Bank Math

PrepBank · পাতা ১৫৫ / ১৬১ · ১৫,৪০১–১৫,৫০০ / ১৬,১২৪

১৫,৪০১.

If today is Monday. After 57 days, it would be:

ক
Sunday
খ
Monday
গ
Tuesday
ঘ
Wednesday

ব্যাখ্যা

Question: If today is Monday. After 57 days, it would be:

Solution:
57/7 = 8 ( Remainder = 1)

It is well known that each day of the week is repeated after 7 days.
So we can say that after multiples of 7 days, the day will repeat itself as monday.
Hence after 56 days Monday will occur again.

So we calculate after after 57 days = Monday + 1day = Tuesday.

১৫,৪০২.

The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is-

ক
ক) 7
খ
খ) 29
গ
গ) 31
ঘ
ঘ) 41

ব্যাখ্যা

Let three prime numbers are x, y + 36 and y.

According to questions,
x + y + 36 + y = 100
x + 2y = 64 .................... (1)

Putting x= 2
2y + 2 = 64
x = 31

Thus, prime numbers are 31, 67 and 2.

১৫,৪০৩.

If the areas of a circle and a square are equal then the ratio of their perimeters is-

ক
ক) π : 1
খ
খ) √π : 4
গ
গ) √π : 2
ঘ
ঘ) π : 2

ব্যাখ্যা

Question: If the areas of a circle and a square are equal then the ratio of their perimeters is-

Solution:
Let the length of each side of the square = a cm and radius of the circle = r cm.
Given that
area of square = area of circle
⇒ a2=πr2
⇒a = r√π

∴ Required ratio = 2πr/4a
= 2πr/4r√π
= √π/2
= √π : 2

১৫,৪০৪.

A trader marks his goods at 40% above the cost price but allows a discount of 20% on the marked price. His profit percentage is-

ক
8%
খ
10%
গ
12%
ঘ
15%

ব্যাখ্যা

Question: A trader marks his goods at 40% above the cost price but allows a discount of 20% on the marked price. His profit percentage is-

Solution:

Let
the C.P. of the goods Tk.100

Marked price of the goods = 100 + 40% of 100
= 100 + (40 × 100)/100
= 100 + 40
= 140

S.P. of the goods = 80% of 140
= (140 × 80)/100
= 112

profit = 112 - 100 = 12 Tk.

profit percentage is = (12/100) × 100%
= 12%

১৫,৪০৫.

In a ∆ABC, AB = BC, ∠B= x° and ∠A = (2x - 20)°. Then, ∠B= ?

ক
30°
খ
40°
গ
44°
ঘ
64°
ঙ
68°

ব্যাখ্যা

Question: In a ∆ABC, AB = BC, ∠B= x° and ∠A = (2x - 20)°. Then, ∠B= ?

Solution:
AB = BC ⇒ ∠C = ∠A = (2x - 20)°.

∠A + ∠B + ∠C =180⁰
⇒ (2x - 20) + x + (2x - 20 ) = 180
⇒ 5x - 40 =180
⇒ 5x = 220
⇒ x = 44.
∴ ∠B = 44°.

১৫,৪০৬.

After the increase of price of oil by 40%, a family decided to reduce its oil consumption so that the expenditure for oil goes up by 26% only. If the total consumption of oil before the price rise was 10 kg per month, then what is the current consumption oil per month (in kg)?

ক
8
খ
8.50
গ
9
ঘ
None of these

ব্যাখ্যা

Question: After the increase of price of oil by 40%, a family decided to reduce its oil consumption so that the expenditure for oil goes up by 26% only. If the total consumption of oil before the price rise was 10 kg per month, then what is the current consumption oil per month (in kg)?

Solution:
40% বৃদ্ধিতে,

বর্তমানমূল্য 140 টাকা হলে পূর্বমূল্য 100 টাকা

বর্তমানমূল্য 1 টাকা হলে পূর্বমূল্য 100/140 টাকা

বর্তমান মূল্য 126 টাকা হলে পূর্ব মূল্য (100 × 126)/140
= 90 টাকা

এখন,
পূর্বে 100 টাকায় পাওয়া যেত 10 কেজি তেল

পূর্বে 1 টাকায় পাওয়া যেত 10/100 কেজি তেল

পূর্বে 90 টাকায় পাওয়া যেত (10 × 90)/100 = 9 কেজি তেল

অর্থাৎ, বর্তমান ব্যবহার 9 কেজি।

১৫,৪০৭.

If the arithmetic mean of 70 numbers is calculated, it is 25. If each number is increased by 5, then mean of new number is-

ক
ক) 30
খ
খ) 35
গ
গ) 40
ঘ
ঘ) 45

ব্যাখ্যা

Question: If the arithmetic mean of 70 numbers is calculated, it is 25. If each number is increased by 5, then mean of new number is-

Solution:
Sum of 70 numbers = (70 × 25) = 1750

∴ Total increase = (70 × 5) = 350

∴ Increased some = (1750 + 350) = 2100

∴ Increased average = 2100/70 = 30

১৫,৪০৮.

A bus travels the first 150 km at 75 km/h and the next 150 km at 50 km/h. What is the average speed for the whole trip?

ক
45 km/h
খ
75 km/h
গ
55 km/h
ঘ
60 km/h

ব্যাখ্যা

Question: A bus travels the first 150 km at 75 km/h and the next 150 km at 50 km/h. What is the average speed for the whole trip?

Solution:
Total distance = 150 km + 150 km = 300 km

Now,
Time for first part,
Time = 150/75 = 2 hours

And time for second part,
time = 150/50 = 3 hours

∴ Total time = 2 + 3 = 5 hours

Average speed = Total distance/Total time
= 300/5
= 60 km/h

So the average speed for the whole trip is 60 km/h.

Shortcut:
When equal distances are covered at speeds a and b,
Average speed = 2ab/(a + b)
= (2 × 75 × 50)/(75 + 50)
= 60 km/h

১৫,৪০৯.

A Teacher distributes x chocolate among 30 students but 3 students absent. For this every one get one chocolate extra. Find the value of x?

ক
180
খ
250
গ
320
ঘ
270

ব্যাখ্যা

Question: A Teacher distributes x chocolate among 30 students but 3 students absent. For this every one get one chocolate extra. Find the value of x?

Solution:
Given that,
Total students = 30
Absent students = 3
Chocolates distributed = x

Now,
Each student initially gets = x/30
Each student after 3 absent = x/27
Difference between both = 1

ATQ,
(x/27) − (x/30) = 1
⇒ x{(30 − 27)/810} = 1
⇒ x(3/810) = 1
⇒ x = 810/3
∴ x = 270

∴ The value of x = 270 chocolates

১৫,৪১০.

ক
2
খ
4
গ
295
ঘ
643

ব্যাখ্যা

Question:

Solution:

১৫,৪১১.

Rakib can do a certain work in 14 days. After half the work is done Rakib got sick and skip the work for 5 days. After he returns, he started doing the rest of the work in half of his previous efficiency. Total time to finish the work is-

ক
24 days
খ
26 days
গ
30 days
ঘ
32 days

ব্যাখ্যা

Question: Rakib can do a certain work in 14 days. After half the work is done Rakib got sick and skip the work for 5 days. After he returns, he started doing the rest of the work in half of his previous efficiency. Total time to finish the work is-

Solution:
half of the work is done in 7 days and the rate of work per day is 1/14
afte the effiency became half, work per day = 1/28
∴ half of the work will take = 28/2 = 14 days

∴ total time to do the work is = 7 + 5 + 14 days
= 26 days

১৫,৪১২.

Kuddus took a loan at simple interest rate of 6 p.c.p.a. in the first year and it increased by 1.5 p.c.p.a. every year. If he pays Tk. 8190 as interest at the end of 3 years, what was his loan amount?

ক
ক) Tk. 35400
খ
খ) Tk. 36000
গ
গ) Tk. 36800
ঘ
ঘ) Cannot be determined
ঙ
ঙ) None of these

ব্যাখ্যা

Let the loan amount be Tk. x
Then,
⇒ (6x/100)+(7.5x/100)+(9x/100) = 8190
⇒ 22.5x = 819000
⇒ x = 36400

১৫,৪১৩.

Mr. Shihab moved 3/4th of his lawn in 5/4 hours. Mr. Anik makes twice as fast and finishes the remaining job. How many minutes did Mr. Anik work?

ক
25 min
খ
20 min
গ
12.5 min
ঘ
10 min

ব্যাখ্যা

Question: Mr. Shihab moved 3/4th of his lawn in 5/4 hours. Mr. Anik makes twice as fast and finishes the remaining job. How many minutes did Mr. Anik work?

Solution:
Mr. Shihab moved 3/4th of his lawn in 5/4 hours.
Mr. Shihab completed work in (5/4) × (4/3)
= 5/3 hours

Mr. Anik makes twice as fast
Mr. Anik takes time 5/6 hours
= (5/6) × 60 min
= 50 min to finish the job

Mr. Anik takes time to finish the remaining job = 50/4 min
= 12.5 min

১৫,৪১৪.

A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

ক
Tk. 1000
খ
Tk. 1200
গ
Tk. 1500
ঘ
Tk. 2000

ব্যাখ্যা

Question: A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

Solution:
১টি বইয়ে দাম কমে ৪ টাকা
∴ ৫০টি বইয়ে দাম কমে (৫০ × ৪) টাকা
= ২০০ টাকা

সে মোট বই কিনে (৫০ + ১০) টি
= ৬০টি

১০টি বইয়ের দাম ২০০ টাকা
∴ ৬০টি বইয়ের দাম (২০০ × ৬০)/১০ টাকা
= ১২০০ টাকা

∴ তার কাছে ১২০০ টাকা আছে।

১৫,৪১৫.

A table fan is quoted for Tk.1500. Saadman pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

ক
5%
খ
8%
গ
10%
ঘ
12%

ব্যাখ্যা

Question: A table fan is quoted for Tk.1500. Saadman pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

Solution:

After first discount = 1500 - 1500 × 15%

= 1500 - 1500 × 15/100

= 1500 -225

= 1275 taka

let second discount is x%

1275 - 1275 × x/100 = 1173

⇒ 1275x/100 = 1275 - 1173 = 102

⇒ x = 102 × 100/1275

= 8

১৫,৪১৬.

A sum of tk. 427 is to be divided among A, B and C such that 3 times A's share, 4 times B's share and 7 times C's share are all equal. The share of C is:

ক
ক) 140
খ
খ) 196
গ
গ) 84
ঘ
ঘ) 240

ব্যাখ্যা

Let,
3A = 4B= 7C= x
A = x/3 , B = x/4 , C= x/7
A: B: C = x/3 : x/4 : x/7
= 28 : 21 : 12

The share of C is= (427 × 12)/ 61
= 84

১৫,৪১৭.

(? - 968) ÷ 79 × 4 = 512

ক
ক) 10185
খ
খ) 10190
গ
গ) 11080
ঘ
ঘ) 11075

ব্যাখ্যা

Question: (? - 968) ÷ 79 × 4 = 512

Solution:
ধরি,
সংখ্যাটি x
(x - 968) ÷ 79 × 4 = 512
⇒ x - 968 = (512 × 79)/4
⇒ x - 968 = 10112
⇒ x = 10112 + 968
∴ x = 11080

১৫,৪১৮.

Mr. X starts a business with Tk. 7000 and after 10 months, Mr. Y joins with Mr. X by investing a certain amount. At the end of 2 years, if 2:3 is the proportion of the profit then Mr. Y's contribution to the capital is:

ক
15000
খ
16000
গ
17000
ঘ
18000

ব্যাখ্যা

Let Mr. Y's capital be Tk. P
Mr.X's investment = Tk. 7000 for 24 months
Mr.Y's investment = Tk. P for 14 months
we know that, Profit ratio = investing ratio
According to the question,
(7000 x 24) : (P x 14) = 2 : 3
⇒ 168000 : 14P = 2 : 3
⇒ 12000 : P = 2 : 3
⇒ 12000/P = 2/3
⇒ P = (3 x 12000)/2
⇒ P = 18000.
The required answer is Tk. 18,000.

১৫,৪১৯.

A 3 digit number 4a3 is added to another 3 digit number 984 to give a 4 digit number 13b7, which is divisible by 11. Then a + b = ?

ক
15
খ
12
গ
11
ঘ
10
ঙ
.

ব্যাখ্যা

Question: A 3 digit number 4a3 is added to another 3 digit number 984 to give a 4 digit number 13b7, which is divisible by 11. Then a + b = ?

Solution:
এখানে
4a3 + 984 = 13b7
a + 8 = b

যেহেতু
13b7 সংখ্যাটি 11 দ্বারা বিভাজ্য

a + 8 = b , a = 0 হলে b = 8 সংখ্যাটি 1387 যা 11 দ্বারা বিভাজ্য নয়
a + 8 = b , a = 1 হলে b = 9 সংখ্যাটি 1397 যা 11 দ্বারা বিভাজ্য

a + b= 1 + 9 = 10

১৫,৪২০.

Which trigonometric ratio is undefined in value?

ক
sec 270°
খ
cosec 270°
গ
tan 0°
ঘ
cot 90°

ব্যাখ্যা

Question: Which trigonometric ratio is undefined in value?

Solution:
• sec 270° = 1/cos 270°
Since cos 270° = 0, we have 1/0, which is undefined (∞).

• cosec 270° = 1/sin 270°
Since sin 270° = −1, we have 1/-1 = −1, which is defined.

• tan 0° = sin 0°/cos 0° = 0/1 = 0, which is defined.

• cot 90° = cos 90°/sin 90° = 0/1 = 0, which is defined.

Therefore, the trigonometric ratio that is undefined is sec 270°.

১৫,৪২১.

It takes two pipes X and Y, running together, to fill a tank in 6 minutes. It takes X, 5 minutes less than Y to fill the tank, then what will be the time taken by Y alone to fill the tank?

ক
11 minutes
খ
15 minutes
গ
25 minutes
ঘ
19 minutes

ব্যাখ্যা

Question: It takes two pipes X and Y, running together, to fill a tank in 6 minutes. It takes X, 5 minutes less than Y to fill the tank, then what will be the time taken by Y alone to fill the tank?

Solution:
Let the time taken by pipe X to fill the tank be a minutes
Time is taken by pipe Y to fill the tank = a + 5 minutes

So,
⇒ (1/a) + {1/(a + 5)} = 1/6
⇒ (2a + 5)/a(a + 5) = 1/6
⇒ a2 + 5a - 12a - 30 = 0
⇒ a2 - 7a - 30 = 0
⇒ (a - 10)(a + 3) = 0
⇒ a = 10, - 3
∴ a = 10 ; [neglecting the negative value of a]

Thus, time taken by Y alone to fill the tank is 10 + 5 = 15 minutes

১৫,৪২২.

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is-

ক
200 m
খ
225 m
গ
245 m
ঘ
250 m

ব্যাখ্যা

Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is-

Solution:

Speed = 45 × (5/18) m/sec = 25/2 m/sec.

Time = 30 sec.

Let the length of bridge be x metres.

Then,
(130 + x)/30 = 25/2

⇒ 2(130 + x) = 750
⇒ 130 + x = 375
∴ x = 245 m.

১৫,৪২৩.

In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?

ক
ক) 40
খ
খ) 44
গ
গ) 48
ঘ
ঘ) 52

ব্যাখ্যা

Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352
=> T = 44

১৫,৪২৪.

A person crosses a 750 m long street in 5 minutes, What is his speed in km per hour?

ক
7 km/h
খ
7.5 km/h
গ
8 km/h
ঘ
9 km/h

ব্যাখ্যা

Question: A person crosses a 750 m long street in 5 minutes, What is his speed in km per hour?

Solution:
Speed = 750/(5 × 60) m/sec
= 2.5 m/sec
= 2.5 × (18/5) km/h
= 9 km/h

১৫,৪২৫.

In how many ways can 5 boys and 4 girls be seated in a row so that they sit alternately?

ক
1880
খ
2880
গ
1550
ঘ
1200

ব্যাখ্যা

Question: In how many ways can 5 boys and 4 girls be seated in a row so that they sit alternately?

Solution:
Let the arrangement be,
B G B G B G B G B

5 boys can be seated in 5! ways
4 girls can be seated in 4! ways

∴ Required number of ways
= 5! × 4!
= 120 × 24
= 2880

১৫,৪২৬.

A mixture contains juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of juice and sugar syrup in the new mixture is -

ক
1 : 7
খ
1 : 5
গ
2 : 7
ঘ
2 : 5

ব্যাখ্যা

Question: A mixture contains juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of juice and sugar syrup in the new mixture is -

Solution:
Let,
New mixture is = 12 liters
Old mixture = 12 × (1/4) = 3 liters

Added sugar syrup = 12 - 9 = 9 liters
New sugar syrup = 9 + (3/2) = 10.5 liters

Ratio of juice and sugar syrup = 1.5 : 10.5
= 15 : 105
= 1 : 7

১৫,৪২৭.

You have saved 1250 Taka by purchasing a laptop with 5% discount on it. what is the quoted price of the laptop in Taka?

ক
ক) Tk 30,000
খ
খ) Tk 35,000
গ
গ) Tk 25,000
ঘ
ঘ) None of the above

ব্যাখ্যা

প্রশ্ন: You have saved 1250 Taka by purchasing a laptop with 5% discount on it. what is the quoted price of the laptop in Taka?

সমাধান :

5% ছাড়ে
5 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/5 টাকা
1250 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 1250)/5 টাকা
= 25,000 টাকা

১৫,৪২৮.

Q. (33-56): Choose the correct answer.
In a container, there are 2 green marbles and 2 red marbles. You randomly pick the marbles. What is the probability that both of them are green?

ক
ক) 1/2
খ
খ) 1/3
গ
গ) 1/4
ঘ
ঘ) 1/6

ব্যাখ্যা

Question: In a container, there are 2 green marbles and 2 red marbles. You randomly pick the marbles. What is the probability that both of them are green?

Solution:
দুইটি সবুজ ও দুইটি লাল মার্বেল।
মোট মার্বেল = ৪ টি
এর মধ্যে একটি তুললে সবুজ হওয়ার সম্ভাবনা = ২/৪ = ১/২

একটি তুলার পর মার্বেল থাকে ৩ টি যার মধ্যে সবুজ আছে ১ টি
এই তিনটির মধ্যে একটি মার্বেল তুললে এটি সবুজ হওয়ার সম্ভাবনা = ১/৩

তাহলে দুইটি মার্বেল সবুজ হওয়ার সম্ভাবনা = (১/২)(১/৩) = ১/৬

১৫,৪২৯.

Train 1 leaves A at 8:00 AM and reaches B at 2 PM. Train 2 leaves B at 10 am and reaches A at 6 pm. Around what time do both trains meet?

ক
12 : 37
খ
02 : 19
গ
12 : 19
ঘ
02 : 17
ঙ
12 : 17

ব্যাখ্যা

Given: Time is taken by train 1 to move from A to B = 6 hours
Time is taken by train 2 to move from B to A = 8 hours
Let be assume the total distance from A to B is D
The speed of train A = D/6
The speed of train B = D/8
Distance travel by A till 10 am = 2 × (D/6) = D/3
The remaining distance = D - D/3 = 2D/3

Time taken by both train to meet
= (2D/3)/(D/6 + D/8)
= {(2D/3)/(4D + 3D)/(24)}
= (2D /3) × (24/7D)
= 16/7 hours
= (2 + 2/7) hours
= 2 hours and (2 × 60) / 7 minutes
= 2 hours and 120 / 7 minutes
= 2 hours and 120 / 7 minutes
= 2 hours and 17 minutes 1/7 minutes
= 2 hours and 17 minutes 9 seconds (approx)
∴ The required result will be (10 : 00 + 2 : 17) pm = 12 : 17 pm

১৫,৪৩০.

In how many ways can 5 balls can be chosen from 9 different balls?

ক
102
খ
110
গ
118
ঘ
126

ব্যাখ্যা

Question: In how many ways can 5 balls can be chosen from 9 different balls?

Solution:

Here,
Total number of different balls, n = 9
Chosen balls from different balls, r = 5

The number of ways 5 balls can be chosen is
= ⁿC_r=n!/r!(n - r)!
= 9!/5!(9 - 5)!
= 9!/(5! × 4!)
= (9 × 8 × 7 × 6 × 5!)/(5! × 4!)
= (9 × 8 × 7 × 6)/4!
= 3024/(4 × 3 × 2 × 1)
= 3024/24
= 126

∴ 5 balls can be chosen from 9 different balls in 126 ways.

১৫,৪৩১.

X can do a piece of work in 40 days. He works at it for 8 days and then Y finishes it in 16 days. How long will they together take to complete the work?

ক
ক) 13(1/3)days
খ
খ) 15 days
গ
গ) 20 days
ঘ
ঘ) 26 days
ঙ
ঙ) None of these

ব্যাখ্যা

Work done by X in 8 days = 1/40×8 = 1/5

Remaining work = 1−1/5 = 4/5

Now, 4/5 work is done by Y in 16 days
Whole work will be done by Y in = 16×5/4 = 20 days
∴ X's 1 day's work = 1/40

∴ Y's 1 day's work = 1/20

(X + Y)'s 1 day's work
=1/40 + 1/20
=3/40

Hence, X and Y will together complete the work in
= 40/3
= 13(1/3) days

১৫,৪৩২.

By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

ক
55000
খ
60000
গ
57500
ঘ
58000

ব্যাখ্যা

Question: By selling a property for Tk. 45000 a person incurs a loss of 10%. Find the selling price to gain the profit of 15%?

Solution:
CP = SP × 100/(100 - L%)
SP = CP × (100 + P%)/100
Here SP → Selling Price, CP → Cost Price, L% → Loss%, P% → Profit%

Calculation:
CP = 45000 × 100/(100 - 10)
⇒ CP = 45000 × (10/9)
= 50000

New Selling price = CP × (100 + 15)/100
⇒ New Selling price = 50000 × (115/100)
= 57500

∴ He should sell the land for Tk. 57500 to gain 15%

১৫,৪৩৩.

(3/4) : (1/2) :: 9y : ?

ক
ক) 3y
খ
খ) 6y
গ
গ) 9y
ঘ
ঘ) 27y

ব্যাখ্যা

Question: (3/4) : (1/2) :: 9y : ?

Solution:
(3/4) : (1/2) :: 9y : p
⇒ (3/4) / (1/2) = 9y / p
⇒ 3/2 = 9y/p
⇒ p = 9y × 2/3
∴ p = 6y

১৫,৪৩৪.

What is the least multiple of 11 which leaves a remainder of 5 when divided by 6, 8, and 10?

ক
605
খ
585
গ
550
ঘ
525

ব্যাখ্যা

Question: What is the least multiple of 11 which leaves a remainder of 5 when divided by 6, 8, and 10?

Solution:
L.C.M. of 6, 8, and 10 is 120.
Let required number be 120k + 5 which is multiple of 11.

Least value of k for which (120k + 5) is divisible by 11 is k = 5 .
Required number = (120 × 5) + 5 = 605

১৫,৪৩৫.

If 35% of a certain number is 49, then find the number-

ক
69
খ
115
গ
91
ঘ
140

ব্যাখ্যা

Question: If 35% of a certain number is 49, then find the number-

Solution:
Let the number be x.
Then,
⇒ 35% of x = 49
⇒ (35/100) × x = 49
⇒ 7x/20 = 49
⇒ x = (20 × 49)/7
∴ x = 140

১৫,৪৩৬.

The quadratic equation 2x² - √5x + 1 = 0 has-

ক
no real roots
খ
two distinct real roots
গ
two equal real roots
ঘ
more than 2 real roots

ব্যাখ্যা

Question: The quadratic equation 2x² - √5x + 1 = 0 has-

Solution:
Given,
2x² - √5x + 1 = 0Comparing with the standard form of a quadratic equation,
a = 2, b = - √5, c = 1

Now,
b² - 4ac = (- √5)² - 4(2)(1)
= 5 - 8
= - 3 < 0

Therefore, the given equation has no real roots.

১৫,৪৩৭.

What will come at the place of question mark?
4, 7, 12, 19, 28, ?

ক
40
খ
30
গ
38
ঘ
49
ঙ
39

ব্যাখ্যা

Question: What will come at the place of question mark?
4, 7, 12, 19, 28, ?

Solution:
7 - 4 = 3
12 - 7 =5
19 - 12 = 7
28 - 19 = 9

Difference increases by 2 each time.

So, next difference is = 9 + 2 = 11

∴ Next term = 28 + 11 = 39

১৫,৪৩৮.

The difference between a two-digit number and the number obtained by changing the positions of its digits is 36. What is the difference between the two digits of that number?

ক
3
খ
4
গ
9
ঘ
Cannot be determined.

ব্যাখ্যা

Question: The difference between a two-digit number and the number obtained by changing the positions of its digits is 36. What is the difference between the two digits of that number?

Solution:
The ten's digit is x and the unit's digit is y.

As per the question:
(10x + y) - (10y + x) = 36
⇒ 10x + y - 10y - x = 36
⇒ 9x - 9y = 36
⇒ 9(x - y) = 36
∴ x - y = 4

১৫,৪৩৯.

The one - third of the complementary angle to 60°is -

ক
ক) 150°
খ
খ) 100°
গ
গ) 40°
ঘ
ঘ) 10°

ব্যাখ্যা

60° কোণের পূরক কোণ = 90° - 60° [দুইটি কোণের সমষ্টি ৯০° বা এক সমকোণ হলে কোণ দুইটির একটিকে অপরটির পূরক কোণ বলে।]
= 30°
30° এর 1/3 = 10°.
Answer: 10°.

১৫,৪৪০.

If cos²θ - sin²θ = 1/2, then 2 + cos⁴θ - sin⁴θ = ?

ক
ক) 1/2
খ
খ) 5/2
গ
গ) 3/2
ঘ
ঘ) 0

ব্যাখ্যা

Question: If cos²θ - sin²θ = 1/2, then 2 + cos⁴θ - sin⁴θ = ?

Solution:
আমরা জানি,
cos²θ + sin²θ = 1

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

1 + cos⁴θ - sin⁴θ = 2 + (1/2) = (4 + 1)/2 = 5/2

১৫,৪৪১.

A square and a circle have the same perimeter. The side of the length of square is 44 cm, what is the area of the circle?

ক
2464 sq. cm.
খ
1864 sq. cm.
গ
375 sq. cm.
ঘ
1456 sq. cm.

ব্যাখ্যা

Question: A square and a circle have the same perimeter. The side of the length of square is 44 cm, what is the area of the circle?

Solution:
Perimeter of the square = 4 × side length
= 4 × 44 cm
= 176 cm

As per the question, the square and circle have the same perimeter.
∴ Circumference of the circle = 176 cm
We know that, Circumference of the circle = 2πr
∴ 2πr = 176
⇒ r = 176 / (2π)
⇒ r = 88 / π
⇒ r = 88 / (22/7)
⇒ r = 88 × 7 / 22
⇒ r = 4 × 7
⇒ r = 28 cm

Area of the circle = πr²
= (22/7) × 28²
= (22/7) × (28 × 28)
= 22 × 4 × 28
= 2464 sq. cm

∴ The area of the circle is 2464 sq. cm.

১৫,৪৪২.

A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

ক
ক) 3 sec
খ
খ) 5 sec
গ
গ) 6 sec
ঘ
ঘ) 8 sec

ব্যাখ্যা

Question: A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

Solution:
Relative speed = 60 km/hr + 6 km/hr
= 66 km/hr
= 66 ×1000/3600 m/sec
= 66 × 5/18 m/sec
= 55/3 m/sec

time needed = 110 /55/3 sec
= 110 × 3/55 sec
= 6 sec

১৫,৪৪৩.

The length of two parallel sides of a trapezium are 30 cm and 60 cm respectively, and the distance between the parallel sides is 8 cm. Find the area of the trapezium.

ক
262 cm²
খ
160 cm²
গ
360 cm²
ঘ
266 cm²

ব্যাখ্যা

Question: The length of two parallel sides of a trapezium are 30 cm and 60 cm respectively, and the distance between the parallel sides is 8 cm. Find the area of the trapezium.
(একটি ট্রাপেজিয়ামের দুইটি সমান্তরাল পার্শ্বের দৈর্ঘ্য যথাক্রমে ৩০ সেমি ও ৬০ সেমি, এবং পার্শ্বগুলোর মধ্যে দুরত্ব ৮ সেমি। ট্রাপেজিয়ামের ক্ষেত্রফল বের করুন।)

Solution:
ট্রাপেজিয়ামের ক্ষেত্রফল = (1/2) × (সমান্তরাল বাহুগুলোর যোগফল) × (সমান্তরাল বাহুগুলোর মধ্যবর্তী দূরত্ব)
= (1/2) × (30 + 60) × 8
= (1/2) × 90 × 8
= 360 cm²

∴ ট্রাপেজিয়ামের ক্ষেত্রফল = 360 cm²

১৫,৪৪৪.

In an essay competition, a winner gets a prize of Tk 100 and a participant who does not win gets a prize of Tk 25. The total prize money distributed is Tk 3,000. Find the number of winners, if the total number of participants is 63.

ক
ক) 15
খ
খ) 17
গ
গ) 19
ঘ
ঘ) 21

ব্যাখ্যা

Question: In an essay competition, a winner gets a prize of Tk 100 and a participant who does not win gets a prize of Tk 25. The total prize money distributed is Tk 3,000. Find the number of winners, if the total number of participants is 63.

Solution:
ধরি
winners এর সংখ্যা = x জন
non-winners এর সংখ্যা = 63 - x জন

প্রশ্নমতে
25(63 - x) + 100x = 3000
⇒ 1575 - 25x + 100x = 3000
⇒ 75x = 3000 - 1575
⇒ 75x = 1425
⇒ x = 1425/75
x = 19

১৫,৪৪৫.

Three rectangular fields having area 60 m², 84 mm² and 108 mm² are to be divided into identical rectangular flower beds, each having length 6m. Find the breadth of each flower bed-

ক
ক) 3m
খ
খ) 5m
গ
গ) 7m
ঘ
ঘ) 9m
ঙ
ঙ) None of the above

ব্যাখ্যা

We need to divide each large field into smaller flower beds such that the area of each bed is same.

So, we find the HCF of the larger fields that gives us the area of the smaller field.

HCF (60, 84, 108) = 12

Now, this HCF is the area (in m²) of each flower bed.

Also, area of a rectangular field = Length x Breadth

=> 12 = 6 x Breadth

=> Breadth = 2m

Hence, each flower bed would be 2m wide.

১৫,৪৪৬.

A farmer had 17 cows. All but 9 died. How many were left alive?

ক
ক) 8
খ
খ) 9
গ
গ) 16
ঘ
ঘ) 17

ব্যাখ্যা

Answer is given in the question. All but 9 died means except 9 all others died. So there are 9 alive cows.

১৫,৪৪৭.

A boat covers 143 km upstream in 13 hours and the same distance downstream in 11 hours. What is the speed (in km/hr) of the boat in still (without stream) water?

ক
10 km/hr
খ
12 km/hr
গ
14 km/hr
ঘ
8 km/hr

ব্যাখ্যা

Question: A boat covers 143 km upstream in 13 hours and the same distance downstream in 11 hours. What is the speed (in km/hr) of the boat in still (without stream) water?

Solution:
Let,
the speed (in km/hr) of the boat in still (without stream) water is x km/hr and speed of stream is y km/hr
Now
143/(x - y) = 13
⇒ 13 (x - y) = 143
⇒ x - y = 11..........(1)

143/(x + y) = 11
⇒ 11 (x + y) = 143
⇒ x + y = 13..........(2)
(1) + (2) ⇒
x - y + x + y = 13 + 11
⇒ 2x = 24
∴ x = 12 km/hr

১৫,৪৪৮.

A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction -

ক
A neither losses nor gains
খ
A makes a profit of 11%
গ
A makes a profit of 20%
ঘ
B loses 20%

ব্যাখ্যা

Let CP was 100 for A originally
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110
Now, B sells it A again with loss 10%
Now, CP for A this time = 110 - 10% of 110 = 99
A makes Profit = 110 - 99 = 11

%profit for A = (11 × 100)/100 = 11%

১৫,৪৪৯.

A tank is filled in 5 hours by three pipes A, B, and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
ক) 20 hours
খ
খ) 25 hours
গ
গ) 35 hours
ঘ
ঘ) None of these

ব্যাখ্যা

Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank
∴ 1/x + 2/x + 4/x = 1/5
7/x = 1/5
x = 35 hours.

১৫,৪৫০.

Peace : Chaos :: Creation : ?

ক
ক) Build
খ
খ) Construction
গ
গ) Destruction
ঘ
ঘ) Manufacture

ব্যাখ্যা

As opposite meaning of peace is chaos similarly opposite meaning of creation is destruction.

১৫,৪৫১.

The difference between two numbers is 5 and the difference between their squares 65. What is the larger number?

ক
ক) 13
খ
খ) 11
গ
গ) 8
ঘ
ঘ) 9

ব্যাখ্যা

Let the larger number is = a
Then, the other number is = a - 5
ATQ,
a² – (a - 5)² = 65
⇒ a² – a² + 10a – 25 = 65
⇒ 10a = 65 + 25 = 90
⇒ a = 90/10 = 9

১৫,৪৫২.

A sum of money is divided among A, B, C and D in the ratio of 3 : 4 : 9 : 10 respectively. If the share of C is Tk. 2,530 more than the share of B, then what is the total amount of money of A and D together?

ক
ক) Tk. 6,078
খ
খ) Tk. 6,578
গ
গ) Tk. 6,478
ঘ
ঘ) Tk. 6,678

ব্যাখ্যা

Let
the shares of A, B, C and D be Tk. 3x, 4x, 9x and 10x respectively.
Now
= 9x - 4x = 2,530
⇒ 5x = 2,530
⇒ x = 2530/5
⇒ x = 506

∴ Required Amount
= 3x + 10x
= 13x
= Tk. (13 × 506)
= Tk. 6,578

১৫,৪৫৩.

If Jack walked 5 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?

ক
4
খ
4.5
গ
6
ঘ
6.25

ব্যাখ্যা

Question: If Jack walked 5 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?

Solution:
Speed = Distance/Time

Distance = 5 miles
Time = 1hr 15 minutes = 1.25 hrs

∴ Speed = 5/1.25
= 4 miles/hr

১৫,৪৫৪.

In a box, there are 5 red, 9 blue, and 10 green balls. One ball is picked randomly. What is the probability that it is neither red nor green?

ক
5/8
খ
3/8
গ
2/5
ঘ
3/5

ব্যাখ্যা

Question: In a box, there are 5 red, 9 blue, and 10 green balls. One ball is picked randomly. What is the probability that it is neither red nor green?

Solution:
Total number of balls = 5 + 9 + 10 = 24

Let, E be the event that the ball is neither red nor green = the event that the ball is blue.
∴ n(E) = 9

∴ Probability = Number of favorable outcomes/Total outcomes
= 9/24
= 3/8

১৫,৪৫৫.

There are 35 people in a room. If each person shakes hands with every other person exactly once, how many handshakes will take place in total?

ক
295
খ
495
গ
595
ঘ
195
ঙ
None

ব্যাখ্যা

Question: There are 35 people in a room. If each person shakes hands with every other person exactly once, how many handshakes will take place in total?

Solution:
Total handshakes = ³⁵C₂
= (35 × 34)/2
= 595

∴ Total handshakes = 595

১৫,৪৫৬.

The fraction equivalent to (4/11)% is

ক
ক) 1/150
খ
খ) 1/280
গ
গ) 1/275
ঘ
ঘ) 1/250

ব্যাখ্যা

(4/11)% = (4/11) × (1/100)
= 1/275

১৫,৪৫৭.

The largest prime factor of (2⁴)² − 1 is -

ক
ক) 3
খ
খ) 5
গ
গ) 17
ঘ
ঘ) 19

ব্যাখ্যা

(2⁴)² − 1
= 2⁸ - 1
= 256 - 1
= 255
= 3 × 5 × 17

So, the largest prime factor is 17

১৫,৪৫৮.

The value of

ক
0
খ
1
গ
Undefined
ঘ
Infinity

ব্যাখ্যা

Question: The value of

Solution:

১৫,৪৫৯.

The ratio of boys to girls in a class is 2:5. If 2 boys leave and 4 girls join the class, the ratio of boys to the girls becomes 1:4. Originally, how many girls were in the class?

ক
16
খ
20
গ
21
ঘ
24
ঙ
None of these

ব্যাখ্যা

Boys = 2X
Girls = 5X
ATQ,
(2X - 2)/(5X + 4) = 1/4
or, 8X - 8 = 5X + 4
or, 3X = 12
or, X = 4
so, girls = 5 × 4 = 20.

১৫,৪৬০.

Rita bought a television set with a 20% discount on the labelled price. She made a profit of Tk. 800 by selling it for Tk. 16800. The labelled price of the set was -

ক
ক) Tk. 10,000
খ
খ) Tk. 20,000
গ
গ) Tk. 20,800
ঘ
ঘ) Tk. 24,000

ব্যাখ্যা

Let the labeled price of TV = Tk. R
∴ SP of the TV = [R x (100 - 20)] / 100
= Tk. 4R/5
But 16,800 - 800 = 4R/5
∴ x = (16,000 x 5)/4
= Tk. 20,000

১৫,৪৬১.

∠A and ∠B are supplementary angle to each other. If ∠A = 40° + 3x and ∠B = 2x, what is the value of ∠B?

ক
42°
খ
56°
গ
64°
ঘ
70°

ব্যাখ্যা

Question: ∠A and ∠B are supplementary angle to each other. If ∠A = 40° + 3x and ∠B = 2x, what is the value of ∠B?

Solution:
We are given:
∠A = 40° + 3x
∠B = 2x

Since ∠A and ∠B are supplementary:
∠A + ∠B = 180°
⇒ (40° + 3x) + 2x = 180°
⇒ 40° + 5x = 180°
⇒ 5x = 180° - 40°
∴ 5x = 140°
∴ x = 28°

∴ ∠B = 2x = 2 × 28° = 56°

১৫,৪৬২.

If log⁡_m243 + log⁡_m81 = 9, find the value of m.

ক
- 5
খ
3
গ
4
ঘ
6

ব্যাখ্যা

Question: If log⁡_m243 + log⁡_m81 = 9, find the value of m.

Solution:
Given that,
log⁡_m243 + log⁡_m81 = 9
⇒ log⁡_m(243 × 81) = 9
⇒ log⁡_m19683 = 9
⇒ m⁹ = 19683
⇒ m⁹ = 3⁹
∴ m = 3

১৫,৪৬৩.

A merchant mixes two types of sugar costing Tk. 250/kg and Tk. 350/kg in the ratio 3:2. If he sells the mixture at Tk. 360/kg, what is his profit percentage?

ক
5%
খ
24%
গ
20%
ঘ
15%

ব্যাখ্যা

Question: A merchant mixes two types of sugar costing Tk. 250/kg and Tk. 350/kg in the ratio 3:2. If he sells the mixture at Tk. 360/kg, what is his profit percentage?

Solution:
Cost of first variety = 250 Taka/kg
Cost of second variety = 350 Taka/kg
Ratio = 3:2

Cost price of mixture = {(3×250) +(2×350)}/(3+2)
= 1450/5
= 290 Taka/kg

Profit = Selling price - Cost price
= 360 - 290
= 70 Taka/kg

Profit percentage = (70/290) × 100%
= 24.13% ≈ 24%

১৫,৪৬৪.

A merchant buys two articles for Taka 1400. He sells one of them at a profit of 20% and the others at a loss of 8%. He makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

ক
ক) 1000
খ
খ) 960
গ
গ) 880
ঘ
ঘ) 920

ব্যাখ্যা

মনে করি,
loss এ sell করা article এর cost price x
profit এ sell করা article এর cost (1400 - x)
এখন, overall কোন profit বা loss নেই,
অর্থ্যাৎ,
দুই article এর profit এবং loss equal.
8x/100 = 20/100(1400 - x)
⇒ 8x = 28000 - 20x
⇒ 28x = 28000
⇒ x = 28000/28
⇒ x = 1000.
অর্থ্যাৎ, Selling price of the article sold at 8% loss = 920 Tk.

১৫,৪৬৫.

If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160

Discount (%) = (160/800) ×100%
= 20%

∴ Therefore, the discount percentage is calculated as 20%.

১৫,৪৬৬.

Evaluate √(41 - √(21 + √(19 - √(9))))

ক
ক) 6
খ
খ) 5
গ
গ) 3
ঘ
ঘ) 6.4

ব্যাখ্যা

√(41 - √(21 + √(19 - √(9))))
= √(41 - √(21 + √(19 - 3)))
= √(41 - √(21 + √(16)))
= √(41 - √(21 + 4))
= √(41 - 5)
= 6

১৫,৪৬৭.

A boat moves downstream at the rate of one km in 5 minutes and upstream at the rate of 4 km an hour. What is the velocity of the current?

ক
ক) 2 km/hr
খ
খ) 4 km/hr
গ
গ) 1 km/hr
ঘ
ঘ) 3 km/hr

ব্যাখ্যা

Speed downstream = 1/(5/60)
= 60/5
= 12 km/hr
Speed upstream = 4/1
= 4 km/hr
velocity of the current = 1/2(12 - 4)
= (1/2) × 8
= 4 km/hr.

১৫,৪৬৮.

Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

ক
14 kmph
খ
12 kmph
গ
11 kmph
ঘ
8 kmph
ঙ
None of these

ব্যাখ্যা

Question: Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

Solution:
Let the distance travelled by x km.
Then,
x/10 - x/15 = 2
⇒ 3x - 2x = 60
∴ x = 60 km.

Time taken to travel 60 km at 10 km/hr = 60/10 hrs = 6 hrs.
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

∴ Required speed = 60/5 kmph. = 12 kmph.

১৫,৪৬৯.

If 4^{2x + 1} = 32, then x = ?

ক
ক) 2
খ
খ) 3
গ
গ) 3/4
ঘ
ঘ) 4/3

ব্যাখ্যা

প্রশ্ন: If 4^{2x + 1}= 32, then x = ?

সমাধান:
4^{2x + 1} = 32
(2²)^{2x + 1} = 32
2^{4x + 2} = 2⁵
4x + 2 = 5
4x = 5 - 2
4x = 3
x = 3/4

১৫,৪৭০.

Harun sells a book to Kabil at a profit of 15%, Kabil sells that book to Rasel for Tk.1012 and makes a profit of 10%. At what cost did Harun purchase the book?

ক
ক) Tk.800
খ
খ) Tk.920
গ
গ) Tk.850
ঘ
ঘ) Tk.782

ব্যাখ্যা

প্রশ্ন: Harun sells a book to Kabil at a profit of 15%, Kabil sells that book to Rasel for Tk.1012 and makes a profit of 10%. At what cost did Harun purchase the book?

সমাধান:
১০% লাভে,
কাবিলের বিক্রয়মূল্য ১১০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ কাবিলের বিক্রয়মূল্য ১০১২ টাকা হলে ক্রয়মূল্য (১০০ × ১০১২)/১১০ টাকা
= ৯২০ টাকা

১৫% লাভে,
হারুনের বিক্রয়মূল্য ১১৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ হারুনের বিক্রয়মূল্য ৯২০ টাকা হলে ক্রয়মূল্য (১০০ × ৯২০)/১১৫ টাকা
= ৮০০ টাকা

১৫,৪৭১.

In a mixture with a 5:2 ratio of milk to water, adding 14 liters of water makes the ratio 5:4. What is the original quantity of milk in the mixture?

ক
30 liters
খ
25 liters
গ
15 liters
ঘ
35 liters
ঙ
None

ব্যাখ্যা

Question: In a mixture with a 5:2 ratio of milk to water, adding 14 liters of water makes the ratio 5:4. What is the original quantity of milk in the mixture?

Solution:
The initial ratio is 5 : 2.
Let ‘b’ be the common ratio.

The initial quantity of milk = 5b liters
The initial quantity of water = 2b liters

Final quantity of milk = 5b liters
Final quantity of water = 2b + 14 liters

Final ratio = 5b : (2b + 14) = 5 : 4

⇒ 20b = 10b + 70
⇒ 10b = 70
⇒ b = 7

Therefore, the initial quantity of milk in the mixture = 5b
= 5 × 7
= 35 liters

১৫,৪৭২.

How many "7" will you pass on the way when you count from 1 to 100?

ক
ক) 18
খ
খ) 19
গ
গ) 20
ঘ
ঘ) 21

ব্যাখ্যা

Just count numbers with 7's: 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77(doubled!), 78, 79, 87, 97.
The answer is 20 7's.

১৫,৪৭৩.

What is the least number which when tripled is exactly divisible by 10, 12, 15, and 18?

ক
80
খ
180
গ
40
ঘ
60

ব্যাখ্যা

Question: What is the least number which when tripled is exactly divisible by 10, 12, 15, and 18?

Solution:
Let the number be x.
tripled the number is 3x.

10 = 2 × 5
12 = 2 × 2 × 3
15 = 3 × 5
18 = 2 × 3 × 3

∴ LCM = 2 × 2 × 3 × 3 × 5
= 180

∴ x = 180/3 = 60

১৫,৪৭৪.

The sum of the first 16 terms of an Arithmetic Progression(AP) whose first term and third term are 5 and 15 respectively is-

ক
640
খ
720
গ
680
ঘ
600
ঙ
700

ব্যাখ্যা

Question: The sum of the first 16 terms of an Arithmetic Progression(AP) whose first term and third term are 5 and 15 respectively is-

Solution:
1^st term = 5
3^rd term =15
∴ 5 + d + d = 15
⇒ 2d = 10
∴ d = 5

16^th term = a + 15d
= 5 + 15 × 5
= 80

∴ The sum of the first 16 terms = (n/2)[2a + (n - 1)d]
= (16/2)[2 × 5 + (16 - 1)5]
= 8 × (10 + 75)
= 8 × 85
= 680

১৫,৪৭৫.

If the number 5 ⋆ 2 is divisible by 6, then ⋆ = ?

ক
ক) 3
খ
খ) 6
গ
গ) 7
ঘ
ঘ) 2

ব্যাখ্যা

প্রশ্নে উল্লেখিত (⋆) এর স্থানে একমাত্র 2 বসালেই সংখ্যাটি হবে (522) যা 6 দ্বারা বিভাজ্য হয়।

১৫,৪৭৬.

The value of [(0.01)² + (0.22)² + (0.333)²]/ [(0.001)² + (0.022)² + (0.0333)²] is-

ক
1/10
খ
10
গ
100
ঘ
1000

ব্যাখ্যা

Question: The value of [(0.01)² + (0.22)² + (0.333)²]/ [(0.001)² + (0.022)² + (0.0333)²] is-

Solution:
The value of [(0.01)² + (0.22)² + (0.333)²]/ [(0.001)² + (0.022)² + (0.0333)²]
We can write the expression as [(0.01)² + (0.22)² + (0.333)²]/ [(0.01/10)² + (0.22/10)² + (0.333/10)²]
= [(0.01)² + (0.22)² + (0.333)²] / [{(0.01)² + (0.22)² + (0.333)²} × (1/100)]
= [(0.01)² + (0.22)² + (0.333)²] × [100/{(0.01)² + (0.22)² + (0.333)²}]

Hence, numerator and denominator will cancel each other, and the remaining value will be 100.

১৫,৪৭৭.

If 7 meters of cloth cost Tk. 140, what is the cost of 3 meters of cloth?

ক
Tk. 45
খ
Tk. 36
গ
Tk. 60
ঘ
Tk. 90

ব্যাখ্যা

Question: If 7 meters of cloth cost Tk. 140, what is the cost of 3 meters of cloth?

Solution:
We know the cost of 7 meters of cloth Tk. 140
Cost per meter = Total cost / Number of meters = 140/7 meters = Tk. 20 per meter.

Cost of 3 meters = Unit value (cost per meter) × Number of meters
= 20 × 3
= 60

১৫,৪৭৮.

What is the probability that an integer selected at random from those between 20 and 100 inclusive is a multiple of 15?

ক
5/81
খ
3/78
গ
7/79
ঘ
4/83

ব্যাখ্যা

Multiple of 15 from 20 to 100 is 30, 45, 60, 75, 90 = 5
∴ Probability = 5/81

১৫,৪৭৯.

A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 12 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

ক
ক) 8.2 hrs
খ
খ) 7.2 hrs
গ
গ) 7 hrs
ঘ
ঘ) 4 hrs

ব্যাখ্যা

Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 12 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

Solution:
চৌবাচ্চাটি 1 ঘণ্টায় পূর্ণ হয় =(1/3) - (1/12) অংশ
= (4 - 1)/12 অংশ
= 3/12

= 1/4
চৌবাচ্চাটির 1/4 অংশ পূর্ণ হয় = 1 ঘণ্টায়
চৌবাচ্চাটির 1 অংশ পূর্ণ হয় = (1 × 4)/1 ঘণ্টায়
=4 ঘণ্টায়

১৫,৪৮০.

The average mark obtained by Ratul in 3 papers is 52 and in the fourth paper, he scored 60 marks. Find the new average of marks scored by Ratul.

ক
53.5
খ
54
গ
52
ঘ
72

ব্যাখ্যা

Question: The average mark obtained by Ratul in 3 papers is 52 and in the fourth paper, he scored 60 marks. Find the new average of marks scored by Ratul.

Solution:
The average mark obtained by Ratul in 3 papers is 52
total marks = 3 × 52 = 156

New average = (156 + 60)/4
= 216/4
= 54

১৫,৪৮১.

An individual is cycling at a speed of 25 km per hour. He catches his predecessor, who started earlier, in two hours. What is the speed of his predecessor, who started three hours earlier?

ক
9 km/hr
খ
11 km/hr
গ
10 km/hr
ঘ
12 km/hr

ব্যাখ্যা

Question: An individual is cycling at a speed of 25 km per hour. He catches his predecessor, who started earlier, in two hours. What is the speed of his predecessor, who started three hours earlier?

Solution:
The distance covered in two hours,
= 2 × 25 = 50 km
Time taken by first individual = (3h + 2h) = 5h
Then, the speed of the predecessor,
= 50/5 = 10 km/hr

১৫,৪৮২.

A man swimming in a stream which flows (3/2) km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

ক
(9/2) km/hr
খ
(11/2) km/hr
গ
(15/2) km/hr
ঘ
(7/2) km/hr

ব্যাখ্যা

Question: A man swimming in a stream which flows (3/2) km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

Solution:
Let the rate of his swim x km/h
When he swim with the flow then speed =(x + 3/2) km/h
∴ S₁ = (x + 3/2) × t
When he swim against the flow stream then speed = (x - 3/2) km/h
∴ S₂ = (x - 32) × t

According to the question,
S₁ = 2S₂⇒ (x + 3/2)t = 2(x - 3/2)t
⇒ (2x + 3)/2 = 2x - 3
⇒ 2x + 3 = 4x - 6
⇒ 9 = 2x
⇒ x = 9/2 km/hr

১৫,৪৮৩.

35 men can complete a work in 15 days. Five days after they started working,15 more men joined them. How man days will they now take to complete the remaining work?

ক
ক) 7 days
খ
খ) 9 days
গ
গ) 12 days
ঘ
ঘ) 15 days

ব্যাখ্যা

Question: 35 men can complete a work in 15 days. Five days after they started working, 15 more men joined them. How man days will they now take to complete the remaining work?

Solution:
After working 5 days, days left = 15 - 5 = 10 dyas
and now total man = 35 + 15 = 50

35 man needed 10 days
1 man needed (10 × 35) days
50 man needed (10 × 35)/50 days = 7 days

১৫,৪৮৪.

There are 4 women and 4 men sitting in a waiting room for a job interview. If two of the applicants are selected at random, what is the probability that both will be women?

ক
ক) 1/2
খ
খ) 3/7
গ
গ) 3/4
ঘ
ঘ) 3/14

ব্যাখ্যা

৮ জনের মধ্যে ৪ জন মহিলা ও ৪ জন পুরুষ।
দুইজনকে দৈবভাবে নিলে মহিলা আসার সম্ভাবনা বের করতে হবে।
প্রথম ১ জন নিলে মহিলা আসার সম্ভাবনা = মোট মহিলা/মোট সংখ্যা
= ৪/৮
= ১/২
তখন মোট সংখ্যা থাকবে ৭ জন ও মহিলা থাকবে ৩ জন।
তারপর ১ জন নিলে মহিলা আসার সম্ভাবনা = ৩/৭।
তাহলে দুইজন নিলে একত্রে সম্ভাবনা হবে = ১/২ × ৩/৭
= ৩/১৪।

১৫,৪৮৫.

The banker’s discount on a sum of money for 1(1/2) years is Tk. 558 and the true discount on the same sum for 2 years is Tk 600. The rate percent is -

ক
ক) 10%
খ
খ) 13%
গ
গ) 12%
ঘ
ঘ) 15%

ব্যাখ্যা

Banker's Discount for 3/2 years = Tk. 558
Banker's Discount for 2 years = Tk. {558 × (2/3) × 2}
= Tk. 744
True Discount for 2 years = Tk. 600
∴ Sum = {(B.D × T.D)/(B.D - T.D)}
= Tk. {(744 × 600)/(744 - 600)
= Tk. (744 × 600)/144
= TK. 3100
Thus, Tk. 744 is Simple Interest on Tk. 3100 for 2 years
∴ Rate = {(100 × 744)/(3100 × 2)}%
= 12%

১৫,৪৮৬.

If x + y = a and x - y = b, then 2xy =

ক
ক) (b² - a²)/2
খ
খ) (a² - b²)/2
গ
গ) (a - b)/2
ঘ
ঘ) ab/2

ব্যাখ্যা

দেওয়া আছে,
x + y = a
x- y = b

আমরা জানি
4xy = (x + y)² - (x - y)²
2xy = (a² - b²)/2

১৫,৪৮৭.

Pipe A can fill the tank 3 times faster in comparison to pipe B. It takes 36 minutes for pipe A and B to fill the tank together. How much time will pipe A alone take to fill the tank?

ক
72 minutes
খ
48 minutes
গ
134 minutes
ঘ
144 minutes

ব্যাখ্যা

Let the time taken by pipe B be x minutes
So, the time taken by pipe A = x/3 minutes

Thus, 1/x + 3/x = 1/36
⇒ 4/x = 1/36
⇒ x = 4×36
⇒ x = 144 minutes

the time taken by pipe A = 144/3 minutes = 48

১৫,৪৮৮.

If in ΔABC, AB = 6cm, BC = 12cm and CA = 6√3cm, then the measure of ∠A is-

ক
90°
খ
75°
গ
60°
ঘ
180°

ব্যাখ্যা

Question: If in ΔABC, AB = 6cm, BC = 12cm and CA = 6√3cm, then the measure of ∠A is-

Solution:

We know,
c²= a² + b²
= 6² + (6√3)² = 36 + 108 = 144 = 12²

So, triangle ABC is a right-angled triangle at A.
∠A = 90°

১৫,৪৮৯.

If 2^x - 2^{x - 1} = 4, the value of x^x is-

ক
ক) 1
খ
খ) 4
গ
গ) 27
ঘ
ঘ) 16

ব্যাখ্যা

Question: If 2^x - 2^{x - 1} = 4, the value of x^x is-

Solution:
2^x - 2^{x - 1} = 4
2^x- 2^x.2^{- 1} = 4
2^x - 2^x/2= 4
2^x(1 - 1/2) = 4
2^x (2 - 1)/2 = 4
2^x (1/2) = 4
2^x = 8
2^x= 2³
x = 3

এখন,
x^x = 3³
= 27

১৫,৪৯০.

How much chicory at Tk. 5 a kg should be added to 20 kg of coffee at Tk. 12 a kg so that the mixture be worth Tk. 7.50 a kg?

ক
21 kg
খ
15 kg
গ
36 kg
ঘ
42 kg

ব্যাখ্যা

Question: How much chicory at Tk. 5 a kg should be added to 20 kg of coffee at Tk. 12 a kg so that the mixture be worth Tk. 7.50 a kg?

Solution:
Ratio in which coffee and chicory should be mixed
= 12 - 7.5 : 7.5 - 5 = 4.5 : 2.5 = 9 : 5.

Let x be quantity at Tk. 5 a kg
∴ 9 : 5 = x : 20
⇒ 5x = 180
⇒ x = 36

১৫,৪৯১.

Wendy has 5 pairs and 8 shirts. How many different combinations can she make with these items?

ক
42
খ
40
গ
38
ঘ
36

ব্যাখ্যা

Question: Wendy has 5 pairs and 8 shirts. How many different combinations can she make with these items?

Solution:
Wendy can make = 5 × 8 = 40 different combinations.

১৫,৪৯২.

The sum of prime numbers that are greater than 60 but less than 70 is:

ক
125
খ
67
গ
63
ঘ
69
ঙ
128

ব্যাখ্যা

The prime numbers that are greater than 60 but less than 70 are 61 and 67. Their sum is = 61 + 67 = 128

১৫,৪৯৩.

If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1?

ক
(a - b)/c
খ
(a - c)/b
গ
(b - c)/a
ঘ
(b - a)/c
ঙ
(c - b)/a

ব্যাখ্যা

Question: If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1?

Solution:
From a + b = c we get,
a = c - b;
b = c - a;

Only option 5:
(c - b)/a
= a/a
= 1

১৫,৪৯৪.

A dealer sells a radio at a gain of 10%. If he had bought it at 10% less and sold it for Tk. 132 less, he would have still gained 10%. The cost price of the radio is:

ক
ক) 1188
খ
খ) 1200
গ
গ) 1320
ঘ
ঘ) 1400
ঙ
ঙ) 1500

ব্যাখ্যা

Cost Price = 100
Selling price = 100 + 10 = 110
New cost price after 10% less = 100 - 10 = 90
New selling price = 90 × (110/100) = 99
difference between two selling price = 110 - 99 = 11%
11% price is equal to Tk. 132
1% price is equal to Tk. 132/11%
100% price is equal to Tk. (132/11%) × 100
= 1200

১৫,৪৯৫.

A box contains 21 balls numbered 1 to 21 . A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls are even numbered?

ক
ক) 2/7
খ
খ) 2/21
গ
গ) 3/14
ঘ
ঘ) 10/21

ব্যাখ্যা

Question: A box contains 21 balls numbered 1 to 21 . A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls are even numbered?

Solution:
The probability that first ball shows the even number =10/ 21

Since, the ball is not replaced there are now 9 even numbered balls and total 20 balls left.
Hence, probability that second ball shows the even number =9/20

Required probability,
=(10/21) × (9/20) = 3/14

১৫,৪৯৬.

Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

ক
Tk. 15
খ
Tk. 20
গ
Tk. 25
ঘ
Tk. 30

ব্যাখ্যা

Question: Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

Solution:

40% discount on 1000 = 1000 × 40% = 400

Two consecutive discount on 1000.
30% discount on 1000 = 30% of 1000
= 300

After 30% discount on 1000 = 1000 - 300

=700

Again,

After 10% discount on 700 = 10% of 700

= 70

Total discount = 300 + 70 = Tk. 370

So, difference = 400 - 370 = Tk. 30

১৫,৪৯৭.

A water tank has two taps (Tap-1 and Tap-2). Tap-1 can fill a tank in 8 hours and Tap-2 can empty the tank in 16 hours. How long will they take to fill the tank if both taps are opened simultaneously but Tap-2 is closed after 8 hours?

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

ব্যাখ্যা

Question: A water tank has two taps (Tap-1 and Tap-2). Tap-1 can fill a tank in 8 hours and Tap-2 can empty the tank in 16 hours. How long will they take to fill the tank if both taps are opened simultaneously but Tap-2 is closed after 8 hours?

Solution:
Tap-1, in 1 hour it fills = 1/8 part
Tap-2, in 1 hour it empties = 1/16 part

When both taps are open, in 1 hour it fills
= (1/8 - 1/16) part
= (2 - 1)/16 part
= 1/16 part

When both taps are open, in 8 hours it fills
= (1/16 × 8) part
= 1/2 part

∴ Remaining part = (1 - 1/2)
= 1/2 part

As Tap-2 is closed after 8 hours,

∴ Tap-1 alone can fill 1 part in = 8 hours
So, remaining 1/2 part will be filled in
= 8 × 1/2
= 4 hours

∴ Total time required = 8 + 4 = 12 hours

১৫,৪৯৮.

In the given triangle, D and E are the mid-points of AF and AG, F and G are the mid-points of AB and AC. If DE = 2.4 cm, then value of BC is-

ক
7.2 cm
খ
39.6 cm
গ
4.8 cm
ঘ
9.6 cm

ব্যাখ্যা

Question: In the given triangle, D and E are the mid-points of AF and AG, F and G are the mid-points of AB and AC. If DE = 2.4 cm, then value of BC is-

Solution:
As D and E are mid-points of AF and AG,
⇒ DE = (1/2)FG
⇒ FG = 2 × DE
⇒ FG = 2 × 2.4
⇒ FG = 4.8 cm
As F and G are the mid-points of AB and AC

⇒ FG = (1/2)BC
⇒ BC = 2 × FG
⇒ BC = 2 × 4.8
⇒ BC = 9.6 cm

১৫,৪৯৯.

If x < 10 and 2x - 3y = 8 which of the following must be true?

ক
y < 4
খ
y < 6
গ
y > 5
ঘ
y = 5
ঙ
None

ব্যাখ্যা

Question: If x < 10 and 2x - 3y = 8 which of the following must be true?

Solution:
Given that,
x < 10 and 2x - 3y = 8
We need to determine which statement must be true from the options.

Now,
2x - 3y = 8
⇒ 3y = 2x - 8
⇒ y = (2x - 8)/3
Since x < 10, substitute into the expression for y,
⇒ y < {(2 × 10) - 8}/3
⇒ y < (20 - 8)/3
⇒ y < 12/3
∴ y = 4
∴ if x < 10, then y < 4.

So the statement that must be true is y < 4.

১৫,৫০০.

Raju hikes up a hill at 4 mph and comes down at 6 mph. If the total time taken for the total journey is 3.5 hours, what was the distance between the hilltop and the foothills?

ক
9.4 miles
খ
8.4 miles
গ
84 miles
ঘ
16.8 miles
ঙ
None of these

ব্যাখ্যা

Question: Raju hikes up a hill at 4 mph and comes down at 6 mph. If the total time taken for the total journey is 3.5 hours, what was the distance between the hilltop and the foothills?

Solution:
Average speed = 2ab/(a + b) = (2 × 6 × 4)/10 = 4.8 mph.
Time taken = 3.5 hours both ways.

So, the two way distance = 4.8 × 3.5 miles = 16.8 miles.

Hence, the distance one-way = 16.8/2 = 8.4 miles.