Bank Math

PrepBank · পাতা ১৫৪ / ১৬১ · ১৫,৩০১–১৫,৪০০ / ১৬,১২৪

১৫,৩০১.

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.5 m away from the wall. The length of the ladder is:

ক
ক) 5 m
খ
খ) 7.5 m
গ
গ) 9 m
ঘ
ঘ) 10 m

ব্যাখ্যা

Question: The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.5 m away from the wall. The length of the ladder is:

Solution:
Let,
AB be the wall and BC be the ladder.
Then, ∠ACB = 60° and AC = 4.5 m.

Here,
AC/BC = cos60°
⇒ AC/BC = 1/2
⇒ BC = 2 × AC
⇒ BC = 2 × 4.5
∴ BC = 9

∴ The length of the ladder is 9 m.

১৫,৩০২.

A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?

ক
Tk. 705
খ
Tk. 625
গ
Tk. 585
ঘ
Tk. 605

ব্যাখ্যা

Question: A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?

Solution:
Given,
Principal, P = 500 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 500 × (1 + 1/10)²
= 500 × (11/10)²
= 500 × (11/10) × (11/10)
= 605

১৫,৩০৩.

Two men X and Y start from a place P, walking at 3 kms/hr, and 4kms/hr. By how much distance apart they will be after 4 hours if they are walking in the same direction?

ক
ক) 4 kms
খ
খ) 3 kms
গ
গ) 2 kms
ঘ
ঘ) 6 kms
ঙ
ঙ) 3.5 kms

ব্যাখ্যা

d = v × t
= (4 - 3) × 4
= 4 km

১৫,৩০৪.

A sum of Tk. 4200 is divided among P, Q, and R such that P gets 3/5 of what Q gets and Q gets 1/4 of what R gets. Q’s share is:

ক
950 Tk
খ
750 Tk
গ
650 Tk
ঘ
550 Tk

ব্যাখ্যা

Question: A sum of Tk. 4200 is divided among P, Q, and R such that P gets 3/5 of what Q gets and Q gets 1/4 of what R gets. Q’s share is:

Solution:
Let,
R’s share = Tk. x
Then,
Q’s share = Tk. x/4
P’s share = Tk. (3/5) × (x/4) = Tk. 3x/20

∴ P + Q + R = 4200
⇒ 3x/20 + x/4 + x = 4200
⇒ (3x + 5x + 20x)/20 = 4200
⇒ 28x/20 = 4200
⇒ 28x = 4200 × 20
⇒ 28x = 84000
⇒ x = 84000/28
⇒ x = 3000

∴ Q’s share = x/4 = 3000/4 = 750 Tk.

১৫,৩০৫.

If two numbers are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both the numbers, then the sum of the two numbers is-

ক
40
খ
56
গ
60
ঘ
80

ব্যাখ্যা

Question: If two numbers are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both the numbers, then the sum of the two numbers is-

Solution:
Let, the numbers be 2x and 3x respectively.

ATQ,
(2x + 8)/(3x + 8) = 3/4
⇒ 9x + 24 = 8x + 32
⇒ 9x - 8x = 32 - 24
⇒ x = 8

∴ Sum of numbers = 2x + 3x
= 5x
= 5 × 8
= 40

১৫,৩০৬.

How much water be mixed in 36 litre of milk worth Tk. 4.80 per litre, so that value of mixture is Tk. 3.60 per litre?

ক
10 litres
খ
12 litres
গ
11 litres
ঘ
14 litres

ব্যাখ্যা

Question: How much water be mixed in 36 litre of milk worth Tk. 4.80 per litre, so that value of mixture is Tk. 3.60 per litre?

Solution:

Ratio of Milk to water will be = 18 : 6,
In 18 litre milk water added = 6 litre
In 1 litre milk water added = 6/18
In 36 litre milk water added = (6/18) × 36 = 12 litres

১৫,৩০৭.

Pipe A fills a tank in 40 seconds, pipe B in 60 seconds, and pipe C empties it in 30 seconds. Initially, A and B are opened, and after 8 seconds, C is also opened. In how much more time will the tank be completely filled?

ক
90 seconds
খ
70 seconds
গ
80 seconds
ঘ
50 seconds

ব্যাখ্যা

Question: Pipe A fills a tank in 40 seconds, pipe B in 60 seconds, and pipe C empties it in 30 seconds. Initially, A and B are opened, and after 8 seconds, C is also opened. In how much more time will the tank be completely filled?

Solution:
Let the capacity of the tank be LCM of 40, 60, 30 = 120 units.

Efficiency of A = 120/40 = 3 units/second
Efficiency of B = 120/60 = 2 units/second
Efficiency of C = –120/30 = –4 units/second

(A + B open) for first 8 seconds,
Combined efficiency = 3 + 2 = 5 units/second
Work done in 8 seconds = 8 × 5 = 40 units
Remaining work = 120 – 40 = 80 units

Now when all three pipes open,
Combined efficiency = 3 + 2 – 4 = 1 unit/second
More time required = 80 ÷ 1 = 80 seconds

১৫,৩০৮.

If A = π/3, B = A/2 then sin (A + B) =?

ক
0
খ
1
গ
2
ঘ
3

ব্যাখ্যা

Question: If A = π/3, B = A/2 then sin (A + B) =?

Solution:
B = A/2
= π/6

A + B = ( π/3) + ( π/6)
= π/2

sin(π/2 )
= 1

১৫,৩০৯.

How many multiples of 7 are there between 100 and 160?

ক
ক) 8
খ
খ) 7
গ
গ) 9
ঘ
ঘ) 10

ব্যাখ্যা

Question: How many multiples of 7 are there between 100 and 160?

Solution:

100 থেকে 160 এর মধ্যে 7 এর গুণিতক আছে = 8 টি
7টি গুণিতক হলো - 105, 112 119 126, 133, 140, 147,154

১৫,৩১০.

The smallest number which must be subtracted from 8112 to make it exactly divisible by 99 is :

ক
ক) 93
খ
খ) 94
গ
গ) 95
ঘ
ঘ) 96

ব্যাখ্যা

On dividing 8112 by 99, we get 93 as remainder.
So, the required number to be subtracted is 93.

১৫,৩১১.

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

ক
1/2
খ
3/4
গ
3/8
ঘ
5/16

ব্যাখ্যা

Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

Solution:
In a simultaneous throw of two dice, we have n(S) = (6 × 6) = 36

Then,
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)}
∴ n(E) = 27

∴ P(E) = n(E)/n(S) = 27/36 = 3/4

১৫,৩১২.

The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number?

ক
ক) 47
খ
খ) 49
গ
গ) 56
ঘ
ঘ) 10

ব্যাখ্যা

Question: The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number?

Solution:
ধরি, সপ্তম সংখ্যাটি x

প্রথম সাতটি সংখ্যার গড় ৬৩
প্রথম সাতটি সংখ্যার সমষ্টি (৬৩ × ৭) = ৪৪১
প্রথম ছয়টি সংখ্যার সমষ্টি = ৪৪১ - x

শেষ সাতটি সংখ্যার গড় ৭০
শেষ সাতটি সংখ্যার সমষ্টি (৭০ × ৭) = ৪৯০
শেষ ছয়টি সংখ্যার সমষ্টি = ৪৯০ - x

সাতটি সংখ্যার সমষ্টি = ৪৪১ - x + ৪৯০ - x + x
= ৯৩১ - x

গড়, (৯৩১ - x)/১৩ = ৬৮
⇒ ৯৩১ - x = ৬৮ × ১৩
⇒ ৯৩১ - x = ৮৮৪
⇒ x = ৯৩১ - ৮৮৪
∴ x = ৪৭

অতএব, সপ্তম সংখ্যাটি ৪৭

১৫,৩১৩.

⁴P₂ - ⁴C₂ =?

ক
12
খ
8
গ
6
ঘ
4

ব্যাখ্যা

প্রশ্ন: ⁴P₂ - ⁴C₂ =?

সমাধান:
⁴P₂
= 4!/(4 - 2)!
= 4!/2!
= 12

⁴C₂
= 4!/2!(4 - 2)!
= 4!/2! 2!
= 6

∴ ⁵P₂ - ⁵C₂ = 12 - 6
= 6

১৫,৩১৪.

A man deposits Tk. 600 in a bank at 10% interest rate compounded annually. At the end of the second year, what will be the total amount including interest?

ক
680 Tk.
খ
710 Tk.
গ
840 Tk.
ঘ
726 Tk.

ব্যাখ্যা

Question: A man deposits Tk. 600 in a bank at 10% interest rate compounded annually. At the end of the second year, what will be the total amount including interest?

Solution:
Given,
Principal, P = 600 Tk
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years

We know,
Compound Amount = P(1 + r)ⁿ
= 600 × (1 + 1/10)²
= 600 × (11/10)²
= 600 × (11/10) × (11/10)
= 600 × 121/100
= 726 Tk

১৫,৩১৫.

A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/h, the journey would take 4 hours less. Find the speed of the train.

ক
32 km/h
খ
28 km/h
গ
25 km/h
ঘ
20 km/h

ব্যাখ্যা

Question: A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/h, the journey would take 4 hours less. Find the speed of the train.

Solution:
Let,
the speed of the train be x km/h

ATQ,
600/x - 600/(x + 5) = 4
⇒ {600(x + 5) - 600x}/x(x + 5) = 4
⇒ (600x + 3000 - 600x)/(x² + 5x) = 4
⇒ 3000/(x² + 5x) = 4
⇒ 4x² + 20x = 3000
⇒ 4x² + 20x - 3000 = 0
⇒ x² + 5x - 750 = 0
⇒ x² + 30x - 25x - 750 = 0
⇒ x(x + 30) - 25(x - 30) = 0
⇒ (x + 30)(x - 25) = 0
⇒ x = - 30 or 25
∴ x = 25 [neglecting the negative value of x]

∴ Speed of the train 25 km/h

১৫,৩১৬.

If xy < 0, which of the following must be true?
i. x + y = 0 ii. 2y - 2x < 0, iii. x² + y²> 0

ক
I only
খ
II only
গ
III only
ঘ
both II and III.

ব্যাখ্যা

Question: If xy < 0, which of the following must be true?

i. x + y = 0 ii. 2y - 2x < 0, iii. x² + y²> 0

Solution:
যেহেতু
xy < 0,
1) হয় x > 0 অথবা y < 0
2) হয় x < 0 অথবা y < 0

আমরা জানি
দুইটি সংখ্যার বর্গের সমষ্টি কখনোই ঋণাত্বক হতে পারে না।
অপশন গ) x² + y² অবশ্যই যেকোন মানের জন সত্য হবে।

১৫,৩১৭.

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

ক
ক) 5(5/11)
খ
খ) 5(6/11)
গ
গ) 6(5/11)
ঘ
ঘ) 6(6/11)
ঙ
ঙ) None of these

ব্যাখ্যা

P's 1 day 1 hrs work = 1/96 part.
Q's 1 day 1 hr's work = 1/80 part.
P & Q together work in 1 hr per day = 1/96 + 1/80 = 11/480 part.
P & Q together completes in 8 hr per day = 11×8/480 = 11/60 part.
So, days required = 60/11 = 5(5/11)

১৫,৩১৮.

If a half kg of tomato costs 80 taka, how many taka will 300 gm cost?

ক
TK. 42
খ
TK. 45
গ
TK. 48
ঘ
TK. 52

ব্যাখ্যা

Question: If a half kg of tomato costs 80 taka, how many taka will 300 gm cost?

Solution:
Let the required cost be P TK
Less weight : Less cost (Direct proportion)
500 : 300 : : 80 : P
⇒ 500/300 = 80/P
⇒5/3 = 80/P
⇒ P = (3 × 80)/5
∴ P = 48

১৫,৩১৯.

Due to a reduction in books price by 10%, the number of books sold increased by 30%. What was the percentage increase in revenue?

ক
12%
খ
15%
গ
17%
ঘ
20%

ব্যাখ্যা

Question: Due to a reduction in books price by 10%, the number of books sold increased by 30%. What was the percentage increase in revenue?

Solution:
ধরি,
বইয়ের মূল্য = 100 টাকা
10% কমে বইয়ের মূল্য = 90 টাকা
30% বৃদ্ধিতে বিক্রয়মূল্য = 90 × (130/100) = 117 টাকা

∴ শতকরা রেভিনিউ = (117 - 100)/100 × 100%
= 17%

১৫,৩২০.

Two pipes A and B can fill a tank in 36 minutes and 45 minutes respectively. Another pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. The tank is filled up in-

ক
40 minutes
খ
46 minutes
গ
52 minutes
ঘ
56 minutes

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 36 minutes and 45 minutes respectively. Another pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. The tank is filled up in-

Solution:
Part of the tank filled by pipes A and B in 1 minute = (1/36) + (1/45)
= (5 + 4)/180
= 9/180
= 1/20
Part of the tank filled by these pipes in 7 minutes = 7/20
Remaining unfilled part = 1- (7/20)
= (20 - 7)/ 20
= 13/20
When all three pipes are opened
= (1/20) − (1/30)
= (3 - 2)/60
= 1/60

∴ Time taken in filling = 13/20 part
= (13/20) × 60
= 39 minutes

So, Required time = 39 + 7
= 46 minutes

১৫,৩২১.

The speed of a boat in still water in 25 km/h and the rate of current is 3 km/h. The distance travelled downstream in 15 minutes is-

ক
5 km
খ
6 km
গ
7 km
ঘ
8 km

ব্যাখ্যা

Question: The speed of a boat in still water in 25 km/h and the rate of current is 3 km/h. The distance travelled downstream in 15 minutes is-

Solution:
Given,
The speed of a boat in still water = 25 km/h
The rate of current = 3 km/h

∴ Speed downstream = (25 + 3) kmph
= 28 kmph.

∴ Distance travelled = (28 × 15/60) km
= 7 km

১৫,৩২২.

In a group of 15, 7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?

ক
ক) 0
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 5
ঙ
ঙ) None of these

ব্যাখ্যা

Question: In a group of 15, 7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?

Solution:
There are a group of 15
3 have not studied either.
∴ The number of student who either studied Latin or Greek = 15 - 3 = 12

Here,
The number of student studied Latin = n(L) = 7
The number of student studied Greek = n(G) = 8

Let,
The number of student studied both Latin and Greek = n(L ∩ G)

Now,
n(L ∪ G) = n(L) + n(G) - n(L ∩ G)
⇒ n(L ∩ G) = n(L) + n(G) - n(L ∪ G)
= 7 + 8 - 12
= 15 - 12
= 3

∴ 3 students of these studied both Latin and Greek.

১৫,৩২৩.

A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cm and its width is increased also by x cm so as to make a square, then its area increased by -

ক
ক) 4cm²
খ
খ) 144cm²
গ
গ) 12cm²
ঘ
ঘ) 140cm²

ব্যাখ্যা

ATQ, 14 - x = 10 + x
Or, 2x = 4
Or, x = 2

Area of the rectangle = 10 × 14 = 140 cm²
And, area of the square = (10 + 2)² = 12² = 144 cm²

So, its area increased by 144 - 140 or 4 cm²

১৫,৩২৪.

In a party every person shakes hands with every other person. If there are 78 hands shakes, find the number of person in the party.

ক
12
খ
13
গ
14
ঘ
15

ব্যাখ্যা

Question: In a party every person shakes hands with every other person. If there are 78 hands shakes, find the number of person in the party.

Solution:
Let n be the number of persons in the party
Number of hands shake = 78
Total number of hands shake is given by = ⁿC₂
Now,
According to the question,
ⁿC₂= 78
⇒ n!/{2!(n - 2)!} = 78
⇒ {n × (n - 1)}/2 = 78
⇒ n^{2 _-}n =156
⇒ n²- 13n + 12n - 156 = 0
⇒ n(n - 13) + 12(n - 13) = 0
or, n = 13, -12

But, we cannot take negative value of n
So, n = 13
∴ number of persons in the party = 13

১৫,৩২৫.

Find the value of n, if 27^{{n - (1/3)}} = 243.

ক
1
খ
2
গ
0
ঘ
1/2
ঙ
5/3

ব্যাখ্যা

Question: Find the value of n, if 27^{{n - (1/3)}} = 243.

Solution:
27^{{n - (1/3)}} = 243
⇒ (3³)^{{n - (1/3)}} = 3⁵
⇒ 3^{(3n - 1)} = 3⁵
⇒ 3n - 1 = 5
⇒ 3n = 5 + 1
⇒ 3n = 6
∴ n = 2

১৫,৩২৬.

15 machine can produce 30 phones in 30 seconds. How much time will 75 machines take to produce 150 phones?

ক
30 minutes
খ
30 seconds
গ
15 seconds
ঘ
45 seconds

ব্যাখ্যা

Question: 15 machine can produce 30 phones in 30 seconds. How much time will 75 machines take to produce 150 phones?

Solution:
15 machine 30 phones 30 sec
1 machine 1 phone = (15 × 30)/30 sec
75 machines 150 phones = (15 × 30 × 150)/(30 × 75)
= 30 sec

১৫,৩২৭.

X = { - 4, - 2, 1, 3}, Y = {- 1, 4, 5}. If x is a number from set X, and y is a number from set Y. The probability that x + y is positive is closest to-

ক
ক) 0.5
খ
খ) 0.6
গ
গ) 0.7
ঘ
ঘ) 0.8

ব্যাখ্যা

Question: X = { - 4, - 2, 1, 3}, Y = {- 1, 4, 5}. If x is a number from set X, and y is a number from set Y. The probability that x + y is positive is closest to-

Solution:
X = { - 4, - 2, 1, 3}
Y = {- 1, 4, 5}

X সেটের উপাদান সংখ্যা = 4
Y সেটের উপাদান সংখ্যা = 3

মোট ফলাফল = ⁴C₁ × ³C₁ = 4 × 3 = 12
অনুকূল ঘটনার সংখ্যা = {( - 4, 5), ( - 2, 4), ( - 2, 5), (1, 4), (1, 5), (3,-1), (3, 4), (3, 5)}
অনুকূল ঘটনার সংখ্যা = 8

নির্ণেয় সম্ভাব্যতা = 8/12
= 2/3
= 0.666
≈ 0.7

১৫,৩২৮.

A mixture of 20kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

ক
4
খ
5
গ
6
ঘ
8

ব্যাখ্যা

Question: A mixture of 20kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

Solution:
20 কেজি মিশ্রনে পানি আছে = 20 এর 10%
= 20 এর 10/100
= 2 কেজি

স্পিরিট আছে = 20 - 2
= 18 কেজি

ধরি,
মিশ্রনে পানি মেশাতে হবে x

প্রশ্নমতে,
18/(2 + x) = 75/25
⇒ 18/(2 + x) = 3/1
⇒ 3(2 + x) = 18
⇒ 6 + 3x = 18
⇒ 3x = 18 - 6
⇒ 3x =12
⇒ x = 4

১৫,৩২৯.

A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

ক
Taka 9,000
খ
Taka 10,000
গ
Taka 11,000
ঘ
Taka 5,000

ব্যাখ্যা

Question: A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

Solution:
Cost Price of 200 books = 200 × Taka 150 = Taka 30,000
Selling Price of 200 books = 200 × Taka 200 = Taka 40,000
∴ Total Profit = Selling Price - Cost Price
= Taka 40,000 - Taka 30,000
= Taka 10,000

১৫,৩৩০.

ক
0.49
খ
1.21
গ
0.77
ঘ
0.44

ব্যাখ্যা

Question:

Solution:
Given that, √{(0.85)² - (0.36)²}
Since, a² - b²= (a - b)(a + b)
= √{(0.85 + 0.36)(0.85 - 0.36)}
= √{(1.21)(0.49)}
= √{(1.1)(1.1) × (0.7)(0.7)}
= 1.1 × 0.7
= 0.77

১৫,৩৩১.

The average of Jewel's marks in 6 subjects is 74. If his average in five subjects excluding science is 70, how many marks he obtained in science?

ক
94
খ
92
গ
90
ঘ
88

ব্যাখ্যা

Question: The average of Jewel's marks in 6 subjects is 74. If his average in five subjects excluding science is 70, how many marks he obtained in science?

Solution:
Total marks obtained in 6 subjects = 6 × 74 = 444

Total marks in 5 subjects excluding science = 5 × 70 = 350

Therefore, marks obtained in science would be = 444 - 350 = 94

১৫,৩৩২.

If 738M6M is divisible by 11, then the value of M is:

ক
12
খ
3
গ
6
ঘ
9
ঙ
None

ব্যাখ্যা

Question: If 738M6M is divisible by 11, then the value of M is:

Solution:
A number is divisible by 11 when the difference between the total number of odd places and the total number of even places is equal to zero or multiple of 11

Therefore, M + M + 3 = 7 + 8 + 6
⇒ 2M = 18
∴ M = 9

১৫,৩৩৩.

Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

ক
1/4
খ
2/3
গ
1/2
ঘ
1/3

ব্যাখ্যা

Question: Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

Solution:
Total outcomes = {TTT, TTH,THT, HTT, THH, HTH, HHT, HHH} = 8
Favorable outcomes = {HHT, HTH, THH, HHH} = 4

So, the probability of getting at least 2 heads = Favorable outcomes/Total outcomes
= 4/8 = 1/2

১৫,৩৩৪.

The ages of Sabiha and Suriya are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?

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

ব্যাখ্যা

Question: The ages of Sabiha and Suriya are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?

Solution:
Let, their ages are 7x, 3x

ATQ,
(7x + 6)/(3x + 6) = 5/3
⇒ 3(7x + 6) = 5(3x + 6)
⇒ 21x + 18 = 15x + 30
⇒ 21x - 15x = 30 - 18
⇒ 6x = 12
∴ x = 2

The difference in their ages is = 7x - 3x
= 4x
= 4 × 2
= 8 years

১৫,৩৩৫.

A MiG-29 fighter jet covers a certain distance at a speed of 1240 km/h in 5 hours. What speed must it maintain to cover the same distance in 250 minutes?

ক
1320 km/h
খ
1420 km/h
গ
1488 km/h
ঘ
1648 km/h

ব্যাখ্যা

Question: A MiG-29 fighter jet covers a certain distance at a speed of 1240 km/h in 5 hours. What speed must it maintain to cover the same distance in 250 minutes?

Solution:
Total distance = Speed × Time
= (1240 × 5) km
= 6200 km

Given time = 250 minutes = (250/60) hours= 25/6 hours

∴ Required speed = Distance/Time
= {6200/(25/6)} km/h
= {6200 × (6/25)} km/h
= (248 × 6) km/h
= 1488 km/h

১৫,৩৩৬.

Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they now take to complete the remaining work?

ক
ক) 3
খ
খ) 4
গ
গ) 6
ঘ
ঘ) 8

ব্যাখ্যা

1 child's 1 day's work = 1/192;
1 adults 1 day's work = 1/96.
Work done in 3 days = (1/96) × 16 × 3
= 1/2
Remaining work = {1 - (1/2)}
= 1/2.
(6 adults + 4 Children)'s 1 day's work = (6/96) + (4/192)
= 1/12
1/12 work is done by them in 1 days
1/2 work is done by them in (12 × (1/2)}
= 6 days.

১৫,৩৩৭.

A certain amount earns simple interest of Tk. 1750 after 7 year. Had the interest been 2% more, how much more interest would it have earned?

ক
ক) Tk.35
খ
খ) Tk.245
গ
গ) Tk.350
ঘ
ঘ) cannot be determined

ব্যাখ্যা

We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.

১৫,৩৩৮.

A square park is surrounded by a path of uniform width 3 meters all around it. The area of the path is 240 sq. meters. Find the perimeter of the park.

ক
52 m
খ
56 m
গ
60 m
ঘ
68 m

ব্যাখ্যা

Question: A square park is surrounded by a path of uniform width 3 meters all around it. The area of the path is 240 sq. meters. Find the perimeter of the park.

Solution:
Let, one side of the park is = x meter.
So, one side of the park with path = x + (3 + 3)
= x + 6

We know,
Area of the park = x²
Area of the path, (x + 6)² - x² = 240
⇒ x² + 12x + 36 - x² = 240
⇒ 12x + 36 = 240
⇒ 12x = 240 - 36
⇒ 12x = 204
⇒ x = 204/12
∴ x = 17

One side of the square = 17 m.
So, perimeter of the square = 4 × 17
= 68 m

১৫,৩৩৯.

What will be the simple interest on Tk. 730 at 9% per annum for the period from January 12, 2026 to May 31, 2026?

ক
30.50 Tk.
খ
28.25 Tk.
গ
29.50 Tk.
ঘ
25.20 Tk.
ঙ
None

ব্যাখ্যা

Question: What will be the simple interest on Tk. 730 at 9% per annum for the period from January 12, 2026 to May 31, 2026?

Solution:
January 12, 2026 to May 31, 2026 = 140 days

100 টাকার 365 দিনের মুনাফা = 9 টাকা
1 টাকার 1 দিনের মুনাফা = 9/(365 × 100) টাকা
730 টাকার 140 দিনের মুনাফা = (9 × 730 × 140)/(365 × 100) টাকা
= 25.20

১৫,৩৪০.

Find the greatest number that will divide 43, 91, and 183 and leave the same remainder.

ক
12
খ
8
গ
3
ঘ
4

ব্যাখ্যা

Question: Find the greatest number that will divide 43, 91, and 183 and leave the same remainder.

Solution:
the number is the H.C.F of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F of 48, 92 and 140
= 4

১৫,৩৪১.

The ratio of two numbers is 3 : 4 and their H.C.F is 6. Find their L.C.M.

ক
32
খ
72
গ
36
ঘ
42

ব্যাখ্যা

Question: The ratio of two numbers is 3 : 4 and their H.C.F is 6. Find their L.C.M.

Solution:
Let the two numbers be 3x and 4x.
∴ H.C.F = x = 6

∴ The two numbers are, 3 × 6 = 18 and 4 × 6 = 24

∴ Product of the two numbers = 18 × 24 = 432
And H.C.F = 6

We know,
L.C.M = (Product of two numbers)/H.C.F
= 432/6
= 72

∴ The L.C.M of the two numbers = 72.

১৫,৩৪২.

A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.

ক
6 km/hr
খ
3 km/hr
গ
4 km/hr
ঘ
5 km/hr

ব্যাখ্যা

Question: A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.

Solution:
Speed of boat in still water = x = 5 km/hr.
Let rate of flow of river = y km/hr.
∴ Speed of u/s = 5 - y
and speed of d/s = 5 + y

∴ 90/(5 + y) + 90/(5 - y) = 100
⇒ 450 - 9y + 450 + 9y = 100(25 - y²)
⇒ 9 = 25 - y²
⇒ y² = 16
⇒ y = 4 km/hr.

১৫,৩৪৩.

The average of 5 terms is 50. If the first 4 terms are 45, 42, 119, and 84, what will be the last term?

ক
56
খ
- 20
গ
- 40
ঘ
- 50
ঙ
None of these

ব্যাখ্যা

Question: The average of 5 terms is 50. If the first 4 terms are 45, 42, 119, and 84, what will be the last term?

Solution:

Sum of all the terms = 250

Sum of first four terms = 45 + 42 + 119 + 84 = 290

So, the 5th term should be 250 - 290 = - 40.

১৫,৩৪৪.

If √24=4.889, the value of √(8/3) is = ?

ক
ক) 1.644
খ
খ) 1.533
গ
গ) 1.633
ঘ
ঘ) 1.666

ব্যাখ্যা

= √(8/3)
= √(8×3)/(3×3)
= √(24/3)
=4.899/3
=1.633

১৫,৩৪৫.

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

ক
44 cm
খ
52 cm
গ
42 cm
ঘ
41 cm

ব্যাখ্যা

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

Solution:
Given,
The perimeter of the equilateral triangle = 84√3 cm.

∴ Each side of the equilateral triangle
= (84√3)/3
= 28√3 cm.

We know,
The height of the equilateral triangle = (a√3)/2

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

১৫,৩৪৬.

Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.

ক
127
খ
132
গ
114
ঘ
108

ব্যাখ্যা

Question: Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.

Solution:
The number on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
Hence, make the dividend completely divisible by the divisor. This is possible, if we subtract remainder from the dividend.
Therefore,
1657 - 6 = 1651
2037 - 5 = 2032

H.C.F. of 1651 and 2032 is 127. 127 is the common factor.
127 × 13 = 1651
Thus by adding 6, we get 1651 + 6 = 1657
127 is the correct answer.

১৫,৩৪৭.

An amount of Tk. 10,000 becomes Tk. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest?

ক
ক) 25%
খ
খ) 20%
গ
গ) 40%
ঘ
ঘ) 30%

ব্যাখ্যা

Question: An amount of Tk. 10,000 becomes Tk. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest?

Solution:
এখানে
মূলধন P = 10,000 টাকা
চক্রবৃদ্ধি মুলধন C = 20,736 টাকা

আমরা জানি
20,736 = 10000{1 + r/(2× 100)}^{2 × 2}
20736/10000 = {(200 + r)/200}⁴
20736/10000 = (200 + r)⁴/1600000000
20736 × 1600000000/10000 = (200 + r)⁴
20736 × 160000 = (200 + r)⁴
(200 + r)⁴ = 3,317,760,000
(200 + r)⁴ = (240)⁴
200 + r = 240
r = 240 - 200
r = 40

১৫,৩৪৮.

The area of a square field is 24200 sq m. What is the perimeter of the square field?

ক
440√2 m.
খ
440 m
গ
110 m
ঘ
110√2 m

ব্যাখ্যা

Question: The area of a square field is 24200 sq m. What is the perimeter of the square field?

Solution:
The area of a square field is 24200 sq m.
∴ Length of the field √24200 m = √(2 × 121 × 100) = √(2 × 11² × 10²) = 110√2 m.

∴ The perimeter of the square = 4 × 110√2 = 440√2 m.

১৫,৩৪৯.

If secθ - tanθ = 1/√3, the value of secθ.tanθ = ?

ক
2/√3
খ
2/3
গ
1/2
ঘ
2

ব্যাখ্যা

Question: If secθ - tanθ = 1/√3, the value of secθ.tanθ = ?

Solution:
sec²θ - tan²θ = 1
⇒ (secθ - tanθ) (secθ + tanθ) = 1
⇒ 1/√3 (secθ + tanθ) = 1
⇒ secθ + tanθ = √3

2secθ = (1/√3) + √3 = 4/√3
⇒ secθ = 2/√3
⇒ secθ = sec30
⇒ θ = 30°

secθ.tanθ = (2/√3) × (1/√3)
= 2/3

১৫,৩৫০.

A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?

ক
6.2 days
খ
6.6 days
গ
7 days
ঘ
7.2 days

ব্যাখ্যা

Question: A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?

Solution:
B is 50% more efficient than A so he will take less time to do a piece of work.

Therefore, the ratio of the time taken by A and B = 150/100 = 3 : 2

Let B takes X days to do the job.
3 : 2 = 10 : X
⇒ 3X =20
∴ X = 6.6 days

১৫,৩৫১.

A cistern can be filled by two pipes in 20 and 30 minutes respectively. Both pipes being opened, when the first pipe must be turned off so that the cistern may be filled in 10 minutes more?

ক
ক) after 7 minutes
খ
খ) after 8 minutes
গ
গ) after 9 minutes
ঘ
ঘ) after 12 minutes

ব্যাখ্যা

Question: A cistern can be filled by two pipes in 20 and 30 minutes respectively. Both pipes being opened, when the first pipe must be turned off so that the cistern may be filled in 10 minutes more?

Solution:
ধরি, নল A, x মিনিট পর বন্ধ করতে হবে।

A নল,
২০ মিনিটে পূর্ণ করে ১ অংশ
১ মিনিটে পূর্ণ করে ১/২০ অংশ

B নল,
৩০ মিনিটে পূর্ণ করে ১ অংশ
১ মিনিটে পূর্ণ করে ১/৩০ অংশ

দুইটি নল একসাথে ১ মিনিটে সম্পূর্ণ করে = ১/২০ + ১/৩০ অংশ
= ৫/ ৬০ অংশ
= ১/১২ অংশ

সম্পূর্ণ অংশ শেষ করতে সময় লাগে ১২ মিনিট
১০ মিনিট বেশীতে, মোট সময় = ১২ + ১০ মিনিট
= ২২ মিনিট

দুইটি নল একসাথে x মিনিটে সম্পূর্ণ করে = x/১২ অংশ

বাকি থাকে, ১ - x/১২ অংশ
= ১২ - x/১২ অংশ

১২ - x/১২ অংশ নল B পূর্ণ করে ২২ - x মিনিটে
১ অংশ পূর্ণ করতে সময় লাগে {(২২ - x) × ১২}/{১২ - x} মিনিট

এখন
(২২ - x)× ১২/১২ - x = ৩০
⇒ ২৬৪ - ১২x = ৩৬০ - ৩০x
⇒ - ১২x + ৩০X = ২৬৪ - ১২০
⇒ ১৮x = ১৪৪
∴ x = ১৪৪/১৮
= ৮ মিনিট

১৫,৩৫২.

In a college election between two candidates, one candidate got 55% of the total valid votes. 10% of the votes were invalid. If the total number of votes were 16200, what is the number of valid votes the other candidate got?

ক
ক) 5325
খ
খ) 5719
গ
গ) 6327
ঘ
ঘ) 6561

ব্যাখ্যা

Question: In a college election between two candidates, one candidate got 55% of the total valid votes. 10% of the votes were invalid. If the total number of votes were 16200, what is the number of valid votes the other candidate got?

Solution:
Number of valid votes
= (100 - 10)% of 16200
= 90% of 16200
= (90/100) × 16200
= 14580

Valid votes polled by other candidate
= (100 - 55)% of 14580
= 45% of 14580
= (45/100) × 14580
= 6561

∴ The number of valid votes the other candidate got is 6561

১৫,৩৫৩.

Which number will complete the series: 1, 3, 7, 15, 31, 63, __?

ক
120
খ
125
গ
127
ঘ
132

ব্যাখ্যা

Question: Which number will complete the series: 1, 3, 7, 15, 31, 63, __?

Solution:
3 - 1 = 2
7 - 3 = 4 = 2 × 2
15 - 7 = 8 = 4 × 2
31 - 15 = 16 = 8 × 2
63 - 31 = 32 = 16 × 2

∴ The next number of 63 will be 63 + 32 × 2
= 63 + 64
= 127

১৫,৩৫৪.

There is 40% increase in an amount in 4 years at simple interest. What will be the compound interest of Tk.2000 after 2 years at the same rate?

ক
400
খ
380
গ
420
ঘ
440

ব্যাখ্যা

Question: There is 40% increase in an amount in 4 years at simple interest. What will be the compound interest of Tk.2000 after 2 years at the same rate?

Solution:
Let P = Tk. 100
Then, S.I. Tk. = 40 and n = 4 years
Rate = (100 × 40)/(100 × 4) = 10%
Now, P = Tk. 2000
n = 2 years and R = 10% p.a.
C.I. = 2000(1 + 10/100)² - 2000
= 2000(1.1)² - 2000
= 2000 × 1.21 - 2000
= 2420 - 2000
= 420

১৫,৩৫৫.

The first number is 20% greater and the second number is 50% greater than a third number. What is the ratio of the two numbers?

ক
4 : 5
খ
2 : 3
গ
7 : 2
ঘ
5 : 2
ঙ
None of the above

ব্যাখ্যা

Question: The first number is 20% greater and the second number is 50% greater than a third number. What is the ratio of the two numbers?

Solution:
Let the third number be x

Then, first number = 120% of x
= 120x/100
= 6x/5

Second number = 150% of x
= 150x/100
= 3x/2

∴ Ratio of first two numbers = 6x/5 : 3x/2
= 12x : 15x
= 4 : 5

১৫,৩৫৬.

A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 seconds. What is the length of the other train?

ক
ক) 230 m
খ
খ) 240 m
গ
গ) 260 m
ঘ
ঘ) 320 m

ব্যাখ্যা

Relative speed = (120 + 80) km/hr
= (200×5/18) m/s
= 500/9 m/s
Let, The length of other train be x m
Then,
x + 270 = 500/9 × 9
Or, x = 500 - 270 = 230

১৫,৩৫৭.

The slant height of a right circular cone is 10 m, and its height is 8 m. Find the area of its curved surface.

ক
35π sq. meter
খ
50π sq. meter
গ
60π sq. meter
ঘ
90π sq. meter

ব্যাখ্যা

Question: The slant height of a right circular cone is 10 m, and its height is 8 m. Find the area of its curved surface.

Solution:
Here, l = 10 and h = 8
r = √(l² - h²)
= √(10² - 8²)
= √(100 - 64)
= √36
= 6

∴ Curved surface area = πrl
= π × 6 × 10
= 60π sq. meter

১৫,৩৫৮.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

ক
1/3
খ
1/4
গ
1/5
ঘ
1/7
ঙ
None of these

ব্যাখ্যা

Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Solution:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = (3 - 3x/8) + x litres
Quantity of syrup in new mixture =5 - 5x/8 litres

ATQ,
(3 - 3x/8) + x = 5 - 5x/8
⇒ (24 - 3x)/8 + x = (40 - 5x)/8
⇒ 24 - 3x + 8x = 40 - 5x
⇒ 5x + 24 = 40 - 5x
⇒ 10x = 16
∴ x = 8/5.

So, part of the mixture replaced = (8/5) × (1/8) = 1/5.

১৫,৩৫৯.

Mamun can do a piece of work in 24 days. Robin can do the same work in 30 days and Tonmoy in 40 days. Mamun and Tonmoy worked for 4 days and handed it to Rakesh. Robin worked for some days and handed it again to Mamun and Tonmoy 6 days before completing the work. For how many days did Robin work?

ক
ক) 5 days
খ
খ) 10 days
গ
গ) 8 days
ঘ
ঘ) 6 days

ব্যাখ্যা

Combined work done by Mamun and Tonmoy in 4 + 6 days (4 initial days and last 6 days)= 10/24 + 10/40
= (50 + 30)/120
= 80/120
= 2/3

∴ Remaining work = 1 - 2/3 = 1/3
Robin works for = (1/3) × 30 = 10.

১৫,৩৬০.

A motorboat, whose speed in 250 m/min in still water goes 30000 m downstream and comes back in a total of 270 minutes. The speed of the stream is:

ক
ক) 90 m/min
খ
খ) 85.55 m/min
গ
গ) 83.33 m/min
ঘ
ঘ) 87 m/min

ব্যাখ্যা

Question: A motorboat, whose speed in 250 m/min in still water goes 30000 m downstream and comes back in a total of 270 minutes. The speed of the stream is:

Solution:
Let,
The speed of the stream be x m/min
∴ Speed downstream = (250 + x) m/min
And speed upstream = (250 - x) m/min

Now,
30000/(250 + x) + 30000/(250 - x) = 270
⇒ 15000000/(62500 - x²) = 270
⇒ 15000000 = 16875000 - 270x²
⇒ 270x² = 1875000
⇒ x² = 6944.44
∴ x = 83.33 m/min

১৫,৩৬১.

A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

ক
12 days
খ
9 days
গ
10 days
ঘ
8 days

ব্যাখ্যা

Question: A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

Solution:
A একা কাজটি করতে পারে = 24 দিনে
∴ A এর একদিনের কাজ = 1/24 অংশ
এবং,
B একা কাজটি করতে পারে = 16 দিনে
∴ B এর একদিনের কাজ = 1/16 অংশ

∴ A ও B একসাথে একদিনের কাজ = (1/24) + (1/16) = (2 + 3)/48 = 5/48 অংশ
তারা 6 দিনে একসাথে কাজ করে = 6 × (5/48) = 5/8 অংশ

বাকি কাজ = 1 - (5/8) = 3/8 অংশ

অতএব,
A, 1/24 অংশ কাজ করে 1 দিনে
∴ 3/8 অংশ কাজ করে = (24 × 3)/8 = 9 দিনে

অতএব, A একা বাকি কাজ শেষ করতে ৯ দিন লাগবে।

১৫,৩৬২.

A, B, and C enter into a partnership. A invests 3 times as much as B invest s and B invests two-thirds of C's invests. At the end of the year, the profit earned is Tk 8800. What is the share of A?

ক
ক) 3200 Tk
খ
খ) 4800 Tk
গ
গ) 2400 Tk
ঘ
ঘ) 1800 Tk

ব্যাখ্যা

Question: A, B, and C enter into a partnership. A invests 3 times as much as B invest s and B invests two-thirds of C's invests. At the end of the year, the profit earned is Tk 8800. What is the share of A?

Solution:
Let the investment of C = 3x
So, the investment of B = 3x × (2/3) = 2x
And the investment of A = 2x × 3 = 6x

ATQ,
6x + 2x + 3x = 8800
⇒ 11x = 8800
⇒ x = 800

The share of A = 6 × 800 = 4800 Tk

১৫,৩৬৩.

A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbor. Now he is left out with 36 eggs. How many eggs he bought?

ক
ক) 40
খ
খ) 100
গ
গ) 200
ঘ
ঘ) 72

ব্যাখ্যা

Question: A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbor. Now he is left out with 16 eggs. How many eggs he bought?

Solution:
Let he bought 100 eggs.
Eggs after removing rotten one = 90.
Eggs given to neighbour = 80% of 90 = 72 eggs.
Now he left with eggs = 90 - 72 = 18 eggs.

Now,
Comparing,
18 = 36
1 = 36/18
100 = 200.
So, he bought 200 eggs.

১৫,৩৬৪.

The average of a, b, c is б and a - b = 4, ab = 21; What is the value of c?

ক
6
খ
7
গ
8
ঘ
9

ব্যাখ্যা

Question: The average of a, b, c is б and a - b = 4, ab = 21; What is the value of c?

Solution:
দেওয়া আছে
(a + b + c)/3 = 6
a + b + c = 18

আবার
a - b = 4
ab = 21

আমরা জানি
(a + b)² = (a - b)² + 4ab
(a + b)² = (4)² + 4×21
(a + b)² = 16 + 84
(a + b)² = 100
(a + b)² = 10²
a + b = 10

এখন
a + b + c = 18
10 + c = 18
c = 18 - 10
c = 8

১৫,৩৬৫.

The product of the roots of the equation 2a² - 5a + m = 10 is - 3. Find the value of m.

ক
ক) 1
খ
খ) 2
গ
গ) 4
ঘ
ঘ) 8

ব্যাখ্যা

Question: The product of the roots of the equation 2a² - 5a + m = 10 is - 3. Find the value of m.

Solution:
Rearranging the given equation we have 2a² - 5a + (m - 10) = 0

We know that,
if ax² + bx + c = 0 is a quadratic equation, then the product of their roots = c/a

Given the product of the roots = - 3
⇒ (m - 10)/2 = - 3
⇒ (m - 10) = - 6
⇒ m = - 6 + 10
∴ m = 4

১৫,৩৬৬.

24 women or 15 men or 36 boys can finish a piece of work in 12 days, working 8 hours per day, how many men must be associated with 12 women and 6 boys to finish another piece of work 9/4 times as greater in 30 days working 6 hours a day?

ক
15 men
খ
12 men
গ
8 men
ঘ
6 men

ব্যাখ্যা

Question: 24 women or 15 men or 36 boys can finish a piece of work in 12 days, working 8 hours per day, how many men must be associated with 12 women and 6 boys to finish another piece of work 9/4 times as greater in 30 days working 6 hours a day?

Solution:
We have 15 men = 24 women
Or, 12 women = 7.5 men
Also, 36 boys = 15 men
6 boys = 15/6 = 5/2 = 2.5 men
Therefore, 12 women + 6 boys = 7.5 + 2.5 men= 10 men
Now,
The number of day's ratio is 30 : 12
The hour's ratio is 6 hours : 8 hours
The work ratio is 1 work : 9/4 work
Now,
we can say that
(30 × 6 × 1) : (12 × 8 × 9/4) = 15 : x [Where x is the total number of men]
⇒ (30 × 6 × 1) × x = (12 × 8 × 9/4) × 15
⇒ x = 18

Therefore, the total number of men = 18
So, 18 -10 = 8 men must be associated.

১৫,৩৬৭.

In order to obtain an income of Tk. 720 from 8% stock at Tk. 90, one must make an investment of-

ক
Tk. 7200
খ
Tk. 8100
গ
Tk. 9000
ঘ
None of these

ব্যাখ্যা

Question: In order to obtain an income of Tk. 720 from 8% stock at Tk. 90, one must make an investment of-

Solution:
To obtain Tk. 8, investment = Tk. 90.
To obtain Tk. 720
investment = Tk. (90/8) × 720
= Tk. 8100

১৫,৩৬৮.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

ক
2/7
খ
1/5
গ
2/3
ঘ
1/4

ব্যাখ্যা

Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Solution:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = {3 - (3x/8) + x} litres
Quantity of syrup in new mixture = (5 - 5x/8) litres

ATQ,
{3 - (3x/8) + x} = (5 - 5x/8)
⇒ 5x + 24 = 40 - 5x
⇒ 10x = 16
∴ x = 8/5

So, part of the mixture replaced = (8/5) × (1/8)
= 1/5

১৫,৩৬৯.

The value of [(10)¹⁵⁰ ÷ (10)¹⁴⁶] is-

ক
10000
খ
1000
গ
100000
ঘ
10⁶

ব্যাখ্যা

Question: The value of [(10)¹⁵⁰ ÷ (10)¹⁴⁶] is-

Solution:

(10)¹⁵⁰ ÷ (10)¹⁴⁶
=10¹⁵⁰/10¹⁴⁶

= 10^{150 - 146}

= 10⁴

= 10000.

১৫,৩৭০.

Two persons Kamal and Billal started a business in which Kamal invested Tk. 50000, Billal invested Tk. 80000, after 4 months Sweety joined them with a certain amount. At the end of the year, a total profit of Tk. 40000 was recorded. Sweety's share in the profit was Tk. 15000, then find Sweety's investment in the business.

ক
Tk. 120000
খ
Tk. 116000
গ
Tk. 117000
ঘ
Tk. 100000

ব্যাখ্যা

Question: Two persons Kamal and Billal started a business in which Kamal invested Tk. 50000, Billal invested Tk. 80000, after 4 months Sweety joined them with a certain amount. At the end of the year, a total profit of Tk. 40000 was recorded. Sweety's share in the profit was Tk. 15000, then find Sweety's investment in the business.

Solution:
Let,
Sweety's investment in the business be Tk. 1000x

Profit ratio of Kamal, Billal and Sweety
= (50000 × 12) : (80000 × 12) : 1000x(12 - 4)
= 600000 : 960000 : 8000x
= 75 : 120 : x

Total profit = (75 + 120 + x) = 195 + x
Sweety's share in profit = x

ATQ,
40000 × {x/(195+ x)} = 15000
⇒ x/(195+ x) = 15000/40000
⇒ x/(195+ x) = 3/8
⇒ 585 + 3x = 8x
⇒ 5x = 585
⇒ x = 117

Investment by Sweety = 1000 × 117
= 117000

∴ Sweety's investment in the business will be Tk. 117000.

১৫,৩৭১.

Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of two number is

ক
40
খ
50
গ
60
ঘ
70
ঙ
None

ব্যাখ্যা

Question: Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of two number is

Solution:
Let, these two numbers be 3x and 4x then their LCM = 12x
Now, according to question,
12x = 240
Or, x = 20

Thus, the numbers are (3x = 3 × 20) = 60 and (4x = 4 × 20) = 80
Then smaller in this two is 60

১৫,৩৭২.

Ashraf crosses a 600 m long street in 5 minutes, What is his speed?

ক
7.2 km
খ
7.8 km
গ
8.4 km
ঘ
9 km
ঙ
None of the above

ব্যাখ্যা

Question: Ashraf crosses a 600 m long street in 5 minutes, What is his speed?

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

[speed বা বেগের একক kmph বা, km/hr কিন্তু এখানে অপশনে একক শুধু km দেয়া; যা দূরত্বের একক। তাই উত্তর None of the above হবে]

১৫,৩৭৩.

An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the yearly rate of compound interest?

ক
30%
খ
35%
গ
40%
ঘ
50%

ব্যাখ্যা

Question: An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the yearly rate of compound interest?

solution:
let the rate be R%

Then,
625 {1 + R/(2 × 100)} ^{2 × 2} = 1296
⇒ (1 + R/200)⁴ = 1296/625
⇒ (1 + R/200)⁴ = (6/5)⁴
⇒ (1 + R/200) = 6/5
⇒ R/200 = 1/5
⇒ R = 40
∴ R = 40%

১৫,৩৭৪.

The area of a rectangle is equal to the area of a square with side x. If the length of the rectangle is 2x, find its breadth.

ক
2/x
খ
x
গ
x²
ঘ
x/2

ব্যাখ্যা

Question: The area of a rectangle is equal to the area of a square with side x. If the length of the rectangle is 2x, find its breadth.

Solution:
Given that,
A square with side x

We know,
Area of square = x²

ATQ,
Area of a rectangle is equal to the area of a square.
∴ Area of a rectangle = x2

And,
Given Length of the rectangle = 2x
Let the breadth of the rectangle = b

We know,
Area of rectangle = length × breadth
2x⋅b = x²
⇒ b = x²/2x
∴ b = x/2

Therefore, the breadth of the rectangle is x/2

১৫,৩৭৫.

In a simultaneous throw of two dice what is the probability of getting a total of 10 or 11?

ক
ক) 7/12
খ
খ) 1/6
গ
গ) 5/36
ঘ
ঘ) 1/4

ব্যাখ্যা

Question: In a simultaneous throw of two dice what is the probability of getting a total of 10 or 11?

Solution:
If two dices are thrown total events = (6 × 6) = 36
Event of getting a total of 10 or 11 = {(4, 6), (5, 5), (6, 4), (5, 6), (6, 5)}
Expected events = 5

∴ Probability = 5/36

১৫,৩৭৬.

Find an equation of the horizontal line containing the point (3, 2).

ক
x = 3
খ
y = 3
গ
y = 2
ঘ
x = 2

ব্যাখ্যা

Question: Find an equation of the horizontal line containing the point (3, 2).

Solution:
The equation of the horizontal line containing the point (3, 2) is y = 2.
A horizontal line has a constant y-value for all points on the line.
Since the line must pass through the point (3, 2), its y-coordinate must be 2.

১৫,৩৭৭.

A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?

ক
32 hours
খ
48 hours
গ
98 hours
ঘ
58 hours

ব্যাখ্যা

Question: A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?

Solution:
A’s 1 hour’s work = 1/12
B’s 1 hour’s work = 1/16
C’s 1 hour’s work = 1/8

Therefore, (A + B + C)’s 1 hours net work= (1/12) + (1/16) - (1/8)
= (4 + 3 - 6)/48
= 1/48

So, time taken by (A + B + C) to fill the cistern = 48 hours.

১৫,৩৭৮.

In the given figure, ∠ONY = 50° and ∠OMY = 15°. Then the value of the ∠MON is

ক
60°
খ
70°
গ
55°
ঘ
65°

ব্যাখ্যা

Question: In the given figure, ∠ONY = 50° and ∠OMY = 15°. Then the value of the ∠MON is

Solution:
ATQ,
OM = OY = ON
∴ In ΔOMY
∠OMY = ∠OYM = 15°
∴ ∠MOY = 180° - 15° - 15°
∠MOY = 150°
In ΔONY
∠ONY = ∠OYN = 50°
∴ ∠NOY = 180° - 50° - 50°
∠NOY = 80°
∴ ∠MON = 150° - 80°
∠MON = 70°

১৫,৩৭৯.

An unbiased die is tossed.Find the probability of getting a multiple of 3.

ক
ক) 1/3
খ
খ) 1/2
গ
গ) 3/4
ঘ
ঘ) 3/2
ঙ
ঙ) None of the Above

ব্যাখ্যা

Here S = {1, 2, 3, 4, 5, 6}
Let E be the event of getting the multiple of 3
Then,
E = {3,6}
P(E) = n(E)/n(S)
= 2/6
= 1/3

১৫,৩৮০.

The ratio of boys and girls in a dance school is 7 ∶ 5. If, in the next session, 35 boys and 20 girls join the school, the ratio of boys and girls becomes 3 ∶ 2. How many girls are in the school now?

ক
90
খ
60
গ
65
ঘ
105
ঙ
70

ব্যাখ্যা

Question: The ratio of boys and girls in a dance school is 7 ∶ 5. If, in the next session, 35 boys and 20 girls join the school, the ratio of boys and girls becomes 3 ∶ 2. How many girls are in the school now?

Solution:
Given that,
The ratio of number of boys and girls = 7 ∶ 5
In the next session, 35 boys and 20 girls joined

Now,
Let the ratio of boys and girls be 7x ∶ 5x

According to the question,
(7x + 35) : (5x + 20) = 3 ∶ 2
⇒ (7x + 35)/(5x + 20) = 3/2
⇒ 14x + 70 = 15x + 60
⇒ 15x - 14x = 70 - 60
∴ x = 10

∴ The number of girls now = (5 × 10) + 20 = 70

∴ The number of girls in the school now is 70.

১৫,৩৮১.

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

ক
ক) 3 days
খ
খ) 4 days
গ
গ) 6 days
ঘ
ঘ) 7 days

ব্যাখ্যা

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

Solution:
Working 5 hours a day, for 8 days, A can finish the work in = (5 × 8) = 40 hours
Working 6 hours a day, for 10 days, B can finish the work in = (6 × 10) = 60 hours

both together can do in one hour = 1/40 + 1/60
= (3 + 2)/120
= 5/120
= 1/24

so, it will take them 24 hours to do the work.

hence, working 8 hours a day, they need = 24/8 = 3 days

১৫,৩৮২.

If x/a = 4, a/y = 6, a² = 9, and ab² = - 8, then x + 2y =?

ক
- 5
খ
- 13
গ
- 10
ঘ
15

ব্যাখ্যা

Question: If x/a = 4, a/y = 6, a² = 9, and ab² = - 8, then x + 2y =?

Solution:
Square rooting the given equation a² = 9 yields two solutions: a = 3 and a = - 3
In the equation ab² = - 8, b² is positive since the square of any nonzero number is positive.
Since ab² = - 8 is a negative number, a must be negative.
Hence, keep only negative solutions for a. Thus, we get a = - 3

Substituting this value of a in the given equation x/a = 4 yields
x/(- 3) = 4
∴ x = - 12

Substituting of a = - 3 in the given equation a/y = 6 yields
- 3/y = 6
∴ y = - 3/6 = - 1/2

Hence, x + 2y = - 12 + 2(- 1/2)
= - 12 - 1
= - 13

১৫,৩৮৩.

A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, then the work will be completed in?

ক
4.5 days
খ
5 days
গ
9 days
ঘ
10.28 days

ব্যাখ্যা

A can complete work in 9 days.

So, percentage of work A completed in one day = 100/9 = 11.11%.

B can complete work in 12 days.

B's one day work = 100/12 = 8.33%.
A and B together can complete = 11.11 +8.33 = 19.44% of work in one day.

Now,

Take 2 days = 1 unit of time (one day of A and one of B).
In one unit of time A and B can complete work = 19.44% work.
Total time unit they need to complete whole work = 100/(19.44) = 5.14 time unit
Thus, Total time = 5.14 time unit = 5.14 × 2 = 10.28 days.

১৫,৩৮৪.

If the nth term of an arithmetic progression is 7n + 1, then what is the common difference?

ক
5
খ
7
গ
- 6
ঘ
3

ব্যাখ্যা

Question: If the n^th term of an arithmetic progression is 7n + 1, then what is the common difference?

Solution:
The nth term of an arithmetic progression is Tn = 7n + 1
n = 1 then, T₁ = 7 × 1 + 1 = 8
n = 2 then, T₂ = 7 × 2 + 1 = 15
n = 3 then, T₃ = 7 × 3 + 1 = 22
n = 4 then, T₄ = 7 × 4 + 1 = 29
............................

Common difference,
T₂ - T₁ = 15 - 8 = 7
T₄ - T₃ = 29 - 22 = 7

∴ The common difference is 7.

১৫,৩৮৫.

If a sum of BDT 5,000 becomes BDT 6,728 in 2 years at compound interest, what is the rate of interest per annum?

ক
12%
খ
15%
গ
16%
ঘ
18%

ব্যাখ্যা

Question: If a sum of BDT 5,000 becomes BDT 6,728 in 2 years at compound interest, what is the rate of interest per annum?

Solution: Given,
A = Amount after interest = BDT 6,728
P = Principal amount = BDT 5,000
r = Rate of interest per annum
n = Time in years = 2

Thus, the rate of interest per annum is 16%.

১৫,৩৮৬.

A spherical water tank has a radius of 15 m. Find the volume of the tank.

ক
4500π cubic m
খ
1125π cubic m
গ
3375π cubic m
ঘ
9000π cubic m

ব্যাখ্যা

Question: A spherical water tank has a radius of 15 m. Find the volume of the tank.

Solution:
Let,
radius, r = 15 m
Volume spherical = (4/3) × π × r³
Volume = (4/3) × π × 15³ = 4500π cubic m

১৫,৩৮৭.

If 5 × ⁿP₃ = 4 × ^{(n + 1)}P₃, find n?

ক
ক) 10
খ
খ) 12
গ
গ) 13
ঘ
ঘ) 14

ব্যাখ্যা

Question: If 5 × ⁿP₃ = 4 × ^{(n + 1)}P₃, find n?

Solution:
5 × ⁿP₃= 4 × ^{(n + 1)}P₃
5 × n × (n - 1) × (n - 2) = 4 × (n + 1) × n × (n - 1)
Or, 5(n - 2) = 4(n + 1)
Or, 5n - 10 = 4n + 4
Or, 5n - 4n = 4 + 10
Hence, n = 14

১৫,৩৮৮.

In a party, there is enough cake for 120 adults or 200 teenagers. If 150 teenagers have already eaten the cake, how many adults can be served with the remaining cake?

ক
20 adults
খ
30 adults
গ
42 adults
ঘ
50 adults

ব্যাখ্যা

Question: In a party, there is enough cake for 120 adults or 200 teenagers. If 150 teenagers have already eaten the cake, how many adults can be served with the remaining cake?

Solution:
মোট কেকের পরিমাণ = 200 জন কিশোর (Teenagers)
ইতিমধ্যে কেক খেয়েছে = 150 জন কিশোর
অবশিষ্ট কিশোরদের জন্য কেক আছে = 200 - 150 = 50 জনের

প্রশ্নমতে,
200 জন কিশোরের কেক = 120 জন প্রাপ্তবয়স্কের সমান
∴ 1 জন কিশোরের কেক = 120/200 জন প্রাপ্তবয়স্কের সমান
∴ 50 জন কিশোরের কেক = (120 × 50)/200 জন প্রাপ্তবয়স্কের সমান
= 30 জন

∴ অবশিষ্ট কেক দিয়ে আরও 30 জন প্রাপ্তবয়স্ককে পরিবেশন করা যাবে।

১৫,৩৮৯.

Aman takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Aman can do the work alone in -

ক
ক) 6 days
খ
খ) 12 days
গ
গ) 3 days
ঘ
ঘ) 18 days

ব্যাখ্যা

Question: Aman takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Aman can do the work alone in -

Solution:
Let, Aman, Bimol, and Rafi take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively.

Now,
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, Aman takes = 6 × 3 = 18 days

১৫,৩৯০.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 7?

ক
ক) 1/20
খ
খ) 4/9
গ
গ) 2/5
ঘ
ঘ) 4/5

ব্যাখ্যা

Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 7?

Solution:
multiple of 3 = 3, 6, 9, 12, 15, 18
multiple of 7 = 7, 14

So, probability that the ticket drawn has a number which is a multiple of 3 or 7
= probability of getting multiple 3 + probability of getting multiple 7
= (6/20) + (2/20)
= (3/10) + (1/10)
= 4/10
= 2/5

১৫,৩৯১.

A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream -

ক
ক) 4.5 hr
খ
খ) 4 hr
গ
গ) 6 hr
ঘ
ঘ) 4.25 hr

ব্যাখ্যা

Speed of the boat in still water = 12 km/hr.
Speed of the stream = 4 km/hr.
Speed downstream = (12 + 4)
= 16 km/hr.
Time is taken to travel 68 km downstream
= 68/16
=17/4
= 4.25 hrs.

১৫,৩৯২.

A batsman hits boundaries 6 times out of 30 balls. Find the probability that he did not hit the boundaries.

ক
1/5
খ
2/5
গ
3/5
ঘ
4/5
ঙ
2/3

ব্যাখ্যা

No. of boundaries = 6
No. of balls = 30
No. of balls without boundaries = 30 – 6 =24
Probability of no boundary = 24/30 = 4/5

১৫,৩৯৩.

An aeroplane flies from place A to place B at the speed of 500 km/hr. On the return journey, its speed is 700 km/hr. The average speed of the aeroplane for the entire journey is -

ক
ক) 566(2/3) km/hr
খ
খ) 583(1/3) km/hr
গ
গ) 583(2/3) km/hr
ঘ
ঘ) 600 km/hr

ব্যাখ্যা

Average speed = {(2 × 500 × 700)/(500 + 700)} km/hr
= (1750/3) km/hr
= 583(1/3) km/hr.
Hence, The average speed of the aeroplane for the entire journey is 583(1/3) km/hr

১৫,৩৯৪.

If the average of 5, 11, 18, and 'x' is 14, what is the value of 'x'?

ক
ক) 20
খ
খ) 21
গ
গ) 22
ঘ
ঘ) 24

ব্যাখ্যা

Question: If the average of 5, 11, 18, and 'x' is 14, what is the value of 'x'?

Solution:
According to the question,
(5 + 11 + 18 + x) / 4 = 14
⇒ 34 + x = 56
⇒ x = 22

১৫,৩৯৫.

In the first 10 overs of a cricket game, the run rate was only 3.2 runs per over. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

ক
4
খ
4.50
গ
5.75
ঘ
6.25

ব্যাখ্যা

Question: In the first 10 overs of a cricket game, the run rate was only 3.2 runs per over. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

Solution:
Given that,
Target = 282 runs
Runs scored in first 10 overs = 10 × 3.2 = 32 runs
∴ Runs remaining = 282 - 32 = 250 runs

∴ Remaining overs = 50 - 10 = 40 overs

∴ Required run rate in the remaining 40 overs
= 250/40
= 6.25 runs per over

১৫,৩৯৬.

Rifat bought 4 apples at taka 8 and sold 4 apples at taka 6. What will be the rate of loss?

ক
ক) 15%
খ
খ) 25%
গ
গ) 20%
ঘ
ঘ) 30%

ব্যাখ্যা

4টি আপেলের ক্রয়মূল্য 8 টাকা
1টি আপেলের ক্রয়মূল্য 8/4 টাকা
= 2 টাকা

4টি আপেলের বিক্রয়মূল্য 6 টাকা
1টি আপেলের বিক্রয়মূল্য 6/4 টাকা
=1.5 টাকা
ক্ষতি = (2 - 1.5)টাকা = 0.5 টাকা

শতকরা ক্ষতি = {(.5/2) × 100}%
= 25%

১৫,৩৯৭.

The area of a triangular region is 84 sq. yards. The perpendicular drawn from its vertex to the base is 14 yards. Calculate the length of the base?

ক
12 yards
খ
14 yards
গ
16 yards
ঘ
18 yards

ব্যাখ্যা

Question: The area of a triangular region is 84 sq. yards. The perpendicular drawn from its vertex to the base is 14 yards. Calculate the length of the base?

Solution:

আমরা জানি,
ত্রিভুজের ক্ষেত্রফল = (১/২) × ভূমি × উচ্চতা
= (১/২) × ভূমি × ১৪
= ৭ × ভূমি

প্রশ্নমতে,
৭ × ভূমি = ৮৪
⇒ ভূমি = ৮৪/৭
∴ ভূমি = ১২ গজ

১৫,৩৯৮.

The banker's discount of a certain sum of money is Tk. 72 and the true discount on the same sum for the same time is Tk. 60. The sum due is:

ক
ক) 360
খ
খ) 432
গ
গ) 540
ঘ
ঘ) 1080

ব্যাখ্যা

(B.D.×T.D)/(B.D.−T.D)
= Tk (72×60/ 72−60)
= Tk. (72×60/12)
= Tk.360

১৫,৩৯৯.

What would be a compound interest accrued on an amount of Tk. 8000 at the rate of 25% per annum in 3 years?

ক
ক) Tk.5765
খ
খ) Tk.7625
গ
গ) Tk8245
ঘ
ঘ) Tk.9570

ব্যাখ্যা

Question: What would be a compound interest accrued on an amount of Tk. 8000 at the rate of 25% per annum in 3 years?

Solution:
Amount,
= 8000 × (1 + 25/100)³
= [8000 × (125/100)³]
= [8000 × (125/100) × (125/100) × (125/100)]
= [8000 × (5/4) × (5/4) × (5/4)]
= Tk.15625

Compound Interest = Tk.(15625 - 8000) = Tk.7625

১৫,৪০০.

In a hotel, the tariff for every odd dates is Tk. 1000 and for even dates is Tk. 2000. If the man paid total of Tk. 30000 in all. For how many days did he stay in the hotel given that the first day is 5th date of the month?

ক
50
খ
20
গ
40
ঘ
60
ঙ
None of these

ব্যাখ্যা

Question: In a hotel, the tariff for every odd dates is Tk. 1000 and for even dates is Tk. 2000. If the man paid total of Tk. 30000 in all. For how many days did he stay in the hotel given that the first day is 5th date of the month?

Solution:

Total tariff = 30000

So, for odd dates (5th , 7th , and so on) = 1000

And for even dates (6th , 8th and so on ) = 2000

So, the average amount of money for 2 days is Tk. 1500.

So, total amount paid = 30000

So, number of days he stayed in the hotel = 30000/1500 = 20.