Bank Math

PrepBank · পাতা ১০০ / ১৬১ · ৯,৯০১–১০,০০০ / ১৬,১২৪

৯,৯০১.

If a = 4b, what percentage of 2a is 2b?

ক
10%
খ
12%
গ
20%
ঘ
25%
ঙ
None

ব্যাখ্যা

প্রশ্ন: If a = 4b, what percentage of 2a is 2b?

সমাধান:
দেওয়া আছে,
a = 4b

ধরি,
x এর শতকরা 2a হলো 2b

প্রশ্নমতে,
(x/100) × 2a = 2b
⇒ x = (2b × 100)/2a
⇒ x = (2b × 100)/8b [a = 4b বসিয়ে]
∴ x = 25%

৯,৯০২.

(0.8)^{- 5}/(.4)^{- 4} = ?

ক
3/12
খ
5/64
গ
1/2
ঘ
1
ঙ
None of these

ব্যাখ্যা

Question: (0.8)^{- 5}/(.4)^{- 4} = ?

Solution:
= (0.8)^{- 5}/(.4)^{- 4}
= (1/.8⁵)/(1/.4⁴)
= (1/0.32768)/(1/0.0256)
= (1/0.32768) × 0.0256
= 0.7801

Now,
ক) 3/12 = 0.25 ⇒ Incorrect
খ) 5/64 = 0.078125 ⇒ Correct ✓
গ) 1/2 = 0.5 ⇒ Incorrect
ঘ) 1 ⇒ Incorrect
ঙ) None of these ⇒ Incorrect

৯,৯০৩.

The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?

ক
30 m
খ
94.6 m
গ
45 m
ঘ
103.8 m

ব্যাখ্যা

Let BD be the lighthouse and A and C be the two points on the ground.
Then, BD, the height of the lighthouse = 60 m
∠BAD = 45°,∠BCD = 60°
tan45° = BD/BA
1 = 60/BA
BA = 60 m .......(i)
tan60° = BD/BC
√3= 60/BC
BC = 60/√3
= 60 × √3)/(√3 × √3)
= 20√3
= 20 × 1.73
= 34.6 m .......(ii)
Distance between the two points A and C
= AC = BA + BC
= 60 + 34.6 [∵ Substituted value of BA and BC from (1) and (2)]
= 94.6 m

৯,৯০৪.

Mr. A is 5 years senior to Mr. B, Mr. B is 3 years senior to Mr. C, Mr. C is 2 year junior to Mr. D in job experience. If Mr. D has 15 years job experience than how many years of experience possessing Mr. A?

ক
ক) 18
খ
খ) 19
গ
গ) 20
ঘ
ঘ) 22
ঙ
ঙ) 21

ব্যাখ্যা

Question: Mr. A is 5 years senior to Mr. B, Mr. B is 3 years senior to Mr. C, Mr. C is 2 year junior to Mr. D in job experience. If Mr. D has 15 years job experience than how many years of experience possessing Mr. A?

Solution:
Job experience of Mr.D = 15 years

Mr. C is 2 year junior to Mr. D in job experience.
∴Job experience of Mr.c = 15 - 2 = 13 years

Mr. B is 3 years senior to Mr. C in job experience.
∴ Job experience of Mr.b = 13 + 3 = 16 years

Mr. A is 5 years senior to Mr. B in job experience.
∴ Job experience of Mr.A = 16 + 5 = 21 years

৯,৯০৫.

Ruman was told to work 8 hours for the company everyday with 8 days leave for the month of January. But he spent 3 days extra as leave. How much time he has to work extra to equalize the working hour for the month January?

ক
ক) 1.2 hours
খ
খ) 1.3 hours
গ
গ) 1.4 hours
ঘ
ঘ) 1.5 hours

ব্যাখ্যা

Question: Ruman was told to work 8 hours for the company everyday with 8 days leave for the month of January. But he spent 3 days extra as leave. How much time he has to work extra to equalize the working hour for the month January?

Solution:
৮ দিনের বন্ধের পর জানুয়ারি মাসে বাকি থাকে (৩১ - ৮) বা, ২৩ দিন।
২৩ দিনে কাজ করার কথা (২৩ × ৮) ঘণ্টা বা, ১৮৪ ঘন্টা

৩ দিন অতিরিক্ত কাজ না করায় বাকি দিন রইলো = ২৩ - ৩ = ২০ দিন।

তাহলে প্রতিদিন কাজ করতে হবে = ১৮৪/২০ = ৯.২ ঘণ্টা।

প্রতিদিন অতিরিক্ত কাজ করতে হবে = (৯.২ - ৮) = ১.২ ঘণ্টা

৯,৯০৬.

A committee has 5 men and 6 women. What is the number of ways of selecting a group of eight persons?

ক
ক) 165
খ
খ) 185
গ
গ) 205
ঘ
ঘ) 225

ব্যাখ্যা

Question: A committee has 5 men and 6 women. What is the number of ways of selecting a group of eight persons?

Solution:
মোট লোকসংখ্যা = 5 + 6 = 11 জন

11 জন থেকে 8 জন বাছাই করা যাবে = ¹¹C₈ উপায়ে
= 165 উপায়ে

৯,৯০৭.

a, b and c are all positive integers such that a + b + c = 150 and none of these values are equal to each other. What is the smallest possible value for the median of a, b and c?

ক
ক) 5
খ
খ) 4
গ
গ) 3
ঘ
ঘ) 2

ব্যাখ্যা

Question: a, b and c are all positive integers such that a + b + c = 150 and none of these values are equal to each other. What is the smallest possible value for the median of a, b and c?

Solution :
ধরি,
a = 1 , b = 2

a + b + c = 150
1 + 2 + c = 150
c = 150 - 3
c = 147

ক্রমানুসারে সংখ্যাগুলো হলো 1,2,147

সর্বনিম্ন মধ্যক হলো: 2

৯,৯০৮.

The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?

ক
8 kmph
খ
6 kmph
গ
7.5 kmph
ঘ
5.5 kmph
ঙ
5 Kmph

ব্যাখ্যা

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Downstream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph

৯,৯০৯.

A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is

ক
ক) 5 km/hr
খ
খ) 5.5 km/hr
গ
গ) 4 km/hr
ঘ
ঘ) 4.5 km/hr

ব্যাখ্যা

Question: A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is

Solution:
Let,
The speed of the man in still water is x km/hr
The speed of stream is y km/hr

∴ x - y = 24/6 = 4
∴ x + y = 35/7 = 5

∴ x - y + x + y = 4 + 5
⇒ 2x = 9
∴ x = 4.5

∴ The speed of the man in still water is 4.5 km/hr

৯,৯১০.

The ratio of water and salt in a 16 kg of salt - water solution is 3 : 1. How much water in kg must be added to make the ratio of water to salt 4 : 1?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 6

ব্যাখ্যা

salt = 16 × 1/4 = 4 Kg
water = 16 - 4
= 12 kg.
এখন water/salt = 4
∴ water = 4 × 4 = 16 Kg
∴ (16 - 12) = 4 Kg water add করতে হবে।

৯,৯১১.

The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?

ক
32
খ
65
গ
67
ঘ
31

ব্যাখ্যা

Question: The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?

Solution:
Let
P, Q, R represent their respective weights. Then, we have:
P + Q + R = (45 × 3) = 135 ........ (i)
P + Q = (40 × 2) = 80 ....... (ii)
Q + R = (43 × 2) = 86 ....... (iii)

Adding (ii) and (iii), we get: P + 2Q + R = 166 ...... (iv)
Subtracting (i) from (iv), we get: Q = 31

৯,৯১২.

If p, q, r are the digits of a number beginning from the left, the number is -

ক
100q + 10p + r
খ
100p + 10q + r
গ
100r + 10q + p
ঘ
rqp

ব্যাখ্যা

Question: If p, q, r are the digits of a number beginning from the left, the number is -

Solution:
as the sequence is from the left,
the value of p is = 100p
the value of q is = 10q
the value of r = r

∴ the number is = 100p + 10q + r

৯,৯১৩.

If 5x + 2y = 12 and 2x + 5y = 16, what is the value of x?

ক
2
খ
2/5
গ
4/3
ঘ
8/3

ব্যাখ্যা

Question: If 5x + 2y = 12 and 2x + 5y = 16, what is the value of x?

Solution:
Given,
5x + 2y = 12 ....... (1)
and 2x + 5y = 16 ........ (2)

{(1) × 5} - {(2) × 2} we get,
25x + 10y - 4x - 10y = 60 - 32
⇒ 21x = 28
⇒ x = 28/21
∴ x = 4/3

৯,৯১৪.

A man buys a fan for Tk. 1000 and sells it at a loss of 15%. What is the selling price of the fan?

ক
Tk. 950
খ
Tk. 850
গ
Tk. 890
ঘ
Tk. 915

ব্যাখ্যা

Question: A man buys a fan for Tk. 1000 and sells it at a loss of 15%. What is the selling price of the fan?

Solution:
Cost Price of the fan is Tk.1000

Loss percentage is 15%

As we know,
Loss percentage = (Loss/Cost Price) × 100

15 = (Loss/1000) × 100

∴ Loss = 150

As we know,

Loss = Cost Price - Selling Price

∴ Selling Price = Cost Price - Loss

= 1000 - 150

= 850

∴ Selling Price = Tk. 850

৯,৯১৫.

If k is an integer and k = 437/n, then which of the following could be the value of n?

ক
ক) 20
খ
খ) 21
গ
গ) 24
ঘ
ঘ) 23

ব্যাখ্যা

Question: If k is an integer and k = 437/n, then which of the following could be the value of n?

Solution:

দেওয়া আছে,
k = 437/n যেখানে k একটি পূর্ণসংখ্যা।
∴ n এর মান এমন হবে যা দ্বারা 437 কে নিঃশেষে ভাগ করা যাবে। অপশন অনুযায়ী একমাত্র 23 দ্বারা 437 কে ভাগ করা যায়।

সুতরাং, n এর মান 23.

৯,৯১৬.

A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and p. He found the mean to be 12. What should be the number in place of p?

ক
ক) 7
খ
খ) 3
গ
গ) 17
ঘ
ঘ) 31

ব্যাখ্যা

Question: A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and p. He found the mean to be 12. What should be the number in place of p?

সমাধান:
গড় = (৩ + ১১ + ৭ + ৯ + ১৫ + ১৩ + ৮ + ১৯ + ১৭ + ২১ + ১৪ + p)/১২
= (১৩৭ + p)/১২

শর্তমতে,
(১৩৭ + p)/১২ = ১২
বা, ১৩৭ + p = ১৪৪
বা, p = ১৪৪ - ১৩৭
∴ p = ৭

৯,৯১৭.

At the rate of (17/2)% p.a. simple interest, a sum of Tk. 4800 will earn how much interest in 2 years 3 months?

ক
Tk. 956
খ
Tk. 818
গ
Tk. 718
ঘ
Tk. 918

ব্যাখ্যা

Question: At the rate of (17/2)% p.a. simple interest, a sum of Tk. 4800 will earn how much interest in 2 years 3 months?

Solution:
Time, n = 2 years 3 months = 2(1/4) years = 9/4 years.

We know,
I = Pnr
= 4800 × (9/4) × (17/2) × (1/100)
= Tk. 918

৯,৯১৮.

In every 30 minutes the time of a watch increases by 3 minutes. After showing the correct time at 5 a.m. What time will the watch show after 6 hours?

ক
10 : 54 am
খ
11 : 30 am
গ
11 : 36 am
ঘ
11 : 42 am

ব্যাখ্যা

Question: In every 30 minutes the time of a watch increases by 3 minutes. After showing the correct time at 5 a.m. What time will the watch show after 6 hours?

Solution:
যেহেতু, ঘড়িটি প্রতি 30 মিনিটে ঘড়ির সময় 3 মিনিট বৃদ্ধি পায়।

30 মিনিটে বৃদ্ধি পায় 3 মিনিট
1 ঘণ্টায় বা 60 মিনিটে বৃদ্ধি পায় 6 মিনিট
∴ 6 ঘণ্টায় বৃদ্ধি পাবে 6 × 6 মিনিট = 36 মিনিট

ঘড়িটি সকাল 5 টায় সঠিক সময় দেয় এবং 6 ঘণ্টা অর্থাৎ সকাল 11 টা অবধি চলে।
তাই ঘড়িতে তখন সময় দেখাবে (11 + 36) = 11 : 36 ‍

∴ সঠিক উত্তর 11 : 36 ‍am

৯,৯১৯.

With a uniform speed, a car covers a distance in 6 hours. Had the speed been increased by 3 km/hr the same distance could have been covered in 5 hours. What is the distance covered?

ক
ক) 90 km
খ
খ) 120 km
গ
গ) 150 km
ঘ
ঘ) 210 km

ব্যাখ্যা

Question: With a uniform speed, a car covers a distance in 6 hours. Had the speed been increased by 3 km/hr the same distance could have been covered in 5 hours. What is the distance covered?

Solution:
Let, the ditance is x km

ATQ,
(x/5) - (x/6) = 3 [If we devide distance by time we get speed]
⇒ (6x - 5x)/30 = 3
⇒ x/30 = 3
⇒ x = 30 × 3
∴ x = 90

∴ The distance covered is 90 km

৯,৯২০.

If tan (5x - 10°) = cot (5y + 20°), then the value of (x + y) is

ক
14°
খ
16°
গ
19°
ঘ
23°

ব্যাখ্যা

Question: If tan (5x - 10°) = cot (5y + 20°), then the value of (x + y) is

Solution:
tan (90° - θ) = cotθ
∴ tan (5x - 10°) = cot (5y + 20°)
⇒ tan (5x - 10°) = tan {90° - (5y + 20°)}
⇒ 5x - 10° = 90° - (5y + 20°)
⇒ 5x - 10° = 90° - 5y - 20°
⇒ 5x + 5y = 70° + 10°
⇒ 5 (x + y) = 80°
∴ x + y = 16°

৯,৯২১.

If a pole 12 m high casts a shadow 4√3 m long on the ground, then the elevation of the sun is -

ক
30°
খ
45°
গ
60°
ঘ
90°

ব্যাখ্যা

Question: If a pole 12 m high casts a shadow 4√3 m long on the ground, then the elevation of the sun is -

Solution:

ধরি,
AB = 12, BC = 4√3

ABC সমকোণী ত্রিভুজ হতে পাই,
tanθ = AB/BC
⇒ tanθ = 12/4√3
⇒ tanθ = 3/√3
⇒ tanθ = (√3 × √3)/√3
⇒ tanθ = √3
⇒ tanθ = tan60°
∴ θ = 60°

So the elevation of the sun is 60°.

৯,৯২২.

If 35% of a certain number is 84, then find the number-

ক
160
খ
210
গ
240
ঘ
320

ব্যাখ্যা

Question: If 35% of a certain number is 84, then find the number-

Solution:
Let the number be x.
Then,
35% of x = 84
⇒ (35/100) × x = 84
⇒ 7x/20 = 84
⇒ x = (20 × 84)/7
⇒ x = 1680/7
∴ x = 240

৯,৯২৩.

If a + b = 7 and ab = 12, then what is the value of (1/a²) + (1/b²)?

ক
25/121
খ
25/144
গ
49/144
ঘ
5/12

ব্যাখ্যা

Question: If a + b = 7 and ab = 12, then what is the value of (1/a²) + (1/b²)?

Solution:
Given,
a + b = 7 and ab = 12

∴ (1/a²) + (1/b²)
= (b² + a²)/(a²b²)
= (a² + b²)/(a²b²)
= {(a + b)² - 2ab}/(ab)²
= {(7)² - (2 × 12)}/(12)²
= (49 - 24)/144
= 25/144

৯,৯২৪.

A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

ক
Tk. 48
খ
Tk. 28
গ
Tk. 32
ঘ
Tk. 40

ব্যাখ্যা

Question: A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

Solution:
Let original price per kg = p Taka
Reduced price = p - p of 25% = 0.75p
Original quantity for 600 Taka
Q₁ = 600/p kg

And
New quantity for 600 Taka
Q₂ = 600/0.75p = 800/p kg

Now, quantity difference,
Q₂ - Q₁ = 5
(800/p) - (600/p) = 5
200/p = 5
p = 200/5
p = 40

∴ Original price per kg = Tk. 40

৯,৯২৫.

The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.

ক
20 kg
খ
85 kg
গ
67 kg
ঘ
80 kg

ব্যাখ্যা

Question: The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.

Solution:
Total weight increased = (8 × 2.5) kg = 20 kg.
So, weight of new woman = (65 + 20) kg = 85 kg.

৯,৯২৬.

The speed of A and B are in the ratio 4 : 7. B takes 21 minutes less than A to reach a destination. Time in which B reach the destination?

ক
49 minutes
খ
35 minutes
গ
28 minutes
ঘ
30 minutes

ব্যাখ্যা

Question: The speed of A and B are in the ratio 4 : 7. B takes 21 minutes less than A to reach a destination. Time in which B reach the destination?

Solution:
Given
The speed of A and B are in the ratio = 4 : 7

So the ratio of time taken = 7 : 4 [As Speed ∝ 1/Time, When distance remains constant.]

Let,
time taken by A and B be 7x and 4x minutes respectively.

ATQ,
7x - 4x = 21
⇒ 3x = 21
∴ x = 7

Hence, time taken by B = (4 × 7) minutes
= 28 minutes

৯,৯২৭.

If x² - 5x + 1 = 0, and x > 1, then what is the value of x - (1/x)?

ক
6
খ
5
গ
√20
ঘ
√21

ব্যাখ্যা

Question: If x² - 5x + 1 = 0, and x > 1, then what is the value of x - (1/x)?

Solution:
We are given:
x² - 5x + 1 = 0
⇒ x - 5 + 1/x = 0
∴ x + 1/x = 5

Now,
(a - b)² = (a + b)² - 4ab
⇒ (x - 1/x)² = (x + 1/x)² - 4 × x × (1/x) [Here, a = x, b = 1/x]

Substitute the values:
(x - 1/x)² = 25 - 4
⇒ (x - 1/x)²= 21
⇒ (x - 1/x)² = 21
∴ x - 1/x = √21

৯,৯২৮.

A pole 6 m high casts a shadow 2√3m long on the ground, then the Sun’s elevation is?

ক
65°
খ
40°
গ
45°
ঘ
60°
ঙ
70°

ব্যাখ্যা

tanθ = লম্ব/ভূমি
[এখানে, লম্ব = খুঁটির দৈর্ঘ্য এবং ভূমি = ছায়ার দৈর্ঘ্য]
⇒ tanθ = 6/2√3
⇒ tanθ = tan 60°
∴ θ = 60°

৯,৯২৯.

If the parimeter of the triangle is 18m. the perimeter of the circle is :

ক
10π
খ
9π
গ
8π
ঘ
12π

ব্যাখ্যা

Question: If the parimeter of the triangle is 18m. the perimeter of the circle is :

Solution:
as the triangle is equilateral triangle.
Let OA = X
∴ 3X = 18m
X = 6m

the perimeter of the circle is = 2πOA
= 2π × 6
= 12π

৯,৯৩০.

A train travelled from A to B and back in a certain time at the rate of 60 Km/hr. But if the train had travelled from A to B at the rate of 80 Km/hr and back from B to A at the rate of 40 Km/hr it would take two hours longer. The distance between A and B is-

ক
ক) 320 km
খ
খ) 540 km
গ
গ) 180 km
ঘ
ঘ) 210 km
ঙ
ঙ) 480 km

ব্যাখ্যা

(d/80 + d/40) - (d/60 + d/60) = 2
(3d + 6d - 4d - 4d)/240 = 2
d = 480 km

৯,৯৩১.

P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if they work together. How much time will Q take to do the work alone?

ক
ক) 4 days
খ
খ) 5 days
গ
গ) 6 days
ঘ
ঘ) 7 days

ব্যাখ্যা

Let,
The amount of work P does in 1 day = x
Amount of work Q does in 1 day = 2x
Amount of work R does in 1 day = 3x

Amount of work P, Q,R together do in 1 day = x + 2x + 3x = 6x
they can together complete the work in 1 day = (1/6x) days

Given,
1/6x = 2
⇒ 12x = 1
⇒ x = 1/12

Therefore, amount of work Q does in 1 day = 2 × (1/12) = 1/6
That is, Q needs 6 days to complete the work.

৯,৯৩২.

By selling a product for 3500, a seller makes 15% profit. If the profit is decreased to 9%, then selling price will be:

ক
2850
খ
3815
গ
3043
ঘ
3317

ব্যাখ্যা

Question: By selling a product for 3500, a seller makes 15% profit. If the profit is decreased to 9%, then selling price will be:

Solution:
১৫% লাভে,
একটি পণ্যের ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (১০০ + ১৫) = ১১৫ টাকা

বিক্রয়মূল্য ১১৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য (১০০/১১৫) টাকা
বিক্রয়মূল্য ৩৫০০ টাকা হলে ক্রয়মূল্য (১০০/১১৫) × ৩৫০০ টাকা
= ৩০৪৩.৪৮ টাকা

আবার,
৯% লাভে,
একটি পণ্যের ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (১০০ + ৯) = ১০৯ টাকা

ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১০৯ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য (১০৯/১০০) টাকা
ক্রয়মূল্য ৩০৪৩.৪৮ টাকা হলে বিক্রয়মূল্য (১০৯/১০০) × ৩০৪৩.৪৮ টাকা
= ৩৩১৭.৩৯ টাকা

∴ বিক্রয়মূল্য হবে ৩৩১৭.৩৯ টাকা।

৯,৯৩৩.

The least perfect square, which is divisible by each of 21, 36 and 66 is-

ক
213444
খ
214344
গ
214434
ঘ
231444

ব্যাখ্যা

Question: The least perfect square, which is divisible by each of 21, 36 and 66 is-

Solution:

L.C.M. of 21, 36, 66 = 2772.

Now,
2772 = 2 × 2 × 3 × 3 × 7 × 11

To make it a perfect square, it must be multiplied by 7 × 11.

So, required number = 2² × 3² × 7² × 11² = 213444

৯,৯৩৪.

A tap can fill a tank in 12 hours. After one-third of the tank has been filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

ক
4 hours
খ
6 hours 40 minutes
গ
5 hours 40 minutes
ঘ
8 hours

ব্যাখ্যা

Question: A tap can fill a tank in 12 hours. After one-third of the tank has been filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
A tap can fill a tank in 12 hours.
∴ A tap can fill 1/12 part in one hour.
Tap can fill 1 part in 12 hours

⇒ Tap can fill 1/3 part in 12 / 3 = 4 hours
⇒ The rest part = 1 - 1/3 = 2/3.

After one-third of the tank has been filled, two more identical taps are opened.
3 similar tap can fill 3/12 = 1/4 part in one hour.
3 similar tap can fill 1 part in = 4 hour.
3 similar tap can fill 2/3 part in = 4 × 2/3 = 8/3 hour.

8/3 hours means 2 hours 40 minutes.
∴Total time taken: 6 hours 40 minutes.

৯,৯৩৫.

Some persons can do a piece of work in 24 days. Two times the number of such persons will do half of that work in -

ক
ক) 6 days
খ
খ) 3 days
গ
গ) 12 days
ঘ
ঘ) 8 days

ব্যাখ্যা

Question: Some persons can do a piece of work in 24 days. Two times the number of such persons will do half of that work in -

Solution:
Let the initial workers be x
So, workers for 2nd time = 2x

x persons can complete 1 part in 24 days
1 person can complete 1 part in 24x days
2x persons can complete 1/2 part in 24x/(2x × 2) days
= 6 days

৯,৯৩৬.

A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been-

ক
116
খ
120
গ
122
ঘ
124

ব্যাখ্যা

Question: A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been-

Solution:
Let,
the number be = x.

ATQ,
(x + 12)/6 = 112
⇒ x + 12 = 672
⇒ x = 672 - 12
⇒ x = 660

So, Correct answer = (660/6) +12
= 110 + 12
= 122

৯,৯৩৭.

What is the greatest number of four digits which is divisible by 15, 25, 40 and 75?

ক
9400
খ
9800
গ
9600
ঘ
9380

ব্যাখ্যা

Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999/600 = 16,
remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399
= 9600

৯,৯৩৮.

The difference in Taka between simple and compound interest at 5% annually on a sum of Tk. 5,000 after 2 years is

ক
12.5
খ
25
গ
50
ঘ
500

ব্যাখ্যা

Question: The difference in Taka between simple and compound interest at 5% annually on a sum of Tk. 5,000 after 2 years is

Solution:
Given that,
Principal, P = Tk. 5,000
Rate, r = 5% = 5/100 = 0.1
Time, n = 2 years

We know that,
Simple Interest = Prn
= (5000 × 5 × 2)/100
= 500
And
Compound Interest = P(1 + r)ⁿ - P
= 5000(1 + 0.05)² - 5000
= 5000(1.05)² - 5000
= 5512.5 - 5000
= 5512.5 - 5000

∴ Difference = 512.5 - 500 = 12.5
The difference between compound and simple profit is Tk. 12.5

৯,৯৩৯.

A boatman goes 2 km against the current of the stream in 2 hour and goes 1km along the current in 20 minutes. How long will it take to go 5 km in stationary water?

ক
ক) 4 hr 25 min
খ
খ) 3 hr 25 min
গ
গ) 2 hr 30 min
ঘ
ঘ) 1 hr 15 min
ঙ
ঙ) 3 hr 53 min

ব্যাখ্যা

Speed upstream = 2/2 = 1 km/hr
Speed downstream = 1/(20/60) = 3 km/hr
Speed in still water = (1/2)(3+1) = 2 km/hr
Time taken to travel 5 km in still water = 5/2
= 2(1/2)
= 2 hr 30 min

৯,৯৪০.

Which of the following equations is not equivalent to 25x² = y² - 4.

ক
ক) 25x² + 4 = y²
খ
খ) 75x² = 3y² - 12
গ
গ) 25x² = (y + 2)(y - 2)
ঘ
ঘ) 5x = y - 2
ঙ
ঙ) None of these

ব্যাখ্যা

25x² + 4 = y²

Question: Which of the following equations is not equivalent to 25x² = y² - 4.

Solution:
25x² = y² - 4
⇒ 25x² + 4 = y²

25x² = y² - 4
⇒ 3 × 25x² = 3 (y² - 4)
∴ 75x² = 3y² - 12

25x² = y² - 4
⇒ 25x² = y² - 2²
⇒ 25x² = (y - 2) (y + 2)

25x² = y² - 4
⇒ (5x)² = y² - 4
∴ 5x = √(y² - 4)
5x ≠ (y - 2)

৯,৯৪১.

Sara sells his goods 20% cheaper than Rahim and 25% dearer than Monir. How much of the goods of Monir are cheaper than Rahim's?

ক
36%
খ
40%
গ
45%
ঘ
25%

ব্যাখ্যা

Question: Sara sells his goods 20% cheaper than Rahim and 25% dearer than Monir. How much of the goods of Monir are cheaper than Rahim's?

Solution:
Let,
Rahim sells at 100 taka
Sara sells at 80 taka

∴ Monir sells at = 80/1.25 = 64 taka

The goods of Monir are cheaper than Rahim's = (100 - 64) = 36 taka

Percentage cheaper = (36/100 ×100) = 36%

৯,৯৪২.

Kamal can run 1000 meters in 4 minutes. He has a car that has a top speed of 75 km/hr. What percentage of Kamal's speed is his car's top speed?

ক
30%
খ
25%
গ
20%
ঘ
10%
ঙ
None

ব্যাখ্যা

Question: Kamal can run 1000 meters in 4 minutes. He has a car that has a top speed of 75 km/hr. What percentage of Kamal's speed is his car's top speed?

Solution:
এখানে, দূরুত্ব = 1000 মিটার
= 1 কি.মি.

4 মিনিট = 4/60 ঘণ্টা = 1/15 ঘণ্টা

কামালের গতিবেগ = 1/(1/15) কি.মি./ঘণ্টা = 15 কি.মি./ঘণ্টা
গাড়ির গতিবেগ = 75 কি.মি./ঘণ্টা

∴ কামালের গতিবেগ তার গাড়ির গতিবেগের = {(15/75) × 100}%
= 20%

৯,৯৪৩.

The total cost of flooring a room at Tk. 7.50 per square meter is Tk. 375. If the breadth of the room is 5 m, its length is -

ক
ক) 5 meter
খ
খ) 8 meter
গ
গ) 10 meter
ঘ
ঘ) 12 meter

ব্যাখ্যা

Question: The total cost of flooring a room at Tk. 7.50 per square meter is Tk. 375. If the breadth of the room is 5 m, its length is -

Solution:
Tk. 7.50 cost of flooring for 1 square meter.
Tk. 375 cost of flooring for (375/7.50) square meter.
= 50 square meter.

We know,
Length × Breadth = 50 square meter.
∴ Length = 50/5 meter.
= 10 meter.

৯,৯৪৪.

Find the value of sin⁴θ - cos⁴θ if sin²θ - cos²θ = 2.

ক
2
খ
1
গ
1/2
ঘ
- 2

ব্যাখ্যা

Question: Find the value of sin⁴θ - cos⁴θ if sin²θ - cos²θ = 2.

Solution:
given,
sin²θ - cos²θ = 2

sin⁴θ - cos⁴θ
= (sin²θ)² - (cos²θ)²
= (sin²θ + cos²θ)(sin²θ - cos²θ)
= 1 × 2
= 2

৯,৯৪৫.

If the length of the longest side of the triangle shown below is 36, then what is the perimeter of the triangle?

ক
81
খ
63
গ
51
ঘ
25

ব্যাখ্যা

Question: If the length of the longest side of the triangle shown below is 36, then what is the perimeter of the triangle?

Solution:
longest side = 12k = 36
⇒ k = 36/12 = 3

perimeter = 12k + 9k + 6k
= 12 × 3 + 9 × 3 + 6 × 3
= 36 + 27 + 18
= 81

৯,৯৪৬.

Sum of three consecutive multiples of 3 is 396. Find the largest number.

ক
151
খ
135
গ
141
ঘ
138
ঙ
None

ব্যাখ্যা

Question: Sum of three consecutive multiples of 3 is 396. Find the largest number.

Solution:
Let,
First multiple: 3x
Second multiple: 3(x + 1) = 3x + 3
Third multiple: 3(x + 2) = 3x + 6

ATQ,
3x + (3x + 3) + (3x + 6) = 396
⇒ 9x + 9 = 396
⇒ 9x = 387
⇒ x = 387/9
∴ x = 43

∴ The largest number = 3x + 6 = 3 × 43 + 6 = 135

৯,৯৪৭.

Ten years ago, Mahin was half the age of Rahul. If the ratio of their present ages is 3 : 4, what is Rahul's present age?

ক
30 years
খ
25 years
গ
15 years
ঘ
20 years

ব্যাখ্যা

Question: Ten years ago, Mahin was half the age of Rahul. If the ratio of their present ages is 3 : 4, what is Rahul's present age?

Solution:
let,
the present age of Mahin = 3x years
and the present age of Rahul = 4x years

∴ 10 years ago, Mahin was (3x - 10) years old
∴ 10 years ago, Rahul was (4x - 10) years old

ATQ,
2(3x - 10) = 4x - 10
⇒ 6x - 20 = 4x - 10
⇒ 6x - 4x = 20 - 10
⇒ 2x = 10
∴ x = 5

∴ Present age of Rahul = (4 × 5) = 20 years

৯,৯৪৮.

The bankers discount on Tk. 1800 at 12% per annum is equal to the true discount on Tk 1872 for the same time at the same rate. Find the time.

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

ব্যাখ্যা

S.I. on Tk. 1800 = T.D. on Tk. 1872
P.W. of Tk. 1872 is Tk. 1800
Tk. 72 is S.I. on Tk. 1800 at 12%
Time = (100×72)/(12×1800)
= 1/3 years = 4months

৯,৯৪৯.

How many permutations of seven different letters may be made?

ক
ক) 1
খ
খ) 7
গ
গ) 7!
ঘ
ঘ) 6!

ব্যাখ্যা

number of permutations of 7 different letters = 7!

৯,৯৫০.

Bipul ate 2/3 of a cake. His friend Rafi ate 2/3 of what was left. Then Rafi's sister ate 2/3 of what was still left. What fraction of the cake remains uneaten?

ক
1/13
খ
1/27
গ
1/8
ঘ
1/15

ব্যাখ্যা

Question: Bipul ate 2/3 of a cake. His friend Rafi ate 2/3 of what was left. Then Rafi's sister ate 2/3 of what was still left. What fraction of the cake remains uneaten?

Solution:
বিপুল খেয়েছে = 2/3
∴ অবশিষ্ট = 1 - 2/3 = 1/3

রাফি খেয়েছে = 1/3 × 2/3 = 2/9
∴ অবশিষ্ট = 1/3 - 2/9 = (3 - 2)/9 = 1/9

রাফির বোন খেয়েছে = 1/9 × 2/3 = 2/27
∴ অবশিষ্ট = 1/9 - 2/27 = (3 - 2)/27 = 1/27

৯,৯৫১.

Three unbiased coins are tossed. What is the probability of getting at most two heads?

ক
7/8
খ
5/8
গ
1/8
ঘ
1/7
ঙ
1/4

ব্যাখ্যা

Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
(তিনটি নিরপেক্ষ সম্ভাব্য কয়েন নিক্ষেপ করা হয়েছে। সর্বোচ্চ দুইটি হেড আসার সম্ভাবনা কত?)

Solution:
Getting at most Two heads means 0 to 2 but not more than 2
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}

P(E) = n(E)/n(S)
= 7/8

৯,৯৫২.

The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is-

ক
r³/3√3
খ
8r³
গ
8r³/3√3
ঘ
3√3r

ব্যাখ্যা

Question: The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is-

Solution:
let, radius = r, length of cube a cm

Diagonal of cube = 2r
⇒ √3 a = 2r
⇒ a = 2r/√3

∴ volume = a³
= (2r/√3)³
= 8r³/3√3

৯,৯৫৩.

A shopkeeper earns a profit of 12% on selling a book at 60% discount on the printed price. What is the ratio of the cost price and the printed price of the book?

ক
5 : 14
খ
7 : 18
গ
5 : 17
ঘ
7 : 28
ঙ
None

ব্যাখ্যা

Let the Cost Price be100 taka
selling price = 100 + 100 × 12% = 112 taka
After 60% discount on the printed price, then remaining = (100 - 60)% = 40%
If the market price is x, then 40% of x = 112
x = 112 × 100/40 = 280 taka
Required ratio = 100 : 280 = 5 : 14
--------------------------------------------------------------------------------------
Alternative way(easy way):
Let cost price be y taka
Profit = 12% of y taka = 12y/100 taka
Selling price = (y + 12y/100) taka
= 112y/100 taka
Discount = 60% of printed price
Selling price = printed price - discount
112y/100 = printed price - 60% of printed price
112y/100 = (1 - 60/100) × printed price
printed price × 40/100 = 112y/100
printed price = 112y/40
Cost price : Printed Price = y : 112y/40
= 40 : 112
= 5 : 14

৯,৯৫৪.

0.04 x 0.0162 is equal to:

ক
ক) 6.48 x 10^-2
খ
খ) 6.48 x 10^-4
গ
গ) 6.48 x 10^-6
ঘ
ঘ) 6.48 x 10^-8

ব্যাখ্যা

4 x 162 = 648. Sum of decimal places = 6.
So,
0.04 x 0.0162
= 0.000648
= 6.48 x 10^-4

৯,৯৫৫.

The present ratio of ages of A and B is 4 : 5. 18 years ago, this ratio was 11 : 16. Find the average of their present ages.

ক
ক) 90 years.
খ
খ) 40 years.
গ
গ) 45 years.
ঘ
ঘ) 80 years.

ব্যাখ্যা

Question: The present ratio of ages of A and B is 4 : 5. 18 years ago, this ratio was 11 : 16. Find the average of their present ages.

Solution:
Let present age of A and B be 4x and 5x
18 years ago their ages
(4x - 18)/(5x - 18) = 11/16
⇒ 64x - 288 = 55x - 198
⇒ 64x - 55x = -198 + 288
⇒ 9x = 90
⇒ x = 90/9
∴ x = 10
Sum of the present ages = 40 + 50 = 90 years.

∴ Sum of the present ages = 90/2 years = 45 years.

৯,৯৫৬.

√(.01+√0.0064)=?

ক
ক) 0.03
খ
খ) 0.42
গ
গ) 0.3
ঘ
ঘ) None of these

ব্যাখ্যা

√(0.01+√0.0064)= √(0.01 + 0.08) = √( 0.09) = 0.3

৯,৯৫৭.

A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

ক
10√5
খ
10√6
গ
50
ঘ
60

ব্যাখ্যা

Question: A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?

Solution:
Let,
x = Side of Square Playground
∴ x² =the area of the Square Playground

Now,
The rectangle sides are x + 30 and x - 20

Therefore the Area of the rectangle will be (x + 30)(x - 20) = x² + 10x - 600

∴ x² = x² + 10x - 600
⇒ 10x = 600
∴ x = 60

৯,৯৫৮.

The L.C.M of 3/4, 6/7, 9/8 is-

ক
ক) 24
খ
খ) 18
গ
গ) 16
ঘ
ঘ) 14

ব্যাখ্যা

LCM of Numerators ⇒ LCM(3, 6, 9) = 18
HCF of Denominators ⇒ HCF(4, 7, 8) = 1

⇒ LCM (3/4, 6/7, 9/8) = 18/1
⇒ LCM (3/4, 6/7, 9/8) = 18
∴ LCM of 3/4, 6/7 and 9/8 is 18

৯,৯৫৯.

Find the factors of (x² - x - 132).

ক
x - 11x - 12
খ
(x + 12)(x - 11)
গ
(x + 11)(x + 12)
ঘ
(x - 12)(x + 11)

ব্যাখ্যা

Question: Find the factors of (x² - x - 132).

Solution:
x² - x - 132
= x² - 12x + 11x - 132
= x(x - 12) + 11(x - 12)
= (x - 12)(x + 11)

৯,৯৬০.

The present age of son is half of the present age of his mother. Five years ago, his mother's age was thrice the age of her son. What is the present age of the son?

ক
ক) 5 years
খ
খ) 10 years
গ
গ) 15 years
ঘ
ঘ) 20 years

ব্যাখ্যা

Question: The present age of son is half of the present age of his mother. Five years ago, his mother's age was thrice the age of her son. What is the present age of the son?

Solution:
Let the mother's age be 2x years
Then, Son's age = x years

ATQ,
2x - 5 = 3(x - 5)
⇒ 2x - 5 = 3x - 15
⇒ x = 10

∴ The present age of the son = 10 years.

৯,৯৬১.

A man borrowed some money for 120 days. He asked the banker for the money and the banker charged Tk. 360 as interest @6% per annum. What was the amount he borrowed?

ক
ক) Tk. 18,000
খ
খ) Tk. 16,000
গ
গ) Tk. 15,000
ঘ
ঘ) None of these

ব্যাখ্যা

Question: A man borrowed some money for 120 days. He asked the banker for the money and the banker charged Tk. 360 as interest @6% per annum. What was the amount he borrowed?

Solution:
এখানে
সময় n = 120 দিন
= 4 মাস
= 4/12 বছর
= 1/3 বছর

মুনাফা I = 360 টাকা
মুনাফার হার r = 6% = 6/100 = 3/50
আসল P = ?

আমরা জানি
I = Pnr
Pnr = I
P = I/nr
= 360/{(1/3) × (3/50)}
=360/(1/50)
= 360 × 50
= 18000 টাকা

৯,৯৬২.

The least perfect square which is divisible by each of 21, 36 and 66 is = ?

ক
ক) 245564
খ
খ) 217652
গ
গ) 213444
ঘ
ঘ) 213346

ব্যাখ্যা

L.C.M. of (21, 36, 66)
= 21 × 12 × 11
= 7 × 3 × 4 × 3 × 11
= 7 × 3 × 2 × 2 × 3 × 11

For perfect square, we have to multiply (7 × 3 × 2 × 2 × 3 × 11) by (7 × 11)

∴ Required result
= 7 × 7 × 3 × 3 × 2 × 2 × 11 × 11
= 213444
==============================================================
প্রশ্নে বলা হয়েছে যে, এমন ক্ষুদ্রতম পূর্ণ বর্গ সংখ্যা নির্ণয় করুন যা ২১, ৩৬ ও ৬৬ দ্বারা নিঃশেষে বিভাজ্য।
২১, ৩৬ ও ৬৬ এর লসাগু = ৭ ×৩ ×২ × ২ × ৩ × ১১
পূর্ণ বর্গ সংখ্যার জন্য, ৭ × ৩ ×২ × ২ × ৩ × ১১ কে ৭ × ১১ দ্বারা গুণ করতে হবে।
অতএব, নির্ণেয় ফলাফল = ৭ × ৩ × ২ × ২ × ৩ × ১১ × ৭ × ১১ = ২১৩৪৪৪

৯,৯৬৩.

A person goes from place A to another place B at a speed of 4 km/h and returns at a speed of 3 km/h. If this takes 7 h in all, then what is the distance between two places?

ক
ক) 12 km
খ
খ) 8 km
গ
গ) 6 km
ঘ
ঘ) 5 km
ঙ
ঙ) 7 km

৯,৯৬৪.

What is the value of (255 - 55) ÷ 4 × 15 - 504 ÷ 3 = ?

ক
430
খ
582
গ
292
ঘ
480

ব্যাখ্যা

Question: What is the value of (255 - 55) ÷ 4 × 15 - 504 ÷ 3 = ?

Solution:
(255 - 55) ÷ 4 × 15 - 504 ÷ 3
= 200 ÷ 4 × 15 - 504 ÷ 3
= 50 × 15 - 168
= 750 - 168
= 582

৯,৯৬৫.

Which number replaces the question mark?

ক
6
খ
9
গ
8
ঘ
12

ব্যাখ্যা

Question: Which number replaces the question mark?

Solution:
Here, 6 - 4 = 2
9 - 6 = 3, 3 - 2 = 1
19 - 9 = 10, 10 - 3 = 7, 7 - 1 = 6

Correct answer is 6.

৯,৯৬৬.

Which of the following is equivalent to the pair of inequalities x + 11 > 15 and x - 7 < 4?

ক
3 < x < 9
খ
- 3 < x < 9
গ
4 < x < 11
ঘ
2 < x < 7

ব্যাখ্যা

x + 11 > 15 ⇒ x > 4
x - 7 < 4 ⇒ x < 11
We get, 4 < x < 11

৯,৯৬৭.

30% of 50 is what fraction of 75% of 80?

ক
ক) 1/2
খ
খ) 1/4
গ
গ) 1/5
ঘ
ঘ) 1/7

ব্যাখ্যা

30 % of 50 = 15
and 75% of 80 = 60.

∴ The fraction is = 15/60 = 1/4.

৯,৯৬৮.

The value of - 7 - (- 10) is how much greater than the value of - 10 - (- 7)?

ক
ক) 0
খ
খ) 6
গ
গ) 8
ঘ
ঘ) 12

ব্যাখ্যা

দেয়া আছে,
- 7 - (- 10) = - 7 + 10 = 3

- 10 - (- 7) = - 10 + 7 = - 3

- 7 - (- 10) এর মান - 10 - (- 7) এর মান থেকে বেশি = 3 - (- 3)
= 3 + 3
= 6

৯,৯৬৯.

What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm?

ক
12 cm
খ
21 cm
গ
16 cm
ঘ
32 cm

ব্যাখ্যা

Question: What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm?

Solution:
Given that,
Radius of the circle, r = 10 cm
Distance from the center of the circle to the chord, d = 6 cm

Then, the length of the chord = 2 × √(radius² - distance from center²)
= 2 × √(10² - 6²) cm
= 2 × √(100 - 36)
= 2 × √64
= 2 × 8
= 16 cm

So the length of the chord is 16 cm.

৯,৯৭০.

A train, 150 meter long and running at a speed of 60 km per hour, takes 30 seconds to cross a bridge. What is the length (in meter) of the bridge?

ক
350
খ
450
গ
500
ঘ
650

ব্যাখ্যা

Question: A train, 150 meters long and running at a speed of 60 km per hour, takes 30 seconds to cross a bridge. What is the length (in meters) of the bridge?

Solution:
সেকেন্ডে ট্রেনের গতিবেগ = (60×1000)/(60×60) মিটার/সেকেন্ড
= 16.67 মিটার/সেকেন্ড
∴ 30 সেকেন্ডে অতিক্রান্ত দূরত্ব = (30×16.67)m = 500m
ব্রিজের দূরত্ব = 500 - 150 = 350 m

৯,৯৭১.

Three sides of a triangle measure 6 cm, 10 cm and p cm. The minimum integral value of p is:

ক
1
খ
2
গ
3
ঘ
5
ঙ
None

ব্যাখ্যা

Question: Three sides of a triangle measure 6 cm, 10 cm and p cm. The minimum integral value of p is:

Solution:
আমরা জানি,
- ত্রিভুজের যে কোন দুই বাহুর সমষ্টি তার তার তৃতীয় বাহু অপেক্ষা বৃহত্তর।
- ত্রিভুজের যে কোন দুই বাহুর অন্তর বা ব্যবধান তৃতীয় বাহু অপেক্ষা ক্ষুদ্রতর।
অপশন
ক) 1 + 6 = 7 < 10
খ) 2 + 6 = 8 < 10
গ) 3 + 6 = 9 < 10
ঘ) 5 + 6 = 11 > 10

৯,৯৭২.

A rectangular garden has an area of 800 square feet. It will be fenced on three sides, leaving one side of 40 feet uncovered. How many feet of fencing is required?

ক
40 feet
খ
60 feet
গ
80 feet
ঘ
100 feet
ঙ
120 feet

ব্যাখ্যা

Question: A rectangular garden has an area of 800 square feet. It will be fenced on three sides, leaving one side of 40 feet uncovered. How many feet of fencing is required?

Solution:
দেওয়া আছে, আয়তকার বাগানের ক্ষেত্রফল = 800 square feet
এবং যে বাহুটি খোলা থাকবে তার দৈর্ঘ্য = 40 feet

ধরি, আয়তকার ক্ষেত্রের অন্য বাহুর দৈর্ঘ্য = x feet
প্রশ্নমতে,
40 × x = 800
⇒ x = 800/40
⇒ x = 20 feet

যেহেতু বাগানটির তিন দিকে বেড়া দেওয়া হবে এবং 40 feet দৈর্ঘ্যের একটি বাহু খোলা থাকবে,
∴ প্রয়োজনীয় বেড়ার দৈর্ঘ্য = x + x + 40
= 20 + 20 + 40
= 80

∴ বাগানটি ঘেরাও করতে মোট 80 feet বেড়া লাগবে।

৯,৯৭৩.

Tk 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

ক
ক) Tk 1290
খ
খ) Tk 1380
গ
গ) Tk 1250
ঘ
ঘ) Tk 1360

ব্যাখ্যা

Question: Tk 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Solution:
A = p(1 + nr)
= 1200{1 + (3 × 5)/100}
= 12000 × (115/100)
= 1380

৯,৯৭৪.

Which of the following can never be ending of a perfect square?

ক
ক) 1
খ
খ) 4
গ
গ) 6
ঘ
ঘ) 8

ব্যাখ্যা

Question: Which of the following can never be ending of a perfect square?

Solution:
A perfect square number never ends with 2, 3, 7 or 8

৯,৯৭৫.

When number 6 is added to 1/3 of a number, the result is 28. What is that number?

ক
44
খ
84
গ
66
ঘ
42

ব্যাখ্যা

Question: When number 6 is added to 1/3 of a number, the result is 28. What is that number?

Solution:
let the number be x

ATQ,
(x/3) + 6 = 28
⇒ x/3 = 22
∴ x = 66

৯,৯৭৬.

How many kgs of Basmati rice costing Tk. 42 per kg should a shopkeeper mix with 25 kgs of ordinary rice costing Tk. 24 per kg so that he makes a profit of 25% on selling the mixture at Tk. 40 per kg?

ক
20.0 kgs
খ
12.5 kgs
গ
16.0 kgs
ঘ
200.0 kgs

ব্যাখ্যা

Question: How many kgs of Basmati rice costing Tk. 42 per kg should a shopkeeper mix with 25 kgs of ordinary rice costing Tk. 24 per kg so that he makes a profit of 25% on selling the mixture at Tk. 40 per kg?

Solution:
Let the amount of Basmati rice being mixed be x kgs.
As the trader makes 25% profit by selling the mixture at Tk. 40 per kg
∴ His cost per kg of the mixture = (100 × 40)/125 = Tk. 32 per kg

∴ (x × 42) + (25 × 24) = 32(x + 25)
⇒ 42x + 600 = 32x + 800
⇒ 10x = 200
∴ x = 20

৯,৯৭৭.

A factory employs 130 workers on Fridays and 250 workers on other days. If a month has 30 days and starts on a Friday, what is the average number of workers per day over the month?

ক
239
খ
236
গ
233
ঘ
230

ব্যাখ্যা

Question: A factory employs 130 workers on Fridays and 250 workers on other days. If a month has 30 days and starts on a Friday, what is the average number of workers per day over the month?

Solution:
Since,
the month begins with a Friday, so there will be 5 Fridays and 25 other days in this month.

Total workers on Fridays = 5 × 130 = 650
Total workers on other days = 25 × 250 = 6250

∴ Total workers in the whole month = (650 + 6250) = 6900

∴ Average number of workers per day of the month = 6900/30 = 230

৯,৯৭৮.

If three cubes of copper, each with an edge of 6 cm, 8 cm and 10 cm respectively are melted to form a single cube, then the diagonal of new cube will be-

ক
ক) 12 cm
খ
খ) 36 cm
গ
গ) 18√3 cm
ঘ
ঘ) 12√3 cm

ব্যাখ্যা

Volume of the new cube of edge x cm
x³ which is same as 6³+ 8³+ 10³
x³ =(6³+ 8³+ 10³)cm³
x³=(216 + 512 + 1000) cm³
x³=1728 cm³
x³= (12)³cm³
x =12 cm

length of diagonal = a√3 = 12√3 cm

৯,৯৭৯.

3 different pieces of iron are of varying length are given to a student which are 44cm, 22 cm,55 cm respectively. He has to form rods of maximum length such that no iron waste is left. Find the maximum length of such rod.

ক
28 cm
খ
14 cm
গ
42 cm
ঘ
63 cm
ঙ
11 cm

ব্যাখ্যা

Question: 3 different pieces of iron are of varying length are given to a student which are 44cm, 22 cm,55 cm respectively. He has to form rods of maximum length such that no iron waste is left. Find the maximum length of such rod.

Solution:
Maximum possible length of such rod = (H.C.F. of 44, 22, 55) cm = 11 cm.

৯,৯৮০.

Tanvir’s present age is two-fifths of the age of his father. After 8 years, Tanvir will be one-half of the age of his father. What is the present age of the father?

ক
40 years
খ
41 years
গ
42 years
ঘ
43 years

ব্যাখ্যা

Question: Tanvir’s present age is two-fifths of the age of his father. After 8 years, Tanvir will be one-half of the age of his father. What is the present age of the father?

Solution:
Let,
Present age of father = p year
So, Tanvir's present age = p × (2/5) year

After 8 years father will be = (p + 8) year
After 8 years Tanvir will be = {(2p/5) + 8} year

According to the conditions,
(1/2)(p + 8) = {(2p/5) + 8}
or, (p + 8)/2 = (2p + 40)/5
or, 5p + 40 = 4p + 80
or, 5p - 4p = 80 - 40
∴ p = 40

So, Present age of father = 40 years.

৯,৯৮১.

A man purchased 400 shares of the face value of Tk. 100 each from the market at Tk. 125 per share. If a dividend of 20% is declared, find his earning percent on the investment.

ক
10%
খ
24%
গ
20%
ঘ
16%

ব্যাখ্যা

Question: A man purchased 400 shares of the face value of Tk. 100 each from the market at Tk. 125 per share. If a dividend of 20% is declared, find his earning percent on the investment.

Solution:
Given,
Price of 1 share = Tk. 125.
∴ Price of 400 share = Tk. (125 × 400)
= Tk. 50000

Dividend per share=20% of 100 = Tk. 20
∴ Total dividend income = 400 × 20 = Tk. 8000

∴ Earning % = (Dividend/Market Price) × 100
=(8000/50000) × 100
= 16%.

৯,৯৮২.

How many prime numbers are there from 1 to 50?

ক
13
খ
14
গ
15
ঘ
None of the above

ব্যাখ্যা

Question: How many prime numbers are there from 1 to 50?

Solution:

মৌলিক সংখ্যা:
১ এর চেয়ে বড় যে সকল সংখ্যাকে শুধু ১ এবং ঐ সংখ্যা ছাড়া আর কোনো সংখ্যা দ্বারা ভাগ করা যায় না, তাদেরকে মৌলিক সংখ্যা বলে। অর্থাৎ মৌলিক সংখ্যার উৎপাদক হবে দুইটি: ১ এবং শুধুমাত্র সেই সংখ্যাটি।

১ থেকে ৫০ পর্যন্ত মোট মৌলিক সংখ্যা ১৫টি। এগুলো হলো ⇒ ২, ৩, ৫, ৭, ১১, ১৩, ১৭, ১৯, ২৩, ২৯, ৩১, ৩৭, ৪১, ৪৩, ৪৭।

৯,৯৮৩.

A 24 liters of milk and water mixture contains milk and water in the ratio 3: 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

ক
28/5 L
খ
32/5 L
গ
20/3 L
ঘ
24/5 L

ব্যাখ্যা

Question: A 24 liters of milk and water mixture contains milk and water in the ratio 3: 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

Solution:
In 24 l of mixture, milk = (3/8) × 24 = 9 L
So water = 24 - 9 = 15 L
Now since the mixture is to be replaced with pure milk, the amount of mixture will remain same after replacement too.
In 24 L mixture, to have 12 L water and 12 L milk, 3 L of water should be taken out, since we are only adding milk.
Let x L of mixture taken out.
So (5/8) × x = 3
⇒ 5x = 24
Solve, x = 24/5 L

৯,৯৮৪.

If the simple interest on a sum of money at 6% per annum for 4 years is Tk.1600, then find the compound interest on the same sum for the same period at the same rate.

ক
ক) Tk. 1625.35
খ
খ) Tk. 1645.45
গ
গ) Tk. 1662.35
ঘ
ঘ) Tk. 1660.66

ব্যাখ্যা

From the question, you know that R = 6%, T = 4 years, S.I. = Tk.1600

If you apply the above values in the simple interest formula S.I. = PRT/100, you will get
1600 = (P x 4 x 6)/100
⇒ P = (1600 x 100)/6 × 4
⇒ P = 6333.33

Using the above value of P, you have to now calculate C.I. as shown below:
CI = [P(1 + R/100)ⁿ] – P
= [6333.33(1 + 6/100)⁴] - 6333.33
= [6333.33 (106/100)⁴] - 6333.33
= [6333.33× 53/50 × 53/50 × 53/50 × 53/50] - 6333.33
= 7995.68 - 6333.33
= Tk.1662.35

৯,৯৮৫.

A, B, and C start together from the same place to walk around a circular path of length 12km. A walk at the rate of 4 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

ক
12 hours.
খ
18 hours.
গ
24 hours
ঘ
28 hours

ব্যাখ্যা

Question: A, B, and C start together from the same place to walk around a circular path of length 12km. A walk at the rate of 4 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

Solution:
We know,
Time = Distance/speed

Time taken to complete the revolution
A = 12/4 = 3 hours
B = 12/3 = 4 hours
C = 12 × (2/3) = 8 hours

Now, required time = LCM of 3, 4, and 8
= 24 hours

৯,৯৮৬.

If the numbers from 1 to 28, which are divisible by 2 in arranged in descending order, which number will be at 7th place from the bottom?

ক
ক) 16
খ
খ) 14
গ
গ) 12
ঘ
ঘ) 18

ব্যাখ্যা

These numbers are:
28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2

7th place from the bottom is = 14

৯,৯৮৭.

If x + 5y = 16 and x = - 3y, then y =?

ক
- 24
খ
- 8
গ
- 2
ঘ
2
ঙ
8

ব্যাখ্যা

Question: If x + 5y = 16 and x = - 3y, then y =?

Solution:
x + 5y = 16 ....................(i)
x = - 3y ................(ii)

Substituting x in (i)
- 3y + 5y = 16
⇒ 2y = 16
∴ y = 8

৯,৯৮৮.

By selling a bicycle for 2,850 taka, a shopkeeper gains 14%. If the profit is reduced to 8%. What is the selling price?

ক
2600
খ
2700
গ
2780
ঘ
2820
ঙ
2950

ব্যাখ্যা

Let Cost Price was y.
or, y + 14% of y = 2850
or, y + 14y/100 = 2850
∴ y = 2500.
So, Cost Price = 2500 taka.
Now, When profit remains at 8%,
Selling Price = 2500 taka + 8% of 2500 taka
= 2700 taka.

৯,৯৮৯.

A train can cross a pole in 32 sec and a 420-meter platform in 62 seconds. Find the length of the train.

ক
520 m
খ
448 m
গ
552 m
ঘ
360 m

ব্যাখ্যা

Question: A train can cross a pole in 32 sec and a 420-meter platform in 62 seconds. Find the length of the train.

Solution:
Let the length of the train be x m

Speed equal in both case,
then
x/32 = (x + 420)/62
⇒ 62x = 32x + 420 × 32
⇒ 62x - 32x = 420 × 32
⇒ 30x = 420 × 32
⇒ x = (420 × 32)/30
∴ x = 448 m

∴ Length of train is 448 m.

৯,৯৯০.

Find the value of 7⁵× 7^-4 × 7⁶

ক
ক) 7⁶
খ
খ) 7⁷
গ
গ) 7^{- 90}
ঘ
ঘ) 7⁹⁰

ব্যাখ্যা

Question: Find the value of 7⁵× 7^-4 × 7⁶

Solution:
7⁵× 7^-4 × 7⁶
=7^{5 + (- 4) + 6}
=7^{5 - 4 + 6}
=7⁷

৯,৯৯১.

Two numbers are in ratio of 21 : 26. If 8 is added in each, the new numbers are in ratio of 5 : 6. Find the ratio of numbers, if 6 subtracted from each number?

ক
ক) 18 : 23
খ
খ) 19 : 25
গ
গ) 6 : 7
ঘ
ঘ) 9 : 16

ব্যাখ্যা

ধরি,
একটি সংখ্যা = 21x
অপর সংখ্যা = 26x

প্রশ্নমতে
(21x + 8)/(26x + 8) = 5/6
130x + 40 = 126x + 48
130x - 126x = 48 - 40
4x = 8
x = 8/4
x = 2

নতুন অনুপাত = (21x - 6)/(26x - 6)
= (21 × 2 - 6)/(26 × 2 - 6)
= 36/46
= 18/23
= 18 : 23

৯,৯৯২.

In a room, there are six Bengali, twelve engineers and fifteen football players. Only one of them was a bengali Engineer who played Football. Two were Bengali Engineers but did not play football and two were Bengali football players and were not engineers. If there were 24 people in the room, and at least one of them were Bengali, engineer or a football player, how many were engineers and played football but not Bengali?

ক
ক) 1
খ
খ) 9
গ
গ) 6
ঘ
ঘ) 3

ব্যাখ্যা

We know,
n(B U E U F) = n(B) + n(E) + n(F) - n(B ∩ E) - n(B ∩ F) - n(E ∩ F) + n(B ∩ E ∩ F)
Or, 24 = 6 + 12 + 15 + 1 - 2 - 2 - n(E ∩ F)
Or, n(E ∩ F) = 6

৯,৯৯৩.

A canteen requires 651 liters of water for a week. Totally, how many liters will it require for the months of December, January, February?

ক
ক) 8370 liters
খ
খ) 8470 liters
গ
গ) 8650 liters
ঘ
ঘ) 9857 liters

ব্যাখ্যা

Question: A canteen requires 651 liters of water for a week. Totally, how many liters will it require for the months of December, January, February?

Solution:

একদিনে পানি লাগে = 651/7 = 93 লিটার

ডিসেম্বর, জানুয়ারি, ফেব্রুয়ারি তে মোট দিন = (31 + 31 + 28) = 90 দিন।

মোট পানি লাগবে = (90 × 93) = 8370 লিটার

৯,৯৯৪.

A sum of Tk.12,500 amounts to Tk.15,500 in 4 years at the rate of simple interest. What is the rate of interest?

ক
ক) 7%
খ
খ) 5.5%
গ
গ) 6.5%
ঘ
ঘ) 6%

ব্যাখ্যা

S.I. = Tk. (15500 - 12500)
= Tk. 3000.

Rate ={(100 x 3000)/(12500 x 4)}%
= 6%

৯,৯৯৫.

A boat can travel 35 km upstream in 5 hours. If the speed of the stream is 2.5 kmph, how much time will the boat take to cover a distance of 96 km downstream?

ক
ক) 3 hours
খ
খ) 5 hours
গ
গ) 8 hours
ঘ
ঘ) 11 hours

ব্যাখ্যা

Question: A boat can travel 35 km upstream in 5 hours. If the speed of the stream is 2.5 kmph, how much time will the boat take to cover a distance of 96 km downstream?

Solution:
Upstram speed = 35/5 = 7 kmph
Speed of straem given = 2.5 kmph
Speed of boat in still water = (7 + 2.5) kmph = 9.5 kmph
Rate downstream of boat = (9.5 + 2.5) = 12 kmph
Time taken in covering 96 km distance downstream = 96/12 = 8 hours

৯,৯৯৬.

Karim weighs 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight in kg.

ক
55.25
খ
52.56
গ
57.20
ঘ
61.25

ব্যাখ্যা

Question: Karim weighs 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight in kg.

Solution:
মনেকরি,
করিমের পূর্বের ওজন = 5x
করিমের পরের ওজন = 4x

প্রশ্নমতে,
⇒ 5x = 65.7
⇒ x = 65.7/5
∴ x = 13.14

∴ ওজন কমে যাওয়ার পর হবে = 4 × 13.14
= 52.56 kg

৯,৯৯৭.

The average of the first five multiples of 3 is:

ক
12
খ
15
গ
9
ঘ
3

ব্যাখ্যা

Question: The average of the first five multiples of 3 is:

Solution:
The first five multiples of 3 are:
3, 6, 9, 12, 15.

∴ Average = (3 + 6 + 9 + 12 + 15)/5
= 45/5
= 9

৯,৯৯৮.

A 225 m long train can cover a 405 m platform in 21 seconds. Find the speed of the train in km/hr is?

ক
ক) 98 km/hr
খ
খ) 90 km/hr
গ
গ) 96 km/hr
ঘ
ঘ) 108 km/hr

ব্যাখ্যা

Length of platform = 405 m
Length of train = 225 m
Time taken to cover the length of train = 21 seconds
Distance need to cover = Length of platform + length of train
= 405 + 225
= 630 m
Speed of train = 630/21 = 30 m/s

∴ Speed of train = 30 × (18/5) = 6 × 18 = 108 km/hr.

৯,৯৯৯.

For a rhombus with diagonals 8 m and 16 m, determine the diagonal of a square that covers the same area as the rhombus.

ক
8 m
খ
8√2 m
গ
5√2 m
ঘ
2√2 m
ঙ
7 m

ব্যাখ্যা

Question: For a rhombus with diagonals 8 m and 16 m, determine the diagonal of a square that covers the same area as the rhombus.

Solution:
area of rhombus = (1/2) × 8 × 16
= 64 m²

area of square = 64 m²
side of square = √64 m
= 8 m

∴ diagonal of the square = 8√2 m

১০,০০০.

Two numbers when divided by 13, leaves remainder 11 and 9 respectively. If the sum of those two numbers is divided by 13, the remainder will be ?

ক
5
খ
7
গ
9
ঘ
11

ব্যাখ্যা

Question: Two numbers when divided by 13, leaves remainder 11 and 9 respectively. If the sum of those two numbers is divided by 13, the remainder will be ?

Solution:
Dividend = divisor × quotient + remainder
First number = (13 × n) + 11
Second number = (13 × n) + 9

Let,
n = 1
∴ first number = 24
and, second number = 22

after adding these two the reminder is = (24 + 22)/13
∴ reminder = 7