Bank Math

PrepBank · পাতা ৮ / ১৬১ · ৭০১–৮০০ / ১৬,১২৪

৭০১.

The three rational numbers between 3 and 4 are :

ক
ক) 5/2, 6/2, 7/2
খ
খ) 13/4, 14/4, 15/4
গ
গ) 12/7, 13/7, 14/7
ঘ
ঘ) 11/4,12/4, 13/4

ব্যাখ্যা

Rational number is any number that can express in the form of qp of two integers, where 'q' cannot be zero.

i) First rational number between 3 and 4 can be calculated by finding average between them, which is
(3 + 4)/2 = 7/2 or 14/4
Now, we have three numbers i.e. 3, 7/2 and 4, so other remaining rational numbers can be calculated by taking average between 3 and 7/2, and between 7/2 and 4.

ii) Second rational number between 3 and 7/2 can be calculated by finding average between them.
(7/2 + 3) / 2 = {(7 + 6)/2} / 2 = 13/4

iii) The third rational number between 4 and 7/2 can be calculated by finding the average between them.
(7/2 + 4)/2 = {(7 + 8)/2}/2 = 15/4

iv) Similarly fourth rational number between 3 and 13/4 can be calculated by finding the average between them.
(13/4 + 3) / 2 = {(13 + 12)/4}/2 = 25/8

v) Similarly, fifth rational number between 4 and 13/4 can be calculated by finding average between them.
{(13/4) + 4}/2 = {(13 + 16)/4} / 2 = 29/8

Then the rational numbers between 3 and 4 are : 7/2 or 14/4, 13/4, 15/4, 25/8, 29/8

৭০২.

A boy has 75 litres oil in one cane and 45 litres in another. The maximum capacity of container which can measure oil of either container in exact number?

ক
ক) 1 litre
খ
খ) 5 litres
গ
গ) 25 litres
ঘ
ঘ) 15 litres

ব্যাখ্যা

প্রশ্ন: একজন বালকের দুইটি পাত্রে যথাক্রমে 75 লিটার ও 45 লিটার তেল আছে। সর্বোচ্চ কত লিটারের পাত্র দিয়ে সঠিক ভাবে মাপা যাবে?

সমাধান:
75 = 5 × 5 × 3
45 = 5 × 3 × 3

∴ 75 এবং 45 এর গ.সা.গু = 15

অর্থাৎ 15 লিটার এর পাত্র দিয়ে সঠিক ভাবে মাপা যাবে।

৭০৩.

In a trapezoid, the lengths of the two parallel bases are 10 and 16. If the height of the trapezoid is 4, find the area of the trapezoid.

ক
48
খ
52
গ
56
ঘ
104

ব্যাখ্যা

Question: In a trapezoid, the lengths of the two parallel bases are 10 and 16. If the height of the trapezoid is 4, find the area of the trapezoid.

Solution:
Given that,
Trapezoid with bases a = 10 and b = 16
Height, h = 4

We know,
Area of trapezoid = (1/2) × (sum of bases) × height = (1/2) × (a + b) × h
= (1/2) × (10 + 16) × 4
= (1/2) × 104
= 52

So the area of the trapezoid is 52 square units.

৭০৪.

A train 240 m long passed a pole in 24 seconds. How long will it take to pass a platform 650 m long?

ক
ক) 63 sec
খ
খ) 69 sec
গ
গ) 89 sec
ঘ
ঘ) 91 sec

ব্যাখ্যা

Question: A train 240 m long passed a pole in 24 seconds. How long will it take to pass a platform 650 m long?

Solution:
Speed = 240/24 = 10 m/s

∴ Required time = (240 + 650) / 10 = 89 sec

৭০৫.

A covers a certain distance in 3 hours with a constant speed of 60 km/h. What should be the speed of B to cover the same distance in 2 hours 30 minutes?

ক
ক) 78 km/h
খ
খ) 71 km/h
গ
গ) 72 km/h
ঘ
ঘ) 79 km/h

ব্যাখ্যা

A's time = 3 hours
A's speed = 60 km/h

B's time = 2 hours 30 minutes

Speed = Distance/time

D = 60 × 3 = 180 km

B's speed = 180/2.5
⇒ B's speed = 72 km/h
∴ B's speed is 72 km/h

৭০৬.

If an exponent or index has base 100 and power zero, then which of the following will be its value?

ক
100
খ
5
গ
10
ঘ
1

ব্যাখ্যা

Question: If an exponent or index has base 100 and power zero, then which of the following will be its value?
(Officer Cash 2022 অনুযায়ী)

Solution:
x⁰ = 1 (for any non-zero base a)

Now,
= 100⁰
= 1

৭০৭.

Average speed of a bus is 1/3 of that of a train. The train covers 936 km in 12 hours. across the distance. Then how much distance will the bus cover in 30 minutes?

ক
12 Km
খ
13 Km
গ
14 Km
ঘ
15 Km

ব্যাখ্যা

প্রশ্ন: Average speed of a bus is 1/3 of that of a train. The train covers 936 km in 12 hours. across the distance. Then how much distance will the bus cover in 30 minutes?

সমাধান:

ট্রেনটির গতিবেগ = 936/12 = 78 কি.মি./ঘণ্টা

বাসটির গতিবেগ = 78/3 = 26 কি.মি./ঘণ্টা

বাসটি 60 মিনিটে অতিক্রম করে = 26 কি.মি.

বাসটি 1 মিনিটে অতিক্রম করে = 26/60 কি.মি.

বাসটি 30 মিনিটে অতিক্রম করে = (26 × 30)/60 কি.মি.
= 13 কি.মি

৭০৮.

If x + y = a, x² + y² = b² and x³ + y³ = c³ then find the value of a³ + 2c³ = ?

ক
2ab²
খ
a³b²
গ
ab
ঘ
3ab²

ব্যাখ্যা

Question: If x + y = a, x² + y² = b² and x³ + y³ = c³ then find the value of a³ + 2c³ = ?

Solution:
Given that,
x + y = a .........(1)
x² + y² = b² .........(2)
And x³ + y³ = c³

Now,
a³ + 2c³
= (x + y)³ + 2(x³ + y³)
= x³ + 3x²y + 3xy² + y³ + 2x³ + 2y³ ; [(a + b)³ = a³ + 3a²b + 3ab² + b³]
= 3x³ + 3y³ + 3xy(x+ y)
= 3(x³ + y³) + 3xy(x + y)
= 3{(x + y)(x² - xy + y²)} + 3xy(x + y) ; [a³ + b³ = (a + b)(a² - ab + b²)]
= 3(x + y)(x² - xy + y² + xy)
= 3(x + y)(x² + y²)
= 3ab² ; [From 1 and 2]

৭০৯.

An employee may claim Tk. 8 for each kilometer when he travels by taxi and Tk. 7 for each kilometer when he drives his own car. If in one week he claimed Tk. 1075 for travelling 140 km, how many kilometers did he travel by taxi?

ক
90 km
খ
95 km
গ
97 km
ঘ
100 km

ব্যাখ্যা

Question: An employee may claim Tk. 8 for each kilometer when he travels by taxi and Tk. 7 for each kilometer when he drives his own car. If in one week he claimed Tk. 1075 for travelling 140 km, how many kilometers did he travel by taxi?

Solution:
Let the distance travelled by taxi x km
Let the distance travelled by own car 140 - x km

Now
8x + 7(140 - x) = 1075
⇒ 8x + 980 - 7x = 1075
⇒ x + 980 = 1075
⇒ x = 1075 - 980
∴ x = 95

৭১০.

In a circle, if the central angle subtended by an arc is 100°, what is the value of the inscribed angle on the same arc?

ক
30°
খ
40°
গ
55°
ঘ
50°

ব্যাখ্যা

Question: In a circle, if the central angle subtended by an arc is 100°, what is the value of the inscribed angle on the same arc?
(কোন বৃত্তের একই চাপের উপর দণ্ডায়মান কেন্দ্রস্থ কোণ ১০০° হলে, বৃত্তস্থ কোণের পরিমাণ কত?)

Solution:
আমরা জানি,
কোন বৃত্তের বৃত্তস্থ কোণ তার কেন্দ্রস্থ কোণের অর্ধেক।

∴ বৃত্তের কেন্দ্রস্থ কোণ ১০০° হলে, বৃত্তস্থ কোণ হবে = ১০০°/২
= ৫০°

৭১১.

A man bought 40 shares of Tk. 50 at 5tk discount, the rate of dividend being 27%. The rate of interest obtained is-

ক
35%
খ
30%
গ
38%
ঘ
32%
ঙ
25%

ব্যাখ্যা

Question: A man bought 40 shares of Tk. 50 at 5tk discount, the rate of dividend being 27%. The rate of interest obtained is-

Solution:
Given,
Total investment = Tk. [40 × (50 - 5)] = Tk. 1800.
Face value = Tk. (50 × 40) = Tk. 2000.

∴ Dividend = (27/100) × 2000
= Tk. 540

∴ Interest obtained = (540/1800) × 100%
= 30%

৭১২.

If m = 1 + √7 and n = 1 - √7, find the value of m³ + n³ = ?

ক
44
খ
- 28
গ
36
ঘ
- 6
ঙ
38

ব্যাখ্যা

Question: If m = 1 + √7 and n = 1 - √7, find the value of m³ + n³ = ?

Solution:
Given that,
m = 1 + √7
n = 1 - √7

Now,
m + n = 1 + √7 + 1 - √7 = 2
And, mn = (1 + √7)(1 - √7) = 1² - (√7)² = 1 - 7 = - 6

We know that,
m³ + n³ = (m + n)³ - 3mn(m + n)
= 2³ - 3 × (- 6) × 2
= 8 + 36 = 44
∴ m³ + n³ = 44

৭১৩.

What is the least number of soldiers that can be drawn up in troops of 12, 15, 18 and 20 soldiers and also in the form of a solid square?

ক
900
খ
400
গ
1600
ঘ
2500

ব্যাখ্যা

In this type of question, We need to find out the LCM of the given numbers.
LCM of 12, 15, 18 and 20;
12=2 × 2 × 3;
15=3 × 5;
18=2 × 3 × 3;
20=2 × 2 × 5

Hence, LCM = 2 × 2 × 3 × 5 × 3

Since, the soldiers are in the form of a solid square.
Hence, LCM must be a perfect square. To make the LCM a perfect square, We have to multiply it by 5,
hence,
The required number of soldiers = 2 × 2 × 3 × 3 × 5 × 5
= 900

৭১৪.

The average of 15 numbers is 15. If the average of the first five numbers is 14 and that of the other 9 numbers is 16, then find the middle number.

ক
ক) 12
খ
খ) 11
গ
গ) 10
ঘ
ঘ) 9

ব্যাখ্যা

Average of 15 numbers = 15, Average of 5 numbers = 14, Average of 9 numbers = 16

Average = Total numbers/Number of Numbers
15 = Total numbers/15
Therefore, total numbers = 15 x 15 = 225.

Middle number = (Total numbers) – [(Average of 5 num x no of num) + ( Average of 9 num x no of num)]
= (225) – [(14 x 5) + (16 x 9)]
= (225) – (214)
= 11.

৭১৫.

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Tk. 30 in all, how many 5 p coins are there?

ক
ক) 50
খ
খ) 100
গ
গ) 150
ঘ
ঘ) 200
ঙ
ঙ) 250

ব্যাখ্যা

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, the sum of their values = Tk. (25x/100) + (10 × 2x/100) + (5 × 3x/100) = Tk. 60x
Or, 60x/100 = 30
Or, x = (30 x 100)/60 = 50.
Hence, the number of 5 p coins = (3 x 50) = 150.

৭১৬.

The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. Time in which A reach the destination?

ক
4/5 hr
খ
4/3 hr
গ
5/3 hr
ঘ
5/4 hr

ব্যাখ্যা

Question: The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. Time in which A reach the destination?
Solution:
here, ratio of speed is 3 : 4
as the ratio of time is inversly proportional to speed,
ratio of time = 4 : 3

ATQ,
4x - 3x = 20 min
x = 20 min = 1/3 hr

A takes total time of = 4 × 1/3 = 4/3 hr

৭১৭.

20 + 8 × 0.5/(20 - ?) = 12. Find the value in place of (?).

ক
ক) 2
খ
খ) 8
গ
গ) 18
ঘ
ঘ) 27

ব্যাখ্যা

Let the missing number be x.
Given,
20 + 8 × 0.5/(20 - x) = 12
⇒ (20 + 4)/(20 - x) = 12
⇒ 24/(20 - x) = 12
⇒ 20 - x = 24/12
⇒ 20 - x = 2
⇒ x = 20 - 2
⇒ x = 18.

৭১৮.

If a 26 m ladder is placed against a 13 m wall such that it just reaches the top of the wall. What will be the elevation of the wall?

ক
ক) 30^∘
খ
খ) 45^∘
গ
গ) 50^∘
ঘ
ঘ) 60^∘

ব্যাখ্যা

Question: If a 26 m ladder is placed against a 13 m wall such that it just reaches the top of the wall. What will be the elevation of the wall?

Solution:

AC = 26 meters
AB = 13 meters
∠ACB = θ

∴ sinθ = AB/AC
⇒ sinθ =13/26
⇒ sinθ =1/2
⇒ sinθ = sin30^∘⇒ θ = 30^∘

৭১৯.

Rasel bought accessories worth Tk. 150. Out of the amount spent for buying accessories, Tk. 10 was spent on sales tax due to taxable purchases. If the tax rate was 10%, calculate the price of the tax-free items.

ক
Tk. 50
খ
Tk. 60
গ
Tk. 40
ঘ
Tk. 45

ব্যাখ্যা

Question: Rasel bought accessories worth Tk. 150. Out of the amount spent for buying accessories, Tk. 10 was spent on sales tax due to taxable purchases. If the tax rate was 10%, calculate the price of the tax-free items.

Solution:
Total Price = 150
Tax paid = 10
Paid Price of accessories without Tax = 150 - 10 = 140
Tax = 10%

Let the taxable purchases = Tk. x

⇒ 10% of x = 10

⇒ 0.1x = 10

∴ x = 100

∴ Price of Tax free items = 140 - 100 = 40

৭২০.

The value of - 5 - (- 5) is how much greater than the value of (- 5 - 5)?

ক
0
খ
5
গ
8
ঘ
10

ব্যাখ্যা

Question: The value of - 5 - (- 5) is how much greater than the value of (- 5 - 5)?

Solution:
- 5 -(- 5)
= - 5 + 5
= 0

And,
- 5 - 5
= - 10

Now,
0 - (- 10)
= 10

∴ The value of - 5 - (- 5) is 10 greater than the value of - 10 -(- 5)

৭২১.

In how many years, Tk. 150 will produce the same interest @ 8% as Tk. 800 produce in 3 years @ (9/2)% ?

ক
6
খ
8
গ
9
ঘ
12

ব্যাখ্যা

Question: In how many years, Tk.150 will produce the same interest at 8% as Tk.800 produce in 3 years at 9/2%

Solution:
Here
P =Tk.800,
r = 9/2%.
n = 3 years
∴S.I.=Tk.(800 × 9 × 3)/(2 × 100) = Tk.108

Now,
S.I.= Tk.108
P = Tk.150,
r = 8% =8/100

We know
I = Pnr
n = I/Pr
= 108/(150 × 8/100)
= (100 × 108)/(150 × 8)
= 9 years

৭২২.

A trader marks his goods at 20% above the cost price . If he allows a discount of 5% for each down payment, his profit for such a transaction is

ক
ক) 15%
খ
খ) 12%
গ
গ) 14%
ঘ
ঘ) 17%

ব্যাখ্যা

ধরি
পণ্যটির ক্রয়মূল্য ১০০ টাকা
বিক্রেতা মূল্য নির্ধারণ করলো = ১০০ + ২০ টাকা
৫% ছাড়ে
পণ্যটির বিক্রয়মূল্য = ১২০ - (১২০ × ৫০) /১০০
= ১১৪ টাকা

শতকরা লাভ হবে = ১১৪ - ১০০
= ১৪%

৭২৩.

A man throws two dice simultaneously on the floor. What is the probability of getting two numbers whose product is even?

ক
2/3
খ
4/5
গ
1/2
ঘ
3/4

ব্যাখ্যা

Question: A man throws two dice simultaneously on the floor. What is the probability of getting two numbers whose product is even?

Solution:
In a simultaneous throw of the two dice, the sample space, S = 6 × 6 = 36
So, n (S) = 36

The event "E" = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

So, n (E) = 27

∴ Probability = 27/36 = 3/4

৭২৪.

A wheel that has 12 cogs is meshed with a larger wheel of 24 cogs. If the smaller wheel has made 44 revolutions, then find the number of revolutions made by the larger wheel.

ক
20
খ
16
গ
24
ঘ
22

ব্যাখ্যা

Question: A wheel that has 12 cogs is meshed with a larger wheel of 24 cogs. If the smaller wheel has made 44 revolutions, then find the number of revolutions made by the larger wheel.

Solution:
As number of cogs increase, the revolutions made decrease. Hence, this is a problem related to indirect proportion.
Let the number of wheels be x.
More cogs (↑),Less revolutions (↓)

24 : 12 : : 44 : x
⇒ 24 × x = 12 × 44
⇒ x = (12 × 44)/24
∴ x = 22

৭২৫.

What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?

ক
Tk. 1600
খ
Tk. 1750
গ
Tk. 1850
ঘ
Tk. 1800

ব্যাখ্যা

Question: What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?

Solution:
15% stock at Tk. 120 বলতে বুঝায় স্টকটির ফেস ভ্যালু ১০০ টাকায় ১৫ টাকা লাভ হয় এবং স্টকটির বাজার মূল্য ১২০ টাকা।

এখানে,
১২০ টাকা বিনিয়োগ করে আয় হয় ১৫ টাকা
∴ ১ টাকা বিনিয়োগ করে আয় হয় ১৫/১২০ টাকা
∴ ১৪৪০০ টাকা বিনিয়োগ করে আয় হয় (১৪৪০০ × ১৫)/১২০ টাকা
= ১৮০০ টাকা

৭২৬.

What is the probability of rolling a number less than or equal to 4 on a six-sided die?

ক
2/3
খ
1/2
গ
3/4
ঘ
None of these

ব্যাখ্যা

Question: What is the probability of rolling a number less than or equal to 4 on a six-sided die?

Solution:
A standard six-sided die has the numbers,
1, 2, 3, 4, 5, 6
Numbers less than or equal to 4 are- 1, 2, 3, and 4.
Number of favorable outcomes = 4.
And total possible outcomes = 6

∴ Probability = Favorable outcomes/Total outcomes
= 4/6
= 2/3

∴ The probability of rolling a number less than or equal to 4 on a six-sided die is 2/3.

৭২৭.

A borrows sum of TK. 90000 for 4 years at 5% simple interest. He lends it to B at 7% for 4 years at simple interest. What is his gain?

ক
8690
খ
7200
গ
5820
ঘ
6470
ঙ
7890

ব্যাখ্যা

Question: A borrows sum of TK. 90000 for 4 years at 5% simple interest. He lends it to B at 7% for 4 years at simple interest. What is his gain?

Solution:
A's, Principal = TK. 90000
simple interest rate = 5%
time = 4 years

∴ simple interest = TK. (90000 × 4 × 5)/100
= TK. 18000

B's, Principal = TK. 90000
simple interest rate = 7%
time = 4 years

∴ simple interest = TK. (90000 × 4 × 7)/100
= TK. 25200

∴ Profit of A = TK. (25200 - 18000) = TK. 7200

৭২৮.

From P and Q, two trains start moving towards each other at the same time. Their speeds are 120 km/h and 100 km/h, respectively. When the two trains meet each other, one train has covered 40 km more than the other train. Find the distance between P and Q?

ক
380 km
খ
440 km
গ
520 km
ঘ
400 km

ব্যাখ্যা

Question: From P and Q, two trains start moving towards each other at the same time. Their speeds are 120 km/h and 100 km/h, respectively. When the two trains meet each other, one train has covered 40 km more than other train. Find the distance between P and Q?

Solution:
Speeds are in the ratio 120 : 100 = 6 : 5
So distances covered in the same time are also in the ratio 6 : 5

Let distances be 6k and 5k.

∴ Difference = 6k - 5k = 40
∴ k = 40

∴ Total distance = 6k + 5k = 11k = 11 × 40 = 440 km

So the distance between P and Q is 440 km.

৭২৯.

Mother's age today is thrice as her daughter's. After 10 years it would be just double. How old is the daughter today?

ক
ক) 10 years
খ
খ) 9 years
গ
গ) 8 years
ঘ
ঘ) 11 years

ব্যাখ্যা

কন্যার বর্তমান বয়স xবছর
মাতার বর্তমান বয়স 3x বছর

প্রশ্নমতে,
3x + 10 = 2(x + 10)
3x + 10 = 2x + 20
3x - 2x =20 - 10
x = 10

৭৩০.

A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

ক
ক) 15 years
খ
খ) 30 years
গ
গ) 45 years
ঘ
ঘ) 60 years

ব্যাখ্যা

Question: A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

Solution:
let the sum P

2P = P (1 + r)¹⁵
⇒ (1 + r)¹⁵ = 2

let, sum will 4 times in n years
8P = P(1 + r)ⁿ
⇒ 8 = (1 + r)ⁿ
⇒ 2³ = (1 + r)ⁿ
⇒ ((1 + r)¹⁵)³ = (1 + r)ⁿ
⇒ (1 + r)⁴⁵ = (1 + r)ⁿ
∴ n = 45 years

৭৩১.

The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?

ক
y/R
খ
y/(R - x)
গ
xy/(R - x)
ঘ
xy/{R(R - x)}

ব্যাখ্যা

Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?

Solution:
যদি R সংখ্যক শিক্ষার্থী সমান সমান টাকা দেয় তাহলে টাকা উঠে = y টাকা
∴ একজন শিক্ষার্থী দেয় y/R টাকা

x জন শিক্ষার্থী টাকা না দেয়ায় মোট টাকা দেয় (R - x) জন
∴ একজন শিক্ষার্থী দেয় y/(R - x) টাকা

বাড়তি দিতে হয় = y/(R - x) - y/R
= (yR - yR + xy)/{R(R - x)}
= xy/{R(R - x)}

৭৩২.

The average of the two numbers is 6.5 and square root of their product is 6. What are the numbers?

ক
ক) 11 and 2
খ
খ) 8 and 5
গ
গ) 10 and 3
ঘ
ঘ) 9 and 4

ব্যাখ্যা

Question: The average of two numbers is 6.5 and square root of their product is 6. What are the numbers?

Solution:
Let the number be x and y

According to the question,
(x + y)/2 = 6.5,
⇒ x + y = 13

and,
√xy = 6
⇒ xy = 36
⇒ x = 36/y

Now,
(36/y) + y = 13
⇒ (36 + y²)/y = 13
⇒ 36 + y² = 13y
⇒ y² - 13y + 36 = 0
⇒ (y - 9)(y - 4) = 0
So, y = 4 or, 9

If y = 4 then, x = 9
If y = 9 then, x = 4

So, the numbers are 4 and 9

৭৩৩.

X can do a piece of work in 20 days and Y can do the 1/7th of the same work in 5 days. In how many days together can they complete the 11/20th of the total work?

ক
ক) 7 days
খ
খ) 14 days
গ
গ) 10 days
ঘ
ঘ) 12 days

ব্যাখ্যা

X can do in 1 day = 1/20 part
Y can do in 1 day = 1/(7×5) = 1/35 part
X & Y together can do in 1 day = 1/20 + 1/35 = 11/140
11/140 part of the work is done in 1 day
So, 11/20 part of the work is done in = (11/20) × (140/11) = 7 days

৭৩৪.

If A = {a, b, c, d, e, f, g} and B = {d, e, f, g}, then A - B = ?

ক
{a, b, c}
খ
{a, b, c, d}
গ
{d, e, f}
ঘ
{d, e, f, g}

ব্যাখ্যা

Question: If A = {a, b, c, d, e, f, g} and B = {d, e, f, g}, then A - B = ?

Solution:
A - B = {a, b, c, d, e, f, g} - {d, e, f, g}
= {a, b, c}

৭৩৫.

A train runs at the speed of 72 km/hr and crosses a 320 m long platform in 30 seconds. What is the length of the train?

ক
ক) 285 meters
খ
খ) 280 meters
গ
গ) 275 meters
ঘ
ঘ) 270 meters

ব্যাখ্যা

Question: A train runs at the speed of 72 km/hr and crosses a 320 m long platform in 30 seconds. What is the length of the train?

Solution:

Speed = (72 × 1000)/3600 m/sec = 20 m/sec
Time = 30 sec
Let the length of the train be x meters.

Now,
(x + 320)/30 = 20
⇒ x + 320 = 600
⇒ x = 600 - 320
∴ x = 280

∴ The length of the train is 280 meters.

৭৩৬.

Worker P is 50% as efficient as worker Q. Worker R does half of the work done by P and Q together. If R alone does the work in 40 days, then P, Q and R together can do the work in -

ক
ক) 20(1/3) days
খ
খ) 25 days
গ
গ) 15 days
ঘ
ঘ) 13(1/3) days

ব্যাখ্যা

As, R takes 40 days to complete the work, (P + Q) will take = 40/2 = 20 Days
R can do 1/40 part of the work in one day and (P + Q) can do 1/20 part of the work in a day.
So, in 1 day (P + Q + R) can do = (1/20 + 1/40) = (3/40) part of the work
∴ Days required to complete 1 or Total work is = 40/3 = 13(1/3) days

৭৩৭.

A proficient worker is twice as efficient as an apprentice. After 10 days of joint work, they earn Tk. 45,000 together. What is the apprentice’s wage per day?

ক
Tk. 2000
খ
Tk. 1500
গ
Tk. 1600
ঘ
Tk. 1250

ব্যাখ্যা

Question: A proficient worker is twice as efficient as an apprentice. After 10 days of joint work, they earn Tk. 45,000 together. What is the apprentice’s wage per day?

Solution:
Given that,
A seasoned workers efficiency is twice as much as an apprentice's.
They work together for 10 days
And earn Tk. 45000 together

Here, Efficiency of Seasoned Worker : Apprentice = 2 : 1
Now, earning in 1 day = 45000/10 = Tk. 4500
So, Daily wage of Apprentice = 4500 × (1/3) = Tk. 1500

Thus, the daily wage of the apprentice is Tk. 1500.

৭৩৮.

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

ক
3 : 13
খ
9 : 13
গ
36 : 13
ঘ
13 : 9

ব্যাখ্যা

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

Solution:
দেওয়া আছে,
A : B = 3 : 4
⇒ A/B = 3/4

এবং
B : C = 12 : 13
⇒ B/C = 12/13

∴ (A/B) × (B/C) = (3/4) × (12/13)
⇒ A/C = 9/13
∴ A : C = 9 : 13

Then A and C will be in the ratio is 9 : 13.

৭৩৯.

The base of a parallelogram is (p+4) Altitude to the base is (p−3) and the area is (p2−4). Find out its actual area:

ক
ক) 60 square units
খ
খ) 36 square units
গ
গ) 40 square units
ঘ
ঘ) 54 square units

ব্যাখ্যা

In Parallelogram
Let,
b and care sides
b = base
h = height
area = base × height
= b × h
Therefore,
p² - 4 = (p + 4)(p - 3)
p² - 4 = p² + p - 12
p = 8
Hence, actual area
= (p² - 4) = 8² - 4
= 64 - 4
= 60 square units.

৭৪০.

The difference between a number and its square is 72. What is the number?

ক
ক) 6
খ
খ) 7
গ
গ) 9
ঘ
ঘ) 8

ব্যাখ্যা

Question: The difference between a number and its square is 72. What is the number?

Solution:
Let, the number be x.

ATQ,
x² - x = 72
⇒ x² - x - 72= 0
⇒ x² - 9x + 8x - 72 = 0
⇒ x(x - 9) + 8(x - 9) = 0
⇒ (x - 9) (x + 8) = 0
⇒ x - 9 = 0

Here,
x - 9 = 0
∴ x = 9

৭৪১.

The average mark of three subjects is 120. If 44 was misread as 14 during the calculation, what will be the correct average?

ক
ক) 130
খ
খ) 140
গ
গ) 150
ঘ
ঘ) 160

ব্যাখ্যা

Solution: The average mark of three subjects is 120. If 44 was misread as 14 during the calculation, what will be the correct average?

Solution:
Correct average,
= 120 + {(44 − 14)/3}
= 120 + 10
= 130

৭৪২.

If log₂[log₃(log₂x)] = 1, then x is equal to = ?

ক
0
খ
12
গ
128
ঘ
512

ব্যাখ্যা

Question: If log₂[log₃(log₂x)] = 1, then x is equal to = ?

Solution:
Given that,
log₂[ log₃( log₂x)]=1
⇒ log₃(log₂x) = 2¹ = 2
⇒ log₂x = 3² = 9
⇒ x = 2⁹ = 512
∴ x = 512

৭৪৩.

A, B and C each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete the job and earn $2340, what will be C's share of the earnings?

ক
ক) $1,100
খ
খ) $1,080
গ
গ) $630
ঘ
ঘ) $520

ব্যাখ্যা

Question: A, B and C each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete the job and earn $2340, what will be C's share of the earnings?

Solution:
A, B এবং C 1 দিনে করতে পারে কাজটির 1/6,1/8, এবং 1/12 অংশ

A, B এবং C কাজের অনুপাত = 1/6 : 1/8 : 1/12
= (1/6) × 24 : (1/8) × 24 : (1/12) × 24
= 4 : 3 : 2
অনুপাতের রাশিগুলোর যোগফল = 4 + 3 + 2 = 9

C এর অংশ = 2340 এর 2/9
= 520

৭৪৪.

The man was carrying a _____ bag.

ক
ক) black small plasic
খ
খ) small and black
গ
গ) small black plastic
ঘ
ঘ) plastic small black

ব্যাখ্যা

Correct Sentence: The man was carrying a small black plastic bag.
- এই বাক্যে modifier অর্থাৎ adjectives সমূহ হচ্ছে: small, black, plastic.

• The most usual sequence of adjectives:
1. Opinion (unusual, lovely, beautiful, etc).
2. Size (big, small, tall, etc).
3. Physical quality (thin, rough, untidy, etc).
4. Shape (round, square, rectangular, etc).
5. Age (young, old, youthful, etc).
6. Color (blue, red, pink, etc).
7. Origin (Dutch, Japanese, Turkish, etc).
8. Material (metal, wood, plastic, etc).
9. Type (general-purpose, four-sided, U-shaped, etc).
10. Purpose (cleaning, hammering, cooking, etc).

তাই সঠিক sequence হবে: small (size)→ black (color)→ plastic (material).

Source: Cambridge Dictionary.

৭৪৫.

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

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

ব্যাখ্যা

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

Solution:
let, a = 3, b = 2.
a² = 9, b² = 4; a² > b² is true
a² = 9, ab = 6; a² < ab is false
b + a = 5, 2a = 6; b + a > 2a is false
a - b = 1; a - b < 0 is false

৭৪৬.

A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

ক
729 m
খ
2430 m
গ
243 m
ঘ
81 m

ব্যাখ্যা

Question: A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

Solution:
ব্যাসার্ধ, r = 18/2 = 9 সেমি
গোলকটির আয়তন = (4/3) × π × r³
= (4/3) × π × 9³
= 972π

তারটি ব্যাসার্ধ = 4/2 = 2 মিমি = 0.2 সেমি
তারটির আয়তন = πr²l
= π × (0.2)² × l
= 0.04πl

শর্তমতে,
0.04πl = 972π
⇒ l = 972/0.04
⇒ l = 24300 cm
⇒ l = 243 m

৭৪৭.

Which of the following is divisible by 3?

ক
34616
খ
46904
গ
10984
ঘ
14589

ব্যাখ্যা

Question: Which of the following is divisible by 3?

Solution:
We have to simply find the sum of the digits for each option and check if the sum is divisible by 3....

34616 = 3 + 4 + 6 + 1 + 6 = 20
46904 = 4 + 6 + 9 + 0 + 3 = 23
10984 = 1 + 0 + 9 + 8 + 4 = 22
14589 = 1 + 4 + 5 + 8 + 9 = 27

Hence we can see that only 27 is divisible by 3. Thus, 14589 is divisible by 3.

৭৪৮.

Two unbiased coins are tossed. What is the probability of getting at most one tail?

ক
3/4
খ
1/6
গ
1/2
ঘ
1/3

ব্যাখ্যা

Question: Two unbiased coins are tossed. What is the probability of getting at most one tail?

Solution:
Total outcomes = (HH, HT, TH, TT)
Favorable outcomes = (HH, HT, TH)
At most one head refers to a maximum one tail,

Therefore, Probability = Favorable outcomes/Total outcomes = 3/4

৭৪৯.

Using the digits 9, 8, 2, 5 exactly once, how many numbers greater than 5000 can be formed?

ক
10
খ
12
গ
18
ঘ
24

ব্যাখ্যা

Question: Using the digits 9, 8, 2, 5 exactly once, how many numbers greater than 5000 can be formed?

Solution:
To form a number greater than 5000, the first digit must be one of 5, 8, or 9.
If the first digit is 5, the remaining 3 digits can be arranged in ³P₃ = 6 ways.
If the first digit is 8, the remaining 3 digits can be arranged in ³P₃ = 6 ways.
If the first digit is 9, the remaining 3 digits can be arranged in ³P₃ = 6 ways.

Therefore, the total number of ways to form such numbers is: 6 + 6 + 6 = 18
18 numbers greater than 5000 can be formed.

৭৫০.

H.C.F. of 513, 1134 and 1215 is-

ক
18
খ
27
গ
33
ঘ
36

ব্যাখ্যা

Question: H.C.F. of 513, 1134 and 1215 is-

Solution:

H.C.F. of 513, 1134 and 1215 = 3 × 3 × 3 = 27

৭৫১.

If an investor gets Tk. 17,500 as interest after 5 years on his savings of Tk. 14,000. What is the rate of interest?

ক
ক) 12%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 30%

ব্যাখ্যা

Question: If an investor gets Tk. 17,500 as interest after 5 years on his savings of Tk. 14,000. What is the rate of interest?

Solution:
এখানে
মুনাফা I = 17,500 টাকা
আসল P = 14,000টাকা
সময় n = 5 বছর
মুনাফার হার r = ?

আমরা জানি,
I = Pnr
r = I/Pn
= {(17,500 × 100)/(14,000 × 5)}%
= 25%

৭৫২.

In how many years will Tk. 750 amount to Tk. 900 at 4% simple interest per annum?

ক
3.5 years
খ
3 years
গ
4.5 years
ঘ
5 years

ব্যাখ্যা

Question: In how many years will Tk. 750 amount to Tk. 900 at 4% simple interest per annum?

Solution:
Simple Interest = Amount - Principal
= 900 - 750
= 150

Here,
Principal, P = 750
Interest Rate, R = 4%
SI = 150
Time, T = ?

SI = PRT/100
⇒ T = (SI × 100)/(P × R)
= (150 × 100)/(750 × 4)
= 15000/3000
= 5 years

৭৫৩.

The radius of a circle is 6 cm. Find the area of a square inscribed in that circle?

ক
66 square centimeters
খ
72 square centimeters
গ
84 square centimeters
ঘ
98 square centimeters

ব্যাখ্যা

Question: The radius of a circle is 6 cm. Find the area of a square inscribed in that circle?

সমাধান:

দেওয়া আছে,
বৃত্তের ব্যাসার্ধ = 6 সে.মি.
ব্যাস = 2 × 6 = 12 সে.মি.

∴ বর্গক্ষেত্রের কর্ণ = a√2

আমরা জানি,
বর্গক্ষেত্রের কর্ণ = বৃত্তের ব্যাস
⇒ a√2 = 12
⇒ (a√2) = 12²
⇒ a² × 2 = 144
∴ a² = 72 বর্গ সে.মি.

৭৫৪.

ফারহানের জন্মদিন 29 ফেব্রুয়ারি। তাঁর জন্ম গ্রহণের সালটি হতে পারে

ক
1900
খ
2002
গ
2008
ঘ
2010

ব্যাখ্যা

প্রশ্ন: ফারহানের জন্মদিন 29 ফেব্রুয়ারি। তাঁর জন্ম গ্রহণের সালটি হতে পারে

সমাধান:
- ফেব্রুয়ারি মাস 29 দিনে হয় যখন বছরটি লিপ ইয়ার হয়।
- অপশনে প্রদত্ত সালগুলোর মধ্যে শুধুমাত্র 2008 হচ্ছে লিপ-ইয়ার।
- সুতরাং ফারহানের জন্মগ্রহণের সালটি হতে পারে 2008।

[গ্রেগরীয় অ্যালগরিদম অনুযায়ী, কোনো বছর ৪ দ্বারা বিভাজ্য এবং ১০০ দ্বারা বিভাজ্য না হলে তবে সেই বছর অধিবর্ষ হবে। কিন্তু ১০০ দ্বারা বিভাজ্য হলে সেই বছর অধিবর্ষ হবে না যদি ঐ বছর ৪০০ দ্বারা বিভাজ্য না হয়।]

৭৫৫.

What should be the value of "Q" so that the expression (25 - 30x + Qx²) becomes a perfect square?

ক
5
খ
9
গ
4
ঘ
16

ব্যাখ্যা

Question: What should be the value of "Q" so that the expression (25 - 30x + Qx²) becomes a perfect square?

Solution:
(25 - 30x + Qx²)
= (5)² - 2 × 5 × 3x + (3x)² + Qx² - (3x)²= (5 - 3x)² + Qx² - 9x²

∴ The expression becomes a perfect square if,
Qx² - 9x² = 0
⇒ Qx² = 9x²∴ Q = 9

৭৫৬.

Six consecutive whole numbers are given. The sum of the last three numbers is 36. What is the sum of the first three numbers?

ক
22
খ
25
গ
27
ঘ
31

ব্যাখ্যা

Question: Six consecutive whole numbers are given. The sum of the last three numbers is 36. What is the sum of the first three numbers?

Solution:
let,
The numbers be x - 2, x - 1, x, x + 1, x + 2, x + 3

ATQ,
x + 1 + x + 2 + x + 3 = 36
⇒ 3x + 6 = 36
⇒ 3x = 30
⇒ x = 30/3
∴ x = 10

The sum of the first three numbers is = x - 2 + x - 1 + x
= 10 - 2 + 10 - 1 + 10
= 30 - 3
= 27

৭৫৭.

Simplify the expression using BODMAS rule:
(3/2) of (4/7){(10 × 3) - (8 × 2)}

ক
6
খ
12
গ
14
ঘ
18
ঙ
20

ব্যাখ্যা

Question: Simplify the expression using BODMAS rule:
(3/2) of (4/7){(10 × 3) - (8 × 2)}

Solution:
(3/2) of (4/7){(10 × 3) - (8 × 2)}
= (6/7){30 - 16}
= (6/7)(14)
= 6 × 2
= 12

৭৫৮.

Which of the following numbers should be added to 8567 to make it exactly divisible by 4?

ক
ক) 4
খ
খ) 1
গ
গ) 2
ঘ
ঘ) 3

ব্যাখ্যা

On dividing 8567 by 4, the remainder is 3.

To make it divisible by 4, we must add (4 - 3) =1

৭৫৯.

Rafi weighs 72 kg. If he reduces his weight in the ratio 6 : 5, find his new weight in kg.

ক
56 Kg
খ
60 Kg
গ
52.5 Kg
ঘ
58.5 Kg

ব্যাখ্যা

Question: Rafi weighs 72 kg. If he reduces his weight in the ratio 6 : 5, find his new weight in kg.

Solution:
ধরি, রাফির পূর্বের ওজন = 6x
রাফির পরের ওজন = 5x

প্রশ্নমতে,
6x = 72
⇒ x = 72 / 6 = 12

∴ ওজন কমে যাওয়ার পর হবে = 5x = 5 × 12 = 60 kg

৭৬০.

If y = √8 + √7, then what is the value of y³ + (1/y³)?

ক
34√2
খ
64√3
গ
81√2
ঘ
116√2

ব্যাখ্যা

Question: If y = √8 + √7, then what is the value of y³ + (1/y³)?

Solution:
দেওয়া আছে,
y = √8 + √7
⇒ 1/y = 1/(√8 + √7)
⇒ 1/y = (√8 - √7)/(√8 + √7)(√8 - √7)
⇒ 1/y = (√8 - √7)/{(√8)² - (√7)²}
⇒ 1/y = (√8 - √7)/(8 - 7)
∴ 1/y = √8 - √7

এখন, y + 1/y = (√8 + √7) + (√8 - √7)
= 2√8 = 2 × 2√2 = 4√2

এখন,
y³ + (1/y³)
= (y + 1/y)³ - 3(y)(1/y)(y + 1/y)
= (y + 1/y)³ - 3(y + 1/y)
= (4√2)³ - 3(4√2)
= (4³)(√2)³ - 12√2
= 64(2√2) - 12√2
= 128√2 - 12√2
= 116√2

সুতরাং, নির্ণেয় মান হলো 116√2

৭৬১.

If the sum of three consecutive numbers is multiplied by 4, the result is 132. What is the largest number?

ক
10
খ
12
গ
14
ঘ
16

ব্যাখ্যা

Question: If the sum of three consecutive numbers is multiplied by 4, the result is 132. What is the largest number?

Solution:
ধরি,
তিনটি ধারাবাহিক সংখ্যা যথাক্রমে x, x + 1 এবং x + 2

প্রশ্নমতে,
⇒ {x + (x + 1) + (x + 2)} × 4 = 132
⇒ (3x + 3) × 4 = 132
⇒ 3x + 3 = 132 / 4
⇒ 3x + 3 = 33
⇒ 3x = 33 - 3
⇒ x = 30/3
∴ x = 10

বৃহত্তম সংখ্যাটি হলো = x + 2
= 10 + 2
= 12

৭৬২.

If x + 1/x = 5 , then x³ + 1/x³ = ?

ক
90
খ
105
গ
110
ঘ
140

ব্যাখ্যা

Question: If x + 1/x = 5 , then x³ + 1/x³ = ?

Solution:
x³ + 1/x³
=(x + 1/x)³ - 3. x. (1/x)(x + 1/x)
= 5³ - (3 × 5)
= 125 - 15
= 110

৭৬৩.

The average of the marks obtained in a mock test by 8 boys was 50 and by 2 girls was 80. The average marks of all 10 students were-

ক
50
খ
56
গ
60
ঘ
62

ব্যাখ্যা

Question: The average of the marks obtained in a mock test by 8 boys was 50 and by 2 girls was 80. The average marks of all 10 students were-

Solution:
Sum of total number of 8 boys in mock = 8 × 50 = 400
Sum of total number of 2 girls in exam = 2 × 80 = 160
Required average = (400+160)/10 = 560/10 = 56

৭৬৪.

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

ক
ক) 1/2
খ
খ) 1/3
গ
গ) 2/3
ঘ
ঘ) 3/5

ব্যাখ্যা

Total number of balls
= (8 + 7 + 6)
= 21
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue
∴n(E)=7
∴P(E) = n(E)/n(S)
= 7/21
= 1/3

৭৬৫.

3640 ÷ 14 × 16 + 340 = ?

ক
0.70
খ
3525
গ
4480
ঘ
None of these

ব্যাখ্যা

Question: 3640 ÷ 14 × 16 + 340 = ?

Solution:
3640 ÷ 14 × 16 + 340
= 260 × 16 + 340
= 4160 + 340
= 4500

৭৬৬.

The radius of a circle is increased so that in circumference increased by 5%. The area of the circle will be increased by-

ক
ক) 5%
খ
খ) 10%
গ
গ) 10.25%
ঘ
ঘ) 10.5%

ব্যাখ্যা

ধরি
বৃত্তটির ব্যাসার্ধ r
বৃত্তটির পরিধি = 2πr

5% বৃদ্ধিতে বৃত্তটির নতুন পরিধি = 2πr + 2πr এর 5%
= 2πr + 2πr এর 5/100
= 2π(r + r/20)
= 2π × 1.05r
বৃত্তটির নতুন ব্যাসার্ধ = 1.05r

ক্ষেত্রফল বাড়ে = π × (1.05r)² - π × r²
= 1.1025 πr² - πr²
= 0.1025 πr²

ক্ষেত্রফল শতকরা বাড়ে ={(0.1025 πr²/πr²) × 100}%
= 10.25%

৭৬৭.

If three workers can mow a lawn in 4 hours, how many workers are needed to mow the lawn in 2 hours?

ক
3
খ
4
গ
6
ঘ
12

ব্যাখ্যা

Problem: If three workers can mow a lawn in 4 hours, how many workers are needed to mow the lawn in 2 hours?

Solution:
৪ ঘণ্টায় শেষ করতে লোক লাগে ৩ জন
২ ঘণ্টায় শেষ করতে লোক লাগে (৪ × ৩/২) জন
= ৬ জন

৭৬৮.

Let, ABC is a right angle and tanθ = 3, then what is the hypotenuse of ABC triangle?

ক
√3
খ
√10
গ
2
ঘ
√2

ব্যাখ্যা

Question: Let, ABC is a right angle and tanθ = 3, then what is the hypotenuse of ABC triangle?

Solution:
We know,
tanθ = Perpendicular/Base
= 3/1

So the Perpendicular of ABC triangle = 3
and Base of ABC triangle = 1

By Pythagoras,
(Hypotenuse)² = (Perpendicular)² +(Base)²
⇒ (Hypotenuse)² = 3² + 1²
⇒ (Hypotenuse)² = 10
∴ Hypotenuse = √10

৭৬৯.

If a 30 m ladder is placed against a 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to -

ক
5^°
খ
10^°
গ
20^°
ঘ
30^°

ব্যাখ্যা

Question: If a 30 m ladder is placed against a 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to -

Solution:

Here,
Ladder, AC = 30m
Wall, AB = 15m
∠ACB = θ =?

sinθ = AB/AC [ sinθ = লম্ব/অতিভুজ ]
⇒ sinθ = 15/30
⇒ sinθ = 1/2
⇒ sinθ = sin30^°

∴ θ = 30^°

৭৭০.

A team lost 25% of the matches it played. If it won 15 matches, find the number of matches it played.

ক
ক) 30
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 25

ব্যাখ্যা

প্রশ্ন: A team lost 25% of the matches it played. If it won 15 matches, find the number of matches it played.

সমাধান:
জয়ী হয় (১০০ - ২৫)% = ৭৫% ম্যাচ

৭৫ ম্যাচ জয়ী হয় যখন মোট ম্যাচ ১০০টি
∴ ১৫ ম্যাচ জয়ী হয় যখন মোট ম্যাচ (১০০ × ১৫)/৭৫টি
= ২০টি

৭৭১.

Two trains, each 200 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the slower train is:

ক
ক) 60 km/hr
খ
খ) 30 km/hr
গ
গ) 40 km/hr
ঘ
ঘ) 70 km/hr

ব্যাখ্যা

Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.

(200 + 200)/8= 3x
400/8 = 3x
x = (400/(3 × 8)
x = 50/3

Speed of the slower train = (50/3) × (18/5)
= 60 km/hr

৭৭২.

If the price of sugar rises from tk. 6 per kg to tk. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumption of sugar by-

ক
ক) 15%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 30%
ঙ
ঙ) Insufficient Data

ব্যাখ্যা

Increase = 7.5 - 6
= 1.5
percentage of increase= (1.5/6) × 100
= 25%
so, consumption must be reduced by (r/100+r) × 10
= (25/100+25) × 100
= 20%

৭৭৩.

The simple interest at p% for p years will be Tk. p on a sum of?

ক
Tk. p
খ
Tk. 100p
গ
Tk. p/100
ঘ
Tk. 100/p

ব্যাখ্যা

Question: The simple interest at p% for p years will be Tk. p on a sum of?

Given,
Rate of interest, r = p%
Interest, I = p Tk.
Time, n = p years.

We know,
I = Pnr
P = I/nr
= (p × 100)/(p × p)
= 100/p Tk.

৭৭৪.

A train running at a speed of 72 km/hr crosses a platform double its length in 45 seconds. What is the length of the platform in meters?

ক
200m
খ
300m
গ
600m
ঘ
700m

ব্যাখ্যা

Question: A train running at a speed of 72 km/hr crosses a platform double its length in 45 seconds. What is the length of the platform in meters?

Solution:
Let the length of the train be x meters
Then, length of the platform = (2x) meters

∴ Speed of the train = {72 × (5/18)} m/sec
= 20 m/sec

∴(x+2x)/20 = 45
⇒ 3x = 45 × 20
⇒ 3x = 900
⇒ x = 900/3 = 300

Hence, length of platform = 2x = (2×300)m = 600m

৭৭৫.

The average of several exam scores is 80. One make-up exam was given. Included with the other scores. The new average was 84. If the score on the make up exam was 92, how many total exams were given?

ক
ক) 3
খ
খ) 2
গ
গ) 4
ঘ
ঘ) 5

ব্যাখ্যা

Question: The average of several exam scores is 80. One make-up exam was given. Included with the other scores. The new average was 84. If the score on the make up exam was 92, how many total exams were given?

Solution:
Make-up পরীক্ষা বাদে পরীক্ষা নেয়া হয়েছিল x টি

প্রশ্নমতে,
80x + 92 = 84(x + 1)
80x + 92 = 84x + 84
92 - 84 = 84x - 80x
8 = 4x
x = 2

Make-up পরীক্ষা সহ পরীক্ষা নেয়া হয়েছিল = 2 + 1 = 3টি

৭৭৬.

Two cards are drawn at random and without replacement from a standard deck of 52 cards. What is the probability that both cards are face cards?

ক
11/221
খ
13/321
গ
7/158
ঘ
5/109
ঙ
None of these

ব্যাখ্যা

Question: Two cards are drawn at random and without replacement from a standard deck of 52 cards. What is the probability that both cards are face cards?

Solution:
Total card = 52
Total face card = 3 × 4 = 12

Total ways to choose 2 cards from 52 = ⁵²C₂ = (52 × 51)/2 = 1326

Total ways to choose 2 face cards from 12 = ¹²C₂ = (12 × 11)/2 = 66

∴ So, the probability that both cards are face cards = 66/1326
= (2 × 3 × 11)/(2 × 3 × 221)
= 11/221

৭৭৭.

The perimeter of a rectangular field is 104 meters. If the length of the field is 4 meters more than twice the width, what is the area of that field in square meters?

ক
524 square meters
খ
600 square meters
গ
576 square meters
ঘ
424 square meters
ঙ
None of these

ব্যাখ্যা

Question: The perimeter of a rectangular field is 104 meters. If the length of the field is 4 meters more than twice the width, what is the area of that field in square meters?

Solution:
Let,
The width of the rectangular field = x meter
∴ The length of the rectangular field = 2x + 4 meter

ATQ,
2(2x + 4 + x) = 104
⇒ 3x + 4 = 52
⇒ 3x = 48
∴ x = 16
∴ width = 16 m

∴ length L = 2x + 4 = 2 × 16 + 4 = 32 + 4 = 36 m

∴ The area of that field is = (L × W) square meters
= (36 × 16) square meters
= 576 square meters

৭৭৮.

A train 240m long passes a pole in 24 seconds. How long will is take to pass a platform 650m long?

ক
ক) 80 sec
খ
খ) 89 sec
গ
গ) 90 sec
ঘ
ঘ) 95 sec

ব্যাখ্যা

Question: A train 240m long passes a pole in 24 seconds. How long will is take to pass a platform 650m long?

Solution:
ট্রেনটির মোট অতিক্রম করতে হবে = (240 + 650) মিটার = 890 মিটার

ট্রেনটি 240 মিটার অতিক্রম করতে সময় লাগে 24 সেকেন্ড
ট্রেনটি 1 মিটার অতিক্রম করতে সময় লাগে 24/240 সেকেন্ড
ট্রেনটি 890 মিটার অতিক্রম করতে সময় লাগে (24 × 890)/240 সেকেন্ড
= 89 সেকেন্ড

৭৭৯.

A jar is filled with liquid, 2 parts of which are water and 4 parts juice. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half juice?

ক
1/2
খ
1/4
গ
2/3
ঘ
5/2
ঙ
7/5

ব্যাখ্যা

Question: A jar is filled with liquid, 2 parts of which are water and 4 parts juice. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half juice?

Solution:
Let the quantity of liquid in the vessel = 6 units.
Out of this liquid, x units are replaced by water.

Amount of water in the new mixture = {2 - (2x/6) + x} unit
= 2 - (x/3) + x
= (6 - x + 3x)/3
= (2x + 6)/3 unit

Amount of juice in the new mixture = 4 - (4x/6) unit
= 4 - (2x/3)
= (12 - 2x)/3 unit

ATQ,
(2x + 6)/3 = (12 - 2x)/3
⇒ 2x + 6 = 12 - 2x
⇒ 4x = 6
⇒ x = 3/2

∴ The fraction of the mixture that is replaced is = (3/2) × (1/6)
= 1/4

৭৮০.

The sum of four consecutive even numbers A, B, C and D is 180. What is the sum of the set of next four consecutive even numbers?

ক
210
খ
204
গ
202
ঘ
212

ব্যাখ্যা

Question: The sum of four consecutive even numbers A, B, C and D is 180. What is the sum of the set of next four consecutive even numbers?

Solution:
let, the consecutive even numbers are a, a + 2, a + 4, a + 6
∴ a + a + 2 + a + 4 + a + 6 = 180
or, 4a = 180 - 12
or, 4a = 168
∴ a = 42

the numbers are 42, 44, 46, 48.

next 4 consecutive numbers are 50, 52, 54, 56
sum = 50 + 52 + 54 + 56
= 212

৭৮১.

The difference between the greatest and least prime numbers which are less than 100 is = ?

ক
94
খ
91
গ
95
ঘ
97
ঙ
89

ব্যাখ্যা

Greatest prime number = 97
Least prime number = 2
So, their difference 97 - 2 = 95

৭৮২.

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

ক
6
খ
9
গ
1
ঘ
3

ব্যাখ্যা

Question: If 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 = 3/3 = 1
⇒ log₃x = 1
⇒ x = 3¹
∴ x = 3

৭৮৩.

Rizvi and Amin start simultaneously from a place A towards B 60 km apart. Rizvi's speed is 4km/h less than that of Amin. Amin, after reaching B, turns back and meets Rizvi at a place 12 km away from B. Rizvi's speed is -

ক
ক) 12 km/hr
খ
খ) 10 km/hr
গ
গ) 8 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Let the speed of Rizvi be x kmph;
Hence, Amin's speed = (x + 4) kmph;
Distance covered by Amin = 60 + 12 = 72 km;
Distance covered by Rizvi = 60 - 12 = 48 km.

According to question,
⇒ 72/(x + 4) = 48/x
⇒ 3/(x + 4) = 2/x
⇒ 3x = 2x + 8
⇒ x = 8 kmph.

৭৮৪.

If x is 30% greater than y, what percent of y is x?

ক
ক) 70
খ
খ) 77
গ
গ) 120
ঘ
ঘ) 130

ব্যাখ্যা

If, y = 100 then x = 100 + 30 = 130
then, x is 130% of y

৭৮৫.

12/15 is how many percent?

ক
ক) 90 percent
খ
খ) 70 percent
গ
গ) 80 percent
ঘ
ঘ) 60 percent

ব্যাখ্যা

Question: 12/15 is how many percent?

Solution:

12/15

= 4/5

= (4 × 20)/(5 × 20)

= 80/100

= 80%

৭৮৬.

A boat runs at 22 km hour along the stream and 10 km per hour against the stream. Find the ratio of the speed of the boat in still water to that of the speed of the stream.

ক
ক) 2 : 3
খ
খ) 5 : 3
গ
গ) 7 : 3
ঘ
ঘ) 8 : 3

ব্যাখ্যা

ধরি
নৌকার বেগ = x কি.মি./ঘণ্টা
স্রোতের বেগ = y কি.মি./ঘণ্টা

x + y = ২২........... (১)
x - y =১০ ..............(২)
(১)নং ও (২) নং যোগ করে পাই
২x = ৩২
বা, x = ৩২/২
∴ x = ১৬
(১)নং হতে (২) নং বিয়োগ করে পাই
২y = ১২
বা, y = ১২/২
∴ y =৬

নির্ণেয় অনুপাত = ১৬ : ৬
= ৮ : ৩

৭৮৭.

The average weight of 25 students in a class was found to be 48 kg. Later it was discovered that one student's weight was recorded as 35 kg instead of 60 kg. What is the correct average weight of the 25 students?

ক
44 kg
খ
46 kg
গ
49 kg
ঘ
52 kg

ব্যাখ্যা

Question: The average weight of 25 students in a class was found to be 48 kg. Later it was discovered that one student's weight was recorded as 35 kg instead of 60 kg. What is the correct average weight of the 25 students?

Solution:
Given,
The average weight of 25 students in a class was found to be 48 kg
Incorrect sum of the weight of 25 students = (48 × 25) kg
= 1200 kg

Correct sum of the weight of 25 students = (incorrect sum) - (wrongly copied item) + (actual item)
= (1200 - 35 + 60) kg
= 1225 kg

Correct mean = correct sum/number of students
= (1225/25) kg
= 49 kg

∴ Hence, the correct mean weight is 49 kg

৭৮৮.

How many times are the hands of a clock at right angle in a day?

ক
88 times
খ
66 times
গ
22 times
ঘ
44 times

ব্যাখ্যা

Question: How many times are the hands of a clock at right angle in a day?

Solution:
In 12 hours, they are at right angles 22 times.
∴ In 24 hours, they are at right angles 44 times.

৭৮৯.

What is the solution of

ক
secA
খ
1
গ
0
ঘ
secA + 1

ব্যাখ্যা

Question: What is the solution of

Solution:

৭৯০.

Normally a Play Station costs Tk. 5000, but you only want to pay Tk. 4500. How much discount (in percent) do you want?

ক
11.11%
খ
10%
গ
5%
ঘ
15%

ব্যাখ্যা

Question: Normally a Play Station costs Tk. 5000, but you only want to pay Tk. 4500. How much discount (in percent) do you want?

Solution:
Discount = 5000 - 4500 = 500

% Discount = (500/5000) × 100 = 10%

৭৯১.

The average of the first five multiples of 3 is-

ক
ক) 7
খ
খ) 8
গ
গ) 9
ঘ
ঘ) 10

ব্যাখ্যা

First five multiple of 3 are
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12 and
3 × 5 = 15
Average of first five multiples of 3 are (3 + 6 + 9 + 12 + 15)/5
= 9

∴ The average of first five multiples of 3 is 9.

৭৯২.

{(2.39)² - (1.61)²}/(2.39 - 1.61) = ?

ক
3.91
খ
4
গ
4.12
ঘ
3

ব্যাখ্যা

Question: {(2.39)² - (1.61)²}/(2.39 - 1.61) = ?

Solution:
Let, 2.39 = a
And 1.61 = b

Now,
(a² - b²)/(a - b)
= (a + b)(a - b)/(a - b)
= a + b
= 2.39 + 1.61
= 4

৭৯৩.

If 25% of a number is 75, 80% of the number is:

ক
ক) 300
খ
খ) 180
গ
গ) 375
ঘ
ঘ) 240

ব্যাখ্যা

ধরি,
সংখ্যাটি = x

প্রশ্নমতে,
x এর 25% = 75
25x/100 = 75
x/4 = 75
x = 300

300 এর 80% = 300 × 80/100
= 240

৭৯৪.

Solve the inequality (x + 4)².(x - 3) < 0

ক
(3, ∞)
খ
(- 4, 3)
গ
(- ∞, - 4) ∪ (- 4, 3)
ঘ
(- ∞, 3)
ঙ
None

ব্যাখ্যা

Question: Solve the inequality (x + 4)².(x - 3) < 0

Solution:
We have (x + 4)².(x - 3) < 0
The critical points are x = - 4, 3

The solution is (- ∞, - 4) ∪ (- 4, 3)

৭৯৫.

A cylinder of 2m radius and 5m length can store water of -

ক
62852 liters
খ
62832 liters
গ
62532 liters
ঘ
65832 liters

ব্যাখ্যা

Question: A cylinder of 2m radius and 5m length can store water of -

Solution:
here,
r = 2m
h = 5m

volume = πr²h
= 3.1416 × (2)² × 5
= 62.832 m³

we know,
1 m³ = 1000 liters
∴ 62.832 m³ = (62.832 × 1000) liters
= 62832 liters

৭৯৬.

If 10% of X is equal to 20% of Y, then find X : Y.

ক
1:2
খ
2:1
গ
4:1
ঘ
1:4
ঙ
1:3

ব্যাখ্যা

10% of X = 20% of Y
or, (10/100) × X = (20/100) × Y
or, X/10 = Y/5
or, 5X = 10Y
or, X = 2Y
or, X/Y = 2/1
So, X : Y = 2 : 1

৭৯৭.

A man bought oranges at the rate of 8 for Tk. 34 and sold them at the rate of 12 for Tk. 57. How many oranges should be sold to earn a net profit of Tk. 45?

ক
ক) 90
খ
খ) 99
গ
গ) 190
ঘ
ঘ) 150

ব্যাখ্যা

CP of 1 orange
= Tk.34/8
= Tk.4.25
SP of 1 orange
=Tk. 57/12
=Tk.4.75
Profit on each apple = (4.75 - 4.25) = Tk. 0.50
∴ Number of apples required
= 45/ 0.50
=90

৭৯৮.

The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the eldest boy is-

ক
ক) 9 years
খ
খ) 15 years
গ
গ) 21 years
ঘ
ঘ) 27 years

ব্যাখ্যা

Question: The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the eldest boy is-

Solution:
The average age of three boys is 15 years.
sum of three boys = (15 × 3)
= 45 years

their ages are in ratio 3 : 5 : 7
so, there ages are 3x, 5x, 7x

3x + 5x + 7x = 45
⇒ 15x = 45
∴ x = 3

age of the eldest boy is (7 × 3) years
= 21 years

৭৯৯.

A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was?

ক
10 km
খ
15 km
গ
20 km
ঘ
25 km

ব্যাখ্যা

Question: A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was?

Solution:
Let, the distance be = x km
∴Total time = 5 hours 48 minutes
= {5 + (48/60)}
= {5 + (4/5)} hours
= 29/5 hours

ATQ,
(x/25) + (x/4) = 29/5
⇒ (4x + 25x)/100 = 29/5
⇒29x/100 = 29/5
⇒ 5 × 29x = 29 × 100
⇒ x = (29 × 100)/(5 × 29)
⇒ x = 20 km

৮০০.

If 40% of an amount is 250, what will be 60% of that amount?

ক
300
খ
320
গ
375
ঘ
400

ব্যাখ্যা

Question: If 40% of an amount is 250, what will be 60% of that amount?

Solution:
Let,
The amount be x

ATQ,
40% of x = 250
⇒ (40x)/100 = 250
⇒ 40x = 25000
∴ x = 625

60% of 625 = (60 × 625)/100 = 375