখানে,
ধারাটি কে ২ টি অংশে বিভক্ত করা যায়,

প্রথম সংখ্যা ধারা = 2, 7, 31, 127…..
বর্ণ ধারা = u, o, i, e,...

সংখ্যা ধারায়,
১ম সংখ্যা = 2
২য় সংখ্যা = 2³ - 1 = 7
৩য় সংখ্যা = 2⁵- 1 = 31
৪র্থ সংখ্যা = 2⁷- 1 = 127

∴ পরবর্তী সংখ্যা হবে = 2⁹- 1= 511

বর্ণ ধারা থেকে বুঝা যায় সবগুলো (vowel) স্বরবর্ণ।
u, o, i, e এর পরবর্তী বর্ণ হবে ⇒ a

∴ ধারার পরবর্তী অংশ হবে = 511a

৪৮৭.

A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

ক
ক) Tk. 16
খ
খ) Tk. 12
গ
গ) Tk. 14
ঘ
ঘ) Tk. 20

সঠিক উত্তর: ক

ক) Tk. 16

উত্তর

সঠিক উত্তর: ক

ক) Tk. 16

ক

ব্যাখ্যা

Question: A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

Solution:
Cost price of first chair = (100/125) × 120
= Tk. 96

Cost price of second chair = (100/75) × 120
= Tk. 160

∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16

৪৮৮.

If P is 20% less than X, and Q is 10% more than Y, than PQ is what percent of XY?

ক
ক) 84%
খ
খ) 85%
গ
গ) 87%
ঘ
ঘ) 88%

সঠিক উত্তর: ঘ

ঘ) 88%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 88%

ঘ

ব্যাখ্যা

Question: If P is 20% less than X, and Q is 10% more than Y, than PQ is what percent of XY?

Solution:
ধরি,
X = 100
∴ P = 100 - (20% of 100)
= 80

আবার,
Y = 100
∴ Q = 100 + (10% of 100)
= 110

তাহলে,
PQ, XY এর = ((80 × 110)/(100 × 100)} × 100%
= (8800/10000) × 100%
= 88%

৪৮৯.

A letter is taken out at random from ASSISTANT and another is taken out from STATISTICS. The probability that they are the same letters is:

ক
19/96
খ
35/96
গ
31/96
ঘ
19/90

সঠিক উত্তর: ঘ

19/90

উত্তর

সঠিক উত্তর: ঘ

19/90

ঘ

ব্যাখ্যা

Question: A letter is taken out at random from ASSISTANT and another is taken out from STATISTICS. The probability that they are the same letters is:

Solution:
The letters of ASSISTANT are A A S S S T T I N
The letters of STATISTICS are A S S S T T T I I C
Common letters are A, S, T, I
The probability of choosing an A from ASSISTANT & an A from STATISTICS is:
(²C₁/⁹C₁) × (¹C₁/¹⁰C₁)
= (2/9) × (1/10)
= 1/45

The probability of choosing an I from ASSISTANT & an I from STATISTICS is:
(¹C₁/⁹C₁) × (²C₁/¹⁰C₁)
= (1/9) × (2/10)
= 1/45

The probability of choosing a S from ASSISTANT & a S from STATISTICS is:
(³C₁/⁹C₁) × (³C₁/¹⁰C₁)
= (3/9) × (3/10)
= 1/10

The probability of choosing a T from ASSISTANT & a T from STATISTICS is:
(²C₁/⁹C₁) × (³C₁/¹⁰C₁)
= (2/9) × (3/10)
= 1/15

∴ The probability that the chosen letters are the same letters is:
1/45 + 1/45 + 1/10 + 1/15
= (2 + 2 + 9 + 6)/90
= 19/90

৪৯০.

A man runs round a circular field of radius 50m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?

ক
11/7 min
খ
50/7 min
গ
110/7 min
ঘ
220/7 min

সঠিক উত্তর: ঘ

220/7 min

উত্তর

সঠিক উত্তর: ঘ

220/7 min

ঘ

ব্যাখ্যা

Question: A man runs round a circular field of radius 50m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?

Solution:
perimeter of circle = 2 × (22/7) × 50 m

speed = 12 km/hr = 12 × 1000/3600 m/s
= 10/3 m/s

time taken for 1 round = { 2 × (22/7) × 50}/ 10/3
= 660/7 sec
= 11/7 min

time taken for twenty round = (11/7) × 20 min
= 220/7 min

৪৯১.

98.98 ÷ 11.03 + 7.014 × 15.99 = ?

ক
ক) 132
খ
খ) 144
গ
গ) 12
ঘ
ঘ) 121

সঠিক উত্তর: ঘ

ঘ) 121

উত্তর

সঠিক উত্তর: ঘ

ঘ) 121

ঘ

ব্যাখ্যা

98.98 ÷ 11.03 + 7.014 × 15.99
= 121.128 ≈ 121

Another approach:
98.98 ÷ 11.03 + 7.014 × 15.99
Let consider the equation as = 99 ÷ 11 + 7 × 16 = 9 + 112 = 121

৪৯২.

10, 4, 26, 16 what is the median of the numbers shown?

ক
ক) 10
খ
খ) 13
গ
গ) 14
ঘ
ঘ) 15

সঠিক উত্তর: খ

খ) 13

উত্তর

সঠিক উত্তর: খ

খ) 13

খ

ব্যাখ্যা

We arrange the numbers in ascending order:
4, 10, 16, 26
the median of the numbers = (10 + 16)/2 = 26/2 = 13

৪৯৩.

In how many ways can 5 people from a group of 8 people be seated around a circular table?

ক
1224
খ
1344
গ
1564
ঘ
1600

সঠিক উত্তর: খ

1344

উত্তর

সঠিক উত্তর: খ

1344

খ

ব্যাখ্যা

Question: In how many ways can 5 people from a group of 8 people be seated around a circular table?

Solution:
5 people out of 8 = 8C5
= 8!/5!(8 - 5)!
= 8!/(3! × 5!)
= (8 × 7 × 6 × 5!)/(6 × 5!)
= 56

And 5 people around a circular table = (5 - 1)! = 4! = 24

∴ Total ways = 24 × 56 = 1344

৪৯৪.

A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

ক
100bc
খ
(100b)/c
গ
200bc
ঘ
(200b)/c
ঙ
200/(bc)

সঠিক উত্তর: গ

200bc

উত্তর

সঠিক উত্তর: গ

200bc

গ

ব্যাখ্যা

Question: A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

Solution:
We are given that a case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. Thus we can say the following:

c × b × 100 = 100bc paper clips per case.
Thus, 2 cases would contain 2 × 100bc = 200bc paper clips.

৪৯৫.

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

ক
5%
খ
8%
গ
10%
ঘ
14%
ঙ
20%

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

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

Solution:
Given, Cost of 1kg of rice = Tk. 20
∴ Cost of 26kg of rice = 20 × 26 = 520 Tk.

Again, Cost of 1kg of rice = Tk. 36
∴ Cost of 30kg of rice = 36 × 30 =1080 Tk.

∴ Total C.P = Tk. (520 + 1080)
= Tk. 1600

Total rice weight = (30 + 26) kg = 56 kg

So,
Trader sold this 56kg of rice at Tk. 30 per kg
∴ Total S.P = Tk. (56 × 30)
= Tk. 1680.

Hence,
Profit = 1680 - 1600 = Tk. 80
Profit percentage = (80/1600) × 100
= 5%

৪৯৬.

In a circle of radius 10 cm. a chord is drawn at a distance of 6 cm from the center. What is the length of the chord in cm?

ক
12
খ
14
গ
16
ঘ
18

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: In a circle of radius 10 cm. a chord is drawn at a distance of 6 cm from the center. What is the length of the chord in cm?

Solution:

দেওয়া আছে, বৃত্তের ব্যাসার্ধ (r) = 10 সেমি।
কেন্দ্র থেকে জ্যা-এর দূরত্ব (d) = 6 সেমি।
আমরা জানি, বৃত্তের কেন্দ্র থেকে জ্যা-এর ওপর অঙ্কিত লম্ব জ্যা-টিকে সমদ্বিখণ্ডিত করে। এর ফলে কেন্দ্র, লম্ব দূরত্ব এবং জ্যা-এর অর্ধেক অংশ মিলে একটি সমকোণী ত্রিভুজ গঠন করে।

পিথাগোরাসের উপপাদ্য অনুযায়ী,
OB² = OC² + BC²⇒ 10² = 6² + BC²⇒ 100 = 36 + BC²⇒ BC² = 100 - 36
⇒ BC² = 64
⇒ BC = √64
⇒ BC = 8 cm

যেহেতু কেন্দ্র থেকে অঙ্কিত লম্ব জ্যা-কে সমদ্বিখণ্ডিত করে, তাই জ্যা AB-এর মোট দৈর্ঘ্য = 2 × BC

∴ জ্যা-এর দৈর্ঘ্য = 2 × 8 = 16 cm

৪৯৭.

A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English?

ক
ক) 72
খ
খ) 69
গ
গ) 66
ঘ
ঘ) 78

সঠিক উত্তর: গ

গ) 66

উত্তর

সঠিক উত্তর: গ

গ) 66

গ

ব্যাখ্যা

Total marks obtained by the student = 55% of 800
= {(55/100) × 800}
= 440
∴ Marks scored in English
= 15% of 440
= {(15/100) × 440}
= 66

৪৯৮.

If you count from 1 to 100, how many 5s will you pass on the way?

ক
ক) 22
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 21

সঠিক উত্তর: গ

গ) 20

উত্তর

সঠিক উত্তর: গ

গ) 20

গ

ব্যাখ্যা

প্রশ্ন : If you count 1 to 100, how many 5s will you pass on the way?
সমাধান :
১ থেকে 100 পর্যন্ত গণনায় ৫, ১৫, ২৫, ৩৫, ৪৫, ৫০, ৫১, ৫২, ৫৩, ৫৪, ৫৫, ৫৬, ৫৭, ৫৮, ৫৯, ৬৫, ৭৫, ৮৫, ৯৫ এই সংখ্যাগুলোতে ৫ পাওয়া যায় মোট ২০ বার (বিঃ দ্রঃ ৫৫ তে দুটি ৫ গণনা করতে হবে)

৪৯৯.

If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :

ক
ক) 3 : 4
খ
খ) 3 : 20
গ
গ) 20 : 3
ঘ
ঘ) 2 : 3

সঠিক উত্তর: খ

খ) 3 : 20

উত্তর

সঠিক উত্তর: খ

খ) 3 : 20

খ

ব্যাখ্যা

.04 of x = .06 of y
⇒ x/y = .06/.4
⇒ x/y = 3/20
⇒ x : y = 3 : 20

৫০০.

In a simultaneous throw of two dice, what is the probability of getting a total of 8?

ক
ক) 1/6
খ
খ) 1/9
গ
গ) 1/12
ঘ
ঘ) 5/36

সঠিক উত্তর: ঘ

ঘ) 5/36

উত্তর

সঠিক উত্তর: ঘ

ঘ) 5/36

ঘ

ব্যাখ্যা

Question: In a simultaneous throw of two dice, what is the probability of getting a total of 8?

Solution:

The total number of events ⇒ 36.
The number of events of getting total 8 ⇒ 5.

∴ The probability of getting a total of 8 is 5/36.