Bank Math

PrepBank · পাতা ৩২ / ১৬১ · ৩,১০১–৩,২০০ / ১৬,১২৪

৩,১০১.

A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price, how much profit or loss does he make, if any?

ক
1% gain
খ
1% loss
গ
5% gain
ঘ
5% loss
ঙ
No gain, no loss.

ব্যাখ্যা

Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price, how much profit or loss does he make, if any?

Solution:
Let the cost price be Tk. 100.
Marked price = Tk. 110 (10% above CP)
Discount = 10% on the marked price = 10% of 110 = Tk. 11
∴ Selling price = 110 - 11 = Tk. 99
∴ Loss = CP - SP = 100 - 99 = Tk. 1
∴ % of loss = 1%

৩,১০২.

What is the value of: 2³⁰ + 2³⁰ + 2³⁰ + 2³⁰?

ক
16¹²⁰
খ
8³⁰
গ
2³⁰
ঘ
2³²

ব্যাখ্যা

Question: What is the value of: 2³⁰ + 2³⁰ + 2³⁰ + 2³⁰?

Solution:
2³⁰ + 2³⁰ + 2³⁰ + 2³⁰
= 4 × 2³⁰
= 2² × 2³⁰
= 2^{2 + 30}
= 2³²

৩,১০৩.

One year ago Ikbal was 4 times as old as Atif. In 6 years, Ikbal's age exceeds the twice of Atif's age by 9 years. What is the current ratio of their age?

ক
11 : 3
খ
9 : 2
গ
12 : 5
ঘ
14 : 5

ব্যাখ্যা

প্রশ্ন: One year ago Ikbal was 4 times as old as Atif. In 6 years, Ikbal's age exceeds the twice of Atif's age by 9 years. What is the current ratio of their age?

সমাধান:
ধরি,
1 বছর আগে আতিফের বয়স ছিল = x বছর
1 বছর আগে ইকবালের বয়স ছিল = 4x বছর

বর্তমানে আতিফের বয়স = x + 1 বছর
বর্তমানে ইকবালের বয়স = 4x + 1 বছর

6 বছর পর আতিফের বয়স = x + 1 + 6 = x + 7 বছর

6 বছর পর ইকবালের বয়স = 4x + 1 + 6 = 4x + 7 বছর

প্রশ্নমতে,
4x + 7 = 2(x + 7) + 9
⇒ 4x + 7 = 2x + 14 + 9
⇒ 2x = 16
∴ x = 8

অতএব, বর্তমানে তাদের বয়সের অনুপাত = (4 ⋅ 8 + 1) : (8 + 1)
= 33 : 9
= 11 : 3

৩,১০৪.

A money lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. In this way, he gains Tk. 104.50, a year. The amount of money be borrows, is?

ক
Tk. 4000
খ
Tk. 5000
গ
Tk. 6000
ঘ
Tk.7000
ঙ
Tk. 6500

ব্যাখ্যা

Question: A money lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. In this way, he gains Tk. 104.50, a year. The amount of money be borrows, is?

Solution:
Let, the sum Tk. x

Then,
C.I. when compounded half yearly = Tk. [x × {1 + (3/100)}²- x]
= Tk. {(10609x/10000) - x}
= Tk. {(10609x - 10000x)/10000}
= Tk. (609x/10000)

C.I. when compounded yearly = Tk. [x × {1 + (4/100)} - x]
= Tk. {(26x/25) - x}
= Tk. x/25

∴ (609x/10000) - (x/25) = 104.50
⇒ (609x - 400x)/10000 = 104.50
⇒ 209x/10000 = 104.50
⇒ x = {104.50 × (10000/209)}
⇒ x = 5000

৩,১০৫.

On a sum of money, the simple interest for 2 years is Tk. 660, while the compound interest is Tk. 696.30, the rate of interest being the same in both cases. The rate of interest is -

ক
10%
খ
10.5%
গ
11%
ঘ
11.5%

ব্যাখ্যা

Question: On a sum of money, the simple interest for 2 years is Tk. 660, while the compound interest is Tk. 696.30, the rate of interest being the same in both cases. The rate of interest is -

Solution:
Difference of Compound interest and Simple interest for 2 years = Tk. (696.30 - 660) = Tk. 36.30
Simple interest for 1 years = 660/2 = Tk. 330

Simple interest on 330 for 1 year = 36.30
Interst rate = {(36.30 × 100)/330}% = 11%

৩,১০৬.

Which of the following are equal in value?
I) 4⁰
II) 1⁴
III) 4¹
IV) 0⁴

ক
ক) III and IV
খ
খ) II and III
গ
গ) I and II
ঘ
ঘ) I and IV

ব্যাখ্যা

I) 4⁰ = 1
II) 1⁴ = 1
III) 4¹ = 4
IV) 0⁴ = 0
So, I and II are equal in value

৩,১০৭.

Simplify: z² + 11z² - 5z - 11z² + 5z.

ক
z²
খ
- z²
গ
5z
ঘ
- 5z

ব্যাখ্যা

Question: Simplify: z² + 11z² - 5z - 11z² + 5z.

Solution:
z² + 11z² - 5z - 11z² + 5z
= z²

৩,১০৮.

A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?

ক
ক) Tk. 575
খ
খ) Tk. 520
গ
গ) Tk. 495
ঘ
ঘ) Tk. 480

ব্যাখ্যা

Question: A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?

Solution:
Simple interest for 1 years = Tk. (815 - 735)
= Tk. 80
∴ Simple interest for 3 years = Tk.(80 × 3)
= Tk. 240

∴ Sum = (735 - 240)
= Tk. 495

৩,১০৯.

Pritom travels a distance of 9 km from his house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey.

ক
12 km/hr
খ
16.3 km/hr
গ
19.5 km/hr
ঘ
20.4 km/hr

ব্যাখ্যা

Question: Pritom travels a distance of 9 km from his house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey.

Solution:
total distance = 9 + 9 = 18 km

time taken by auto rickshaw = 9/18 hr
= 1/2 hr

time taken by auto rickshaw = 9/15 hr
= 3/5 hr

total time = 1/2 hr + 3/5 hr
= 11/10 hr

average speed = 18/11/10
= 180/11 km/hr
= 16.3 km/hr

৩,১১০.

The number of students in 3 classes is in the ratio of 2 : 3 : 4. If 12 students are increased in each class, this ratio changes to 8 : 11 : 14. The total number of students in the three classes at the start was-

ক
162
খ
142
গ
152
ঘ
122

ব্যাখ্যা

Question: The number of students in 3 classes is in the ratio of 2 : 3 : 4. If 12 students are increased in each class, this ratio changes to 8 : 11 : 14. The total number of students in the three classes at the start was-

Solution:
The number of students in 3 classes is in the ratio of 2 : 3 : 4.
Let the number of students in 3 classes be as follows 2x, 3x, 4x.
Total students = 9x.
According to the question, 2x + 12 : 3x + 12 : 4x + 12 = 8 : 11 : 14

Equating the ratio,
(2x + 12)/(3x + 12) = 8/11
→ 22x + 132 = 24x + 96
→ 2x = 36
→ x= 18

So, the total number of students in the three classes at the start was- 9 × 18 = 162.

৩,১১১.

একটি কলম 11 টাকায় বিক্রি করলে 10% লাভ হয়। কলমটির ক্রয়মূল্য কত?

ক
9 টাকা
খ
10 টাকা
গ
11 টাকা
ঘ
12 টাকা

ব্যাখ্যা

প্রশ্ন: একটি কলম 11 টাকায় বিক্রি করলে 10% লাভ হয়। কলমটির ক্রয়মূল্য কত?

সমাধান:
10% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 110 টাকা

এখন,
বিক্রয়মূল্য 110 টাকা হলে ক্রয়মূল্য = 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য = 100/110 টাকা
বিক্রয়মূল্য 11 টাকা হলে ক্রয়মূল্য = (100 × 11)/110 টাকা
= 10 টাকা

৩,১১২.

The average of a, b, c is 6 and a - b = 4, ab = 21, what is the value of c?

ক
ক) 6
খ
খ) 7
গ
গ) 8
ঘ
ঘ) 9

ব্যাখ্যা

দেয়া আছে,
(a + b + c)/3 = 6
a + b + c = 18 ............ (1)

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 = 10

(1) নং এ a + b এর মান বসিয়ে পাই,
a + b + c = 18
10 + c = 18
c = 18 - 10
c = 8

৩,১১৩.

When is converted into fraction, the result will be?

ক
2/15
খ
4/20
গ
3/15
ঘ
1/4

ব্যাখ্যা

Question: When is converted into fraction, the result will be?

Solution:

৩,১১৪.

A, B and C can complete a piece of work in 14, 6 and 12 days respectively. Working together, they will complete the work in ________ .

ক
ক) 19/9 days
খ
খ) 9/28 days
গ
গ) 28/9 days
ঘ
ঘ) 25/8 days

ব্যাখ্যা

A 1 দিনে করে কাজটির =1/14 অংশ
B 1 দিনে করে কাজটির =1/6 অংশ
C 1 দিনে করে কাজটির =1/12 অংশ

A + B + C 1 দিনে করে কাজটির =(1/14) + (1/6) + (1/12) অংশ
= (6 + 14 + 7 )/84 অংশ
= 27/84 অংশ
= 9/28 অংশ
A + B + C 9/28 অংশ কাজ করে 1 দিনে
A + B + C 1 (সম্পূর্ণ)অংশ কাজ করে (1 × 28)/9 দিনে
= 28/9 দিনে

৩,১১৫.

Which set of three sides cannot form a triangle?

ক
7cm, 10cm, 12cm
খ
6cm, 9cm, 16cm
গ
5cm, 12cm, 13cm
ঘ
8cm, 15cm, 20cm

ব্যাখ্যা

Question: Which set of three sides cannot form a triangle?

Solution:
আমরা জানি,
ত্রিভুজের যেকোনো দুই বাহুর সমষ্টি তৃতীয় বাহু অপেক্ষা বৃহত্তর হতে হবে।

এখানে, আমরা প্রত্যেকটি ত্রিভুজের ক্ষুদ্রতম দুইটি বাহুর যোগফলকে তৃতীয় (বৃহত্তম) বাহুর সাথে তুলনা করে পাই:

ক) 7 + 10 = 17 > 12; ∴ ত্রিভুজ আঁকা সম্ভব।
খ) 6 + 9 = 15 < 16; ∴ ত্রিভুজ আঁকা সম্ভব নয়।
গ) 5 + 12 = 17 > 13; ∴ ত্রিভুজ আঁকা সম্ভব।
ঘ) 8 + 15 = 23 > 20; ∴ ত্রিভুজ আঁকা সম্ভব।

৩,১১৬.

In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is:

ক
ক) 2 hours
খ
খ) 2.5 hours
গ
গ) 3 hours
ঘ
ঘ) 4 hours

ব্যাখ্যা

Ratio of speeds = 3:4
Distance remaining constant, the ratio of time taken = 4:3
A takes 0.5 hours more than B
Hence time taken by A = 4 times 0.5 = 2 hours

৩,১১৭.

Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.

ক
ক) 30 days
খ
খ) 45 days
গ
গ) 60 days
ঘ
ঘ) 90 days

ব্যাখ্যা

Question: Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.

Solution:
পূজা কাজটি করতে পারে = 90 দিনে
আরতি কাজটি করতে পারে = 180 দিনে

পূজা ও আরতি 1 দিনে করতে পারে কাজটির = 1/90 + 1/180 অংশ
= (2 + 1)/180
= 3/180
= 1/60

পূজা ও আরতি 1/60 অংশ কাজ করতে পারে 1 দিনে
পূজা ও আরতি 1 অংশ কাজ করতে পারে (1× 60)/1 দিনে
= 60 দিনে

৩,১১৮.

A company issued 25000 shares of par value tk. 15 each. If the company has decided to give the dividend tk. 30000, what is the rate of dividend paid by the company?

ক
ক) 5%
খ
খ) 7%
গ
গ) 8%
ঘ
ঘ) 10%
ঙ
ঙ) 12%

ব্যাখ্যা

Number of shares = 25000
Face value of each share = Tk. 15
Let R be the rate of interest.

Dividend per share = 15 × R/100
Total dividend = 25000 × 15 × R/100
As per the question: 25000 × 15 × R/100
= 30000
R = 30000/3750 = 8

So, the dividend is 8%.

৩,১১৯.

A shopkeeper sells two items for Tk. 6,000 each, neither gaining nor losing in the overall transaction. If he sold one item at a gain of 20%, what is the cost price of the other item?

ক
Tk. 7000
খ
Tk. 5200
গ
Tk. 8500
ঘ
Tk. 6800

ব্যাখ্যা

Question: A shopkeeper sells two items for Tk. 6,000 each, neither gaining nor losing in the overall transaction. If he sold one item at a gain of 20%, what is the cost price of the other item?

Solution:
প্রথম পণ্যের ক্রয়মূল্য-
ধরি, ক্রয়মূল্য = ১০০ টাকা
২০% লাভে বিক্রয়মূল্য = ১০০ + ২০ = ১২০ টাকা

বিক্রয়মূল্য ১২০ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/১২০ টাকা
বিক্রয়মূল্য ৬০০০ টাকা হলে ক্রয়মূল্য = (১০০ × ৬০০০)/১২০ = ৫০০০ টাকা

আবার,
মোট বিক্রয়মূল্য = ৬০০০ + ৬০০০ = ১২০০০
মোট ক্রয়মূল্য = মোট বিক্রয়মূল্য = ১২০০০ (কারণ কোনো লাভ বা ক্ষতি হয়নি)

∴ অন্য পণ্যের ক্রয়মূল্য = ১২০০০ - ৫০০০ = ৭০০০ টাকা

৩,১২০.

400 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 50% in the solution?

ক
120 grams
খ
140 grams
গ
160 grams
ঘ
240 grams

ব্যাখ্যা

Question: 400 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 50% in the solution?

Solution:
Amount of sugar = 400 × (30/100) = 120 grams
let,
x gm sugar to be added

According to the question,
(120 + x)/(400 + x) = 50%
⇒ (120 + x)/(400 + x) = 50/100
⇒ (120 + x)/(400 + x) = 1/2
⇒ 2 × (120 + x) = (400 + x)
⇒ 240 + 2x = 400 + x
⇒ 2x - x = 400 - 240
⇒ x = 160 grams

৩,১২১.

A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 100000, C receives

ক
ক) Tk. 24,000
খ
খ) Tk. 34,000
গ
গ) Tk. 42,000
ঘ
ঘ) Tk. 35,000

ব্যাখ্যা

Let C subscribes Tk. x
x + x + 5000 + x + 9000 = 50,000
x = 12,000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
C's share = 100000 of 12/50 = 24,000

৩,১২২.

A motorcyclist completes a certain journey in 5 hours. He covers one-third of the distance at 60 km/hr and the rest at 80km/hr. the length of the trip is -

ক
300 km
খ
240 km
গ
360 km
ঘ
420 km

ব্যাখ্যা

Question: A motorcyclist completes a certain journey in 5 hours. He covers one-third of the distance at 60 km/hr and the rest at 80km/hr. the length of the trip is -

Solution:
Let the total length of the trip be = x km
one-third or x/3 distance covered at 60km/hr.
time = (x/3)/60 hr

Two-thirds of the distance covered at 80km/hr
time = (2x/3)/80 hr

ATQ,
(x/3)/60 + (2x/3)/80 = 5
or, (2x + 3x)/360 = 5
or, 5x/360 = 5
∴ x = 360 km

৩,১২৩.

In how many different ways can the letters of the AUCTION be arranged in such a way that the vowels always come together?

ক
ক) 30
খ
খ) 48
গ
গ) 144
ঘ
ঘ) 576

ব্যাখ্যা

The given word contains 7 different letters.
Keeping the vowels (AUIO) together, we take them as 1 letter.
Then,
we have to arrange the letters CTN(AUIO).
Now, 4 letters can be arranged in 4! = 24 ways.
The vowels (AUIO) can be arranged themselves in 4! = 24 ways.
∴ Required number of ways = (24 × 24)
= 576.

৩,১২৪.

Luke drives the first 300 miles of a trip at 60 miles an hour. How fast does he have to drive, in miles per hour, on the final 200 miles of the trip if the total time of the trip is equal to 7 hours?

ক
ক) 100
খ
খ) 110
গ
গ) 115
ঘ
ঘ) 120

ব্যাখ্যা

Let the required speed be x mph
ATQ,
300/60 + 200/x = 7
Or, 200/x = 7 - 5
Or, 200/x = 2
So, x = 100

৩,১২৫.

Sumon started a business with a capital of Tk. 80000. After 6 months Mohan joined as a partner by investing Tk. 65000. After one year they earned total profit Tk. 20000. What is share of Mohan in the profit?

ক
Tk. 5222.2
খ
Tk. 5777.7
গ
Tk. 6222.2
ঘ
Tk. 6777.7

ব্যাখ্যা

Question: Sumon started a business with a capital of Tk. 80000. After 6 months Mohan joined as a partner by investing Tk. 65000. After one year they earned total profit Tk. 20000. What is share of Mohan in the profit?

Solution:
Sumon : Mohan = (80000 × 12) : (65000 × 6)
= 960000 : 390000
= 96 : 39
= 32 : 13

∴ Mohan's Share in the profit = (13/45) × 20000
= 5777.77

৩,১২৬.

If the average of x numbers is y² and that of y number is x², then the average of (x + y) numbers is-

ক
ক) x/y
খ
খ) 2xy
গ
গ) x + y
ঘ
ঘ) xy

ব্যাখ্যা

Sum of x numbers = x × y² = xy²
Similarly,
sum of y numbers = y × x² = x²y
Total number of numbers = x + y
∴ Average of (x + y) numbers = (xy² + x²y)/(x + y)
= [xy × (y + x)]/(x + y)
= xy

৩,১২৭.

The sum of three consecutive multiples of 3 is 72. What is the largest number?

ক
ক) 27
খ
খ) 24
গ
গ) 21
ঘ
ঘ) 36

ব্যাখ্যা

Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?

Solution:
মনে করি,
3 এর তিনটি ধারাবাহিক গুণিতক যথাক্রমে 3x, 3(x + 1) ও 3(x + 2)

প্রশ্নমতে,
3x + 3(x + 1) + 3(x + 2) = 72
বা, 3x+ 3x + 3 + 3x + 6 = 72
বা, 9x + 9 = 72
বা, 9x = 72 - 9
বা, 9x = 63
বা, x = 63/9
∴ x = 7

∴ বৃহত্তম গুণিতক = 3(7 + 2) = 3 × 9 = 27

৩,১২৮.

In an examination, 41% of students failed in Economics, 35% of students failed in Geography and 39% of students failed in History, 5% of students failed in all the three subjects, 14% of students failed in Economics and Geography, 21% of students failed in Geography and History and 18% of students failed in History and Economics. Find the percentage of students who failed in only Economics.

ক
16%
খ
14%
গ
12%
ঘ
10%

ব্যাখ্যা

Question: In an examination, 41% of students failed in Economics, 35% of students failed in Geography and 39% of students failed in History, 5% of students failed in all the three subjects, 14% of students failed in Economics and Geography, 21% of students failed in Geography and History and 18% of students failed in History and Economics. Find the percentage of students who failed in only Economics.

Solution:

Now,
e = 5%
b + e = 14%
⇒ b = 9%

and, d + e = 18%
⇒ d = 13%
Therefore, Percentage of students who failed only in Economics = a = 41% - (b + e + d)
⇒ a = 41% - (9 + 5 + 13)%
⇒ a = 41% - 27%
⇒ a = 14%
Hence, 14% is the correct answer.

৩,১২৯.

Tk. 355 has been divided among A, B, C in such a way that A had Tk. 20 more than B and C had Tk.15 more than A. How much was C’s share?

ক
ক) Tk. 135
খ
খ) Tk. 100
গ
গ) Tk. 120
ঘ
ঘ) Tk. 150

ব্যাখ্যা

Let the share of A was x
A has 20 more than B.
So, Share of B was (x – 20)
And C had 15 more than A So, Share of C was (x + 15)
ATQ,
A + B + C = 355
Or, x + x – 20 + x + 15 = 355
Or, 3x – 5 = 355
Or, 3x = 360
Or, x = 120

So, Share of C = x + 15 = 120 + 15 = 135

৩,১৩০.

If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

ক
y = 1000x
খ
x = 1000y
গ
y = x + 2
ঘ
y = x + 3

ব্যাখ্যা

Question: If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

Solution:
ATQ,
10^x = 0.1% × 10^y
⇒ 10^x = (0.1/100) × 10^y
⇒ 10^x = 0.001 × 10^y
⇒ 10^x = 1 × 10^{y - 3}
⇒ 10^x = 10^{y - 3}
⇒ x = y - 3
∴ y = x + 3

৩,১৩১.

The speed of A and B are in the ratio 3 : 5. A takes 30 minutes more than B to reach a destination. Time in which A reaches the destination?

ক
1 hour 30 minutes
খ
1 hour
গ
1 hour 15 minutes
ঘ
2 hour

ব্যাখ্যা

Question: The speed of A and B are in the ratio 3 : 5. A takes 30 minutes more than B to reach a destination. Time in which A reaches the destination?

Solution:
speed ratio = 3 : 5
time ratio = 5 : 3
∴ 5x - 3x = 30
x = 15

time of A = 5 × 15 = 75 minutes
= 1 hour 15 minutes.

৩,১৩২.

If the average of 'm' numbers is 2n² and the average of 'n' numbers is 2m², what is the average of the combined (m + n) numbers?

ক
6mn/(m + n)
খ
2mn
গ
mn
ঘ
4mn/(m + n)

ব্যাখ্যা

Question: If the average of 'm' numbers is 2n² and the average of 'n' numbers is 2m², what is the average of the combined (m + n) numbers?

Solution:
দেওয়া আছে,
'm' সংখ্যার গড় = 2n²
∴ m সংখ্যার সমষ্টি = m × 2n²

'n' সংখ্যার গড় = 2m²
∴ 'n' সংখ্যার সমষ্টি = n × 2m²

∴ মোট সমষ্টি = (m × 2n²) + (n × 2m²)
= 2mn(n + m)

∴ তাদের গড় = মোট সমষ্টি/(m + n)
= 2mn(m + n)/(m + n)
= 2mn

৩,১৩৩.

In how many years will Tk. 20,000 amount to Tk. 28,800 at 20% per annum compound interest?

ক
2 years
খ
3 years
গ
4 years
ঘ
5 years

ব্যাখ্যা

Question: In how many years will Tk. 20,000 amount to Tk. 28,800 at 20% per annum compound interest?

Solution:
Given that,
Principal, P = Tk. 20,000
Amount, C = Tk. 28,800
Rate, r = 20%

We know,
C = P(1 + r)ⁿ⇒ 28,800 = 20,000 × {(1 + (20/100)}ⁿ
⇒ 28,800 = 20,000 × (6/5)ⁿ⇒ 28,800/20,000 = (6/5)ⁿ
⇒ 36/25 = (6/5)ⁿ⇒ (6/5)²= (6/5)ⁿ

∴ n = 2 years

৩,১৩৪.

If one pipe A can fill a tank in 20 minutes, then 5 pipes, each of 20% efficiency of A, can fill the tank in -

ক
ক) 20 minutes
খ
খ) 25 minutes
গ
গ) 28 minutes
ঘ
ঘ) 30 minutes

ব্যাখ্যা

Question: If one pipe A can fill a tank in 20 minutes, then 5 pipes, each of 20% efficiency of A, can fill the tank in -

Solution:
ধরি,
A পাইপের ইফিসিয়েন্সি = ১০০%
৫ টি পাইপের প্রতিটির ইফিসিয়েন্সি = ১০০%/৫ = ২০%

তাহলে, ৫ টি পাইপের মোট ইফিসিয়েন্সি = ২০% × ৫ = ১০০%

তাহলে, ৫ টি পাইপ এর সমষ্টিগত ইফিসিয়েন্সি A পাইপের সমান।
তাহলে ৫ টি পাইপ একত্রে ২০ মিনিটেই টাঙ্কটি পূর্ণ করতে পারবে।

৩,১৩৫.

The average weight of 40 students in a class is 45 kg. If 10 new students are admitted, the average weight increases by 1 kg. What is the average weight of the new students?

ক
46 kg
খ
47.8 kg
গ
48.5 kg
ঘ
50 kg
ঙ
51 kg

ব্যাখ্যা

Question: The average weight of 40 students in a class is 45 kg. If 10 new students are admitted, the average weight increases by 1 kg. What is the average weight of the new students?

Solution:
40 জন শিক্ষার্থীর মোট ওজন = 40 × 45 = 1800 kg
10 জন নতুন শিক্ষার্থী ভর্তি হওয়ায় মোট শিক্ষার্থীর সংখ্যা = 40 + 10 = 50 জন
নতুন গড় ওজন = 45 + 1 = 46 kg
সুতরাং, 50 জন শিক্ষার্থীর মোট ওজন = 50 × 46 = 2300 kg

নতুন 10 জন শিক্ষার্থীর মোট ওজন = 2300 - 1800 = 500 kg
∴ নতুন 10 জন শিক্ষার্থীর গড় ওজন = 500/10 = 50 kg

সুতরাং, নতুন শিক্ষার্থীদের গড় ওজন 50 kg

৩,১৩৬.

If a + b + c = 15 and a² + b² + c² = 77, what is the value of ab + bc + ca = ?

ক
82
খ
74
গ
66
ঘ
70

ব্যাখ্যা

Question: If a + b + c = 15 and a² + b² + c² = 77, what is the value of ab + bc + ca = ?

Solution:
Given that,
a + b + c = 15 and a² + b² + c² = 77

We know,
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ 15²= 77 + 2(ab + bc + ca) ; [Substitute the given values]
⇒ 225 = 77 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 225 - 77
⇒ 2(ab + bc + ca) = 148
⇒ ab + bc + ca = 148/2
∴ ab + bc + ca = 74

৩,১৩৭.

Joni buys a 40 tk shares in a company, which pays 10% dividend. Joni buys the share at such a price that his profit is 16% on his investment. At what price did Joni buy the share?

ক
ক) 20 tk
খ
খ) 22 tk
গ
গ) 24 tk
ঘ
ঘ) 25 tk

ব্যাখ্যা

Question: Joni buys a 40 tk shares in a company, which pays 10% dividend. Joni buys the share at such a price that his profit is 16% on his investment. At what price did Joni buy the share?

Solution:
Dividend (profit) given by the company on 1 share = 10% of 40 = 4 tk.

Suppose the man buys one share for x.

Therefore, Joni’s profit = 16% of x = 16x/100
According to the problem, 16x/100 = 4
⟹ x = 25

Joni bought the share at 25 tk.

৩,১৩৮.

If A = {x : x is a natural number and a factor of 18} and B = {x : x is a natural number and less than 6}, then find A ∩ B.

ক
{ }
খ
{1, 2, 3}
গ
{1, 2, 3, 4, 5}
ঘ
{1, 2, 3, 4, 5, 6, 9, 18}

ব্যাখ্যা

Question: If A = {x : x is a natural number and a factor of 18} and B = {x : x is a natural number and less than 6}, then find A ∩ B.

Solution:
Here,
A = {1, 2, 3, 6, 9, 18}
B = {1, 2, 3, 4, 5}

Therefore,
A ∩ B = {1, 2, 3, 6, 9, 18} ∩ {1, 2, 3, 4, 5}
= {1, 2, 3}

৩,১৩৯.

What is the H.C.F. of the following fractions?
3/6, 6/9, 9/12

ক
1/6
খ
1/2
গ
2/15
ঘ
1/12

ব্যাখ্যা

Question: What is the H.C.F. of the following fractions?
3/6, 6/9, 9/12

Solution:
আমরা জানি,
ভগ্নাংশের গসাগু = (লবের গসাগু)/(হরের লসাগু)

এখানে লব = 3, 6 এবং 9
3 = 3 × 1
6 = 3 × 2
9 = 3 × 3
∴ লবের গসাগু (H.C.F.) = 3

হর = 6, 9 এবং 12
6 = 2 × 3
9 = 3²
12 = 2² × 3
∴ হরের লসাগু (L.C.M.) = 2² × 3²
= 4 × 9 = 36

ভগ্নাংশের গসাগু = লবের গসাগু/হরের লসাগু
= 3/36
= 1/12

৩,১৪০.

Jamal started a business investing Tk. 9000. After five months, Sakib joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Sakib in the profit?

ক
Tk. 2280
খ
Tk. 2180
গ
Tk. 2350
ঘ
Tk. 2380

ব্যাখ্যা

Question: Jamal started a business investing Tk. 9000. After five months, Sakib joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Sakib in the profit?

Solution:
Jamal invested for 12 months and Sakib invested for 7 months.

So Jamal : Sakib = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14

∴ Sakib Ratio in profit will be
= 6970 × 14/41
= Tk. 2380

৩,১৪১.

A, B, C started a business with their investments in the ratio 1:3:5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is?

ক
ক) 4 : 3 : 5
খ
খ) 5 : 6 : 10
গ
গ) 6 : 5 : 10
ঘ
ঘ) 10 : 5 : 6

ব্যাখ্যা

Let their initial investments be x, 3x and 5x respectively
Then,
=A:B:C
= (x×4+2x×8) : {3x×4+(3x/2)×8} : {5x×4+(5x/2)×8}
= 20x:24x:40x
= 5:6:10

৩,১৪২.

A tap can fill a tank in 4 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

ক
ক) 1 hr 30
খ
খ) 2 hr 30 min
গ
গ) 2 hr
ঘ
ঘ) 3 hr

ব্যাখ্যা

A tap can fill a tank in 4 hours.
Therefore the tap can fill half the tank in 2 hours.

Remaining = 1/2

After half the tank is filled, three more similar taps are opened.
Hence, the total number of taps becomes 4.

Part filled by one tap in 1 hour = 1/4
Part filled by four taps in 1 hour = 4 × (1/4) = 1
i.e., 4 taps can fill the remaining half in 30 minutes.

Total time taken
= 2 hour + 30 minute = 2 hour 30 minutes.

৩,১৪৩.

In a two–digit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is-

ক
35
খ
41
গ
47
ঘ
55
ঙ
31

ব্যাখ্যা

Question: In a two–digit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is-

Solution:
Let, Ten’s digit = x
Unit’s digit = 2x - 1

∴ Original number = 10x + (2x - 1) = 12x - 1

So, New number = 10 (2x - 1) + x
= 20x - 10 + x
= 21x - 10

ATQ,
(21x - 10) - (12x + 1) = 12x - 1 - 20
⇒ 9x - 9 = 12x - 21
⇒ 3x = 12
⇒ x = 4

∴ Original number = 12x - 1
= 12 × 4 - 1
= 47

৩,১৪৪.

If the radius of a circle is increased by 100%, by what % is the area of the circle increased?

ক
300%
খ
100%
গ
200%
ঘ
250%

ব্যাখ্যা

Question: If the radius of a circle is increased by 100%, by what % is the area of the circle increased?
(যদি একটি বৃত্তের ব্যাসার্ধ ১০০% বৃদ্ধি পায়, তবে বৃত্তের ক্ষেত্রফল কত শতাংশ বৃদ্ধি পাবে?)

Solution:
ধরা যাক,
বৃত্তের ব্যাসার্ধ, r = 10

∴ বৃত্তের ক্ষেত্রফল = πr²
= π (10)²
= 100π

আবার,
বৃত্তের ব্যাসার্ধ 100% বৃদ্ধিতে,
বৃত্তের নতুন ব্যাসার্ধ = 10 + 10 এর 100%
= 10 + 10 এর 100/100
= 20

∴ বৃত্তের নতুন ক্ষেত্রফল = πr²
= π (20)²
= 400π

∴ ক্ষেত্রফল বৃদ্ধি পায় = 400π - 100π
= 300π

100π থেকে ক্ষেত্রফল বৃদ্ধি পায় = 300π
1 থেকে ক্ষেত্রফল বৃদ্ধি পায় = 300π/100π
∴ 100 থেকে ক্ষেত্রফল বৃদ্ধি পায় = (300π × 100)/100π
= 300%

∴ বৃত্তের ক্ষেত্রফল শতকরা 300% বৃদ্ধি পায়।

৩,১৪৫.

Azim sells an object to Belal at a profit of 15%, Belal sells that object to karim for Tk. 1012 and makes a profit of 10%. At what cost did Azim purchase the object?

ক
Tk. 950
খ
Tk. 900
গ
Tk. 850
ঘ
Tk. 800

ব্যাখ্যা

Question: Azim sells an object to Belal at a profit of 15%, Belal sells that object to karim for Tk. 1012 and makes a profit of 10%. At what cost did Azim purchase the object?

Solution:

Let the actual cost price at which Azim bought the object be x

When Azim sells the object to Belal

Profit % = 15%

∴ selling price of object = [(100 + 15)/100] × x = 1.15x

Now, this cost price of the object for Belal

When Belal sells the object to karim

Selling Price = Tk. 1012

Profit % = 10%

∴ Selling price = [(100 + 10)/100] × 1.15x

⇒ 1012 = [(100 + 10)/100] × 1.15x
⇒ x = (1012 × 1000)/(11 × 115)
∴ x = 800
Therefore, the price at which Azim bought the object is Tk. 800.

৩,১৪৬.

7 is added to a certain number; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. Thus, if the remainder left is 12, what was the original number?

ক
20
খ
37
গ
30
ঘ
27

ব্যাখ্যা

Question: 7 is added to a certain number; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. Thus, if the remainder left is 12, what was the original number?

Solution:
let the number be x.

ATQ,
[{5(x + 7)}/9] - 3 = 12
or, 5(x + 7) = 15 × 9
or, x + 7 = 135/5
or, x + 7 = 27
or, x = 27 - 7
∴ x = 20

৩,১৪৭.

If √5ⁿ = 625, then the value of n is?

ক
8
খ
18
গ
20
ঘ
22

ব্যাখ্যা

Question: If √5ⁿ = 625, then the value of n is?

Solution:
Given that, √5ⁿ = 625
⇒ √5ⁿ = 5⁴
⇒ (√5ⁿ)² = (5⁴)²
⇒ 5ⁿ = 5⁸
∴ n = 8

৩,১৪৮.

What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Tk. 10 per square meter?

ক
ক) Tk. 3430
খ
খ) Tk. 3440
গ
গ) Tk. 3450
ঘ
ঘ) Tk. 3460

ব্যাখ্যা

In this question, we are having perimeter.
We know Perimeter = 2(l+b), right
So, 2(l+b) = 340
As we have to make 1 meter boundary around this,
so Area of boundary = ((l+2)+(b+2)-lb)
= 2(l+b)+4 = 340+4 = 344
So required cost will be = 344 × 10 = 3440

৩,১৪৯.

In order to obtain an income of Tk. 600 from 10% stock at Tk. 120, one must make an investment of-

ক
Tk. 8000
খ
Tk. 7200
গ
Tk. 6200
ঘ
Tk. 8400

ব্যাখ্যা

Question: In order to obtain an income of Tk. 600 from 10% stock at Tk. 120, one must make an investment of-

Solution:
To obtain Tk. 10,
investment = Tk. 120
To obtain Tk. 600
investment = Tk. (120/10) × 600
= Tk. 7200

৩,১৫০.

If the sum of five consecutive odd integers is 165, what is the middle number?

ক
31
খ
33
গ
35
ঘ
37

ব্যাখ্যা

Question: If the sum of five consecutive odd integers is 165, what is the middle number?

Solution:
ধরি,
মাঝের সংখ্যাটি = x
সুতরাং, ৫ টি ক্রমিক বিজোড় সংখ্যা হবে যথাক্রমে-
x - 4, x - 2, x, x + 2 এবং x + 4 [যেখানে মাঝের সংখ্যা x]

প্রশ্নমতে,
(x - 4) + (x - 2) + x + (x + 2) + (x + 4) = 165
⇒ 5x = 165
⇒ x = 165/5
⇒ x = 33

অর্থাৎ 5 টি ক্রমিক বিজোড় সংখ্যার মধ্যে মাঝের সংখ্যাটি = 33

৩,১৫১.

There are 20 stops for the local trains running between Churchgate and Virar. A passenger travelling between any two stops needs to buy a ticket. How many types of tickets are required to be made to meet all the possibilities?

ক
ক) 72
খ
খ) 190
গ
গ) 380
ঘ
ঘ) 760

ব্যাখ্যা

We need to SELECT people.
[SELECT = Combination = ⁿC_r = n!/r!(n-r)!

There are 20 stations. A ticket is needed between 2 stops.
That means, we simply need to select 2 stops from possible 20 stops.

That can be done by ²⁰C₂ = 20!/2!(20 - 2)! = 20!/2!18! = 190 ways.

This is when we start from one side.
When we travel from the other side we will need a separate ticket.
That means while going from A to B and B to A, we will need separate tickets.
So again on another side, we need 190 tickets.

Total tickets = 190 + 190 = 380 tickets.

৩,১৫২.

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

ক
530
খ
532
গ
580
ঘ
588
ঙ
None

ব্যাখ্যা

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

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

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

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

৩,১৫৩.

After adding some water in a 50 litres milk-water mixture the ratio of milk and water changes to 6 : 4 to 5 : 5. What was the amount of extra water that was added?

ক
ক) 8 litres
খ
খ) 9 litres
গ
গ) 10 litres
ঘ
ঘ) 12 litres

ব্যাখ্যা

Question: After adding some water in a 50 litres milk-water mixture the ratio of milk and water changes to 6 : 4 to 5 : 5. What was the amount of extra water that was added?

Solution:
initially the amount of milk was = 50 × 6/10 = 30 litres
so, the amount of water was = 20 litres

let, X litres of water is added to the mixture

ATQ,
30 : (20 + X) = 5 : 5
100 + 5X = 150
5X = 50
X = 10

hence, 10 litres of water were added to the mixture

৩,১৫৪.

There are deer and peacock in zoo. The total number of their heads is 80 and the total number of their legs is 200. How many peacocks are there?

ক
20
খ
30
গ
50
ঘ
60

ব্যাখ্যা

Question: There are deer and peacock in zoo. The total number of their heads is 80 and the total number of their legs is 200. How many peacocks are there?

Solution:
Let there are "X" deer and "Y" peacocks.

Total heads are 80.
∴ X + Y = 80 .................(1)

Total legs are 200. Deer has 4 legs and peacock has 2.
∴ 4X + 2Y = 200 ..................(2)

Multiplying Equation (1) by 4 and substracting with Equation (2), we get
4X + 4Y - 4X - 2Y = 320 - 200
⇒ 2Y = 120
∴ Y = 60

Putting this value of Y in Equation (1), we get
X + 60 = 80
∴ X = 20

∴ Total peacocks are Y = 60.
Hence, the correct answer is 60.

৩,১৫৫.

What is the cube root of 0.008?

ক
ক) 0.2
খ
খ) 0.02
গ
গ) 0.002
ঘ
ঘ) 1.2

ব্যাখ্যা

প্রশ্ন: What is the cube root of 0.008?

সমাধান:

৩,১৫৬.

What will be the total worth if 135 Tk. is kept for 2 years at simple interest rate 5%?

ক
ক) 13.5 Tk.
খ
খ) 148.5 Tk.
গ
গ) 140.5 Tk.
ঘ
ঘ) 17.5 Tk.

ব্যাখ্যা

Question: What will be the total worth if 135 Tk. is kept for 2 years at simple interest rate 5%?

Solution:
Here,
P = 135,
n = 2,
R = 5%
I = ?

I = Pnr
= 135 × 2 × 5%
= 270 × 5/100
= 13.5

total worth = 135 + 13.5 = 148.5 Tk.

৩,১৫৭.

If f(x) = x/(x - 3), x ≠ 3, then what is the value of f^-1(3)?

ক
4
খ
5
গ
6.5
ঘ
4.5

ব্যাখ্যা

Question: If f(x) = x/(x - 3), x ≠ 3, then what is the value of f^-1(3)?

Solution:
let, f ^-1(3) = a
f(a) = 3

f(a) = a/(a - 3)
So,
a/(a - 3) = 3
⇒ a = 3a - 9
⇒ 2a = 9
∴ a = 4.5

So, f^-1(3) = 4.5

৩,১৫৮.

There were 1000 students in a school in 2024. In 2025, 5% of the male students left, and 15% new female students joined the school. But the total number of students remained unchanged. How many female students were in the school in 2024?

ক
200
খ
225
গ
250
ঘ
275
ঙ
300

ব্যাখ্যা

Question: There were 1000 students in a school in 2024. In 2025, 5% of the male students left, and 15% new female students joined the school. But the total number of students remained unchanged. How many female students were in the school in 2024?

Solution:
ধরি, 2024 সালে ছাত্রীর সংখ্যা ছিল x
এবং ছাত্রের সংখ্যা ছিল (1000 - x)
প্রশ্ন অনুযায়ী, 2025 সালে ছাত্রীর সংখ্যা বৃদ্ধি পায় 15% এবং ছাত্রের সংখ্যা হ্রাস পায় 5%। কিন্তু মোট ছাত্রছাত্রীর সংখ্যা অপরিবর্তিত থাকে।

প্রশ্নমতে,
(x + x এর 15%) + {(1000 - x) - (1000 - x) এর 5%} = 1000
⇒ x + (15x/100) + (1000 - x) - {5(1000 - x)/100} = 1000
⇒ 15x/100 - 5(1000 - x)/100 = 0
⇒ 15x - 5(1000 - x) = 0
⇒ 15x - 5000 + 5x = 0
⇒ 20x = 5000
⇒ x = 5000/20
⇒ x = 250

সুতরাং, 2024 সালে স্কুলে ছাত্রীর সংখ্যা ছিল 250 জন।

৩,১৫৯.

Rina is 15 years older than Tania. In 5 years, Rina will be twice as old as Tania will be at that time. How old is Tania now?

ক
18
খ
15
গ
12
ঘ
10

ব্যাখ্যা

Question: Rina is 15 years older than Tania. In 5 years, Rina will be twice as old as Tania will be at that time. How old is Tania now?

Solution:
Let,
The age of Tania = x
The age of Rina = x + 20

ATQ,
x + 20 = 2(x + 5)
⇒ x + 20 = 2x + 10
⇒ x = 10

৩,১৬০.

predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey and the predator covers as much distance in 2 leaps as 3 leaps of the prey. Will the predator succeed in getting its food?

ক
ক) Yes
খ
খ) In the 6^th leap
গ
গ) Never
ঘ
ঘ) Can't be determined
ঙ
ঙ) None of these

ব্যাখ্যা

Question: predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey and the predator covers as much distance in 2 leaps as 3 leaps of the prey. Will the predator succeed in getting its food?

Solution:
শিকারীর ২ লাফের দূরত্ব = শিকারের ৩ লাফের দূরত্ব
শিকারীর ৪ লাফের দূরত্ব = শিকারের (৩ × ৪)/২ লাফের দূরত্ব
= ৬ লাফের দূরত্ব

আবার, শিকারী যে সময়ে ৪ লাফ দেয়, শিকার যে সময়ে ৬ লাফ দেয়।
∴ ৪ লাফে শিকারী শিকার ধরে ফেলবে।

৩,১৬১.

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

ক
50 kg
খ
60 kg
গ
65 kg
ঘ
54 kg

ব্যাখ্যা

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

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

প্রশ্নমতে,
6x = 72
⇒ x = 72 / 6 = 12

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

৩,১৬২.

Two trains are running in opposite directions. They cross a man standing on a platform in 28 seconds and 10 seconds respectively. They cross each other in 24 seconds. What is the ratio of their speeds?

ক
7 : 5
খ
7 : 2
গ
3 : 5
ঘ
5 : 7

ব্যাখ্যা

Question: Two trains are running in opposite directions. They cross a man standing on a platform in 28 seconds and 10 seconds respectively. They cross each other in 24 seconds. What is the ratio of their speeds?

Solution:
Given that,
Train one crosses a man in 28 seconds
Train two crosses the man in 10 seconds
They both cross each other in 24 seconds

We know,
Time = Distance/speed
As the trains travel in opposite directions, the speed of the trains added

Now,
Let the speed of the first train & second train be x m/s and y m/s respectively.
Length of the first train is 28x metres
Length of the second train is 10y meters

According to the question,
⇒ 24 = (28x + 10y)/(x + y)
⇒ 24x + 24y = 28x + 10y
⇒ 14y = 4x
⇒ x/y = 7/2

∴ The ratio of the speed of the train is 7 : 2

৩,১৬৩.

In what ratio water must be mixed with milk costing Tk. 48 per liter to get a mixture worth Tk. 32 per liter?

ক
2 : 3
খ
3 : 2
গ
3 : 4
ঘ
1 : 2

ব্যাখ্যা

Question: In what ratio water must be mixed with milk costing Tk. 48 per liter to get a mixture worth Tk. 32 per liter?

Solution:
Cost Price of water Tk. 0
Cost Price of milk Tk. 48
Mean Price of mixure Tk. 32
Let,
Quantity of water be x
Quantity of milk be y

Using the formula,

⇒ x/y = (48 - 32)/(32 - 0)
⇒ x/y = 16/32
⇒ x/y = 1/2
∴ x : y = 1 : 2

৩,১৬৪.

X and Y start a business by investing a certain amount in the ratio 9:16. Both of them invest for an equal period of time. At the end of the term, X’s share of profit is what percent less than that of Y?

ক
ক) 62(1/2)
খ
খ) 60
গ
গ) 55(2/3)
ঘ
ঘ) 43(3/4)

ব্যাখ্যা

Let, X’s investment 9x and Y’s investment 16x
X’s profit less than that of Y is = (16x - 9x)/16x × 100
= (7×100)/16
= 175/4
= 43(3/4)

৩,১৬৫.

A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash is

ক
ক) 15%
খ
খ) 9%
গ
গ) 10.5%
ঘ
ঘ) 8.5%

ব্যাখ্যা

ধরি,
বিক্রেতার ক্রয়মূল্য x টাকা
তালিকা মূল্য = x + x এর 30 %
= x + 30x/100
= 130x/100
= 13x/10
15% ছাড়ে,
বিক্রয়মূল্য = 13x/10 - 13x/10 এর 15%
= 13x/10 - (13x × 15)/(10×100)
= 13x/10 - 39x/200
= 260x - 39x/ 200
= 221x/200
লাভ = 221x/200 - x
= 221sx - 200x/ 200
= 21x/200

শতকরা লাভ হয় = (21x/200)/x 100%
= (21x/200 ×1/x 100)%
= 10.5%

৩,১৬৬.

a, b, c, d and e are five consecutive integers in increasing order of size. Which one of the following expression is not odd?

ক
a + b + c
খ
ab + c
গ
ac + e
ঘ
ac + d

ব্যাখ্যা

Question: a, b, c, d and e are five consecutive integers in increasing order of size. Which one of the following expression is not odd?

Solution:
ধরি
a = 1, b = 2, c = 3, d = 4, and e = 5,

অপশন (ক) a + b + c = 1 + 2 + 3 = 6
অপশন (খ) ab + c = 1 × 2 + 3 = 2 + 3 = 5
অপশন (গ) ac + e = 1 × 3 + 5 = 3 + 5 = 8
অপশন (ঘ) ac + d = 1 × 3 + 4 = 3 + 4 = 7

আবার
ধরি
a = 2, b = 3, c = 4, d = 5, and e = 6,

অপশন (ক) a + b + c = 2 + 3 + 4 = 9
অপশন (খ) ab + c = 2 × 3 + 4 = 6 + 4 = 10
অপশন (গ) ac + e = 2 × 4 + 6 = 8 + 6 = 14
অপশন (ঘ) ac + d = 2 × 4 + 5 = 8 + 5 = 13

উভয় ক্ষেত্রে অপশন (গ) জোড় সংখ্যা। তাই সঠিক উত্তর হিসেবে অপশন (গ) নেওয়া হয়েছে।

৩,১৬৭.

A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. How many times can it go round a cylinder with radius 20 cm?

ক
ক) 40
খ
খ) 49
গ
গ) 70
ঘ
ঘ) 100
ঙ
ঙ) None of these

ব্যাখ্যা

Let the required number of rounds be x
More radius, Less rounds (Indirect proportion)
∴ 20:14::70:x
⇔ (20×x) = (14×70)
⇔ x = (14×70)/20
⇔ x = 49

৩,১৬৮.

Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 350 kg what is total weight when it was fresh?

ক
1225 kg
খ
1475 kg
গ
1545 kg
ঘ
1575 kg

ব্যাখ্যা

Question: Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 350 kg what is total weight when it was fresh?

Solution:
Quantity of water in 350 kg dry grapes = 350 × (10/100)
= 35 kg
Then, pulp of grapes = (350 - 35) kg = 315 kg.

We get 20 kg pulp in 100 kg fresh grapes
To get 315 kg pulp, we need fresh grapes = (100 × 315)/20 kg
= 1575 kg.

৩,১৬৯.

Find the median of the given set of numbers 2, 6, 6, 8, 4, 2, 7, 9.

ক
6
খ
8
গ
4
ঘ
5

ব্যাখ্যা

Question: Find the median of the given set of numbers 2, 6, 6, 8, 4, 2, 7, 9.

Solution:
Arranging the given data in ascending order 2, 2, 4, 6, 6, 7, 8, 9
Total terms in the given data, (n) = 8 (It is even)

Median = {(8/2)^th term + (8/2 + 1)^th term}/2
= (4^th term + 5^th term)/2
= (6 + 6)/2
= 12/2
= 6

৩,১৭০.

Average cost of 5 apples and 4 mangoes is Tk. 36. The average cost of 7 apples and 8 mangoes is Tk. 48. Find the total cost of 24 apples and 24 mangoes.

ক
1044
খ
2088
গ
720
ঘ
3240

ব্যাখ্যা

Average cost of 5 apples and 4 mangoes = Tk. 36
Total cost = 36 × 9 = 324

Average cost of 7 apples and 8 mangoes = Tk. 48
Total cost = 48 × 15 = 720

Total cost of 12 apples and 12 mangoes = 324 + 720 = 1044
Therefore, cost of 24 apples and 24 mangoes = 1044 × 2 = 2088

৩,১৭১.

tanA = 3/4 হলে sinA এর মান কত?

ক
1/4
খ
3/5
গ
2/5
ঘ
4/5
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: tanA = 3/4 হলে sinA এর মান কত?

সমাধান:
sec²A = 1 + tan²A
⇒ sec²A = 1 + (3/4)²
⇒ sec²A = 1 + (9/16)
⇒ sec²A = 25/16
⇒ secA = 5/4
⇒ 1/cosA = 5/4
∴ cosA = 4/5

আমরা জানি,
sin²A = 1 - cos²A
= 1 - (4/5)²
= 1 - (16/25)
= (25 - 16)/25
∴ sin²A = 9/25
∴ sinA = 3/5

৩,১৭২.

A, B and C start a business. A invests 2 times as much as B invests 5/2 times as much as C invests. Find the ratio of capitals of A, B and C?

ক
ক) 5 : 10 : 2
খ
খ) 10 : 5 : 2
গ
গ) 10 : 5 : 3
ঘ
ঘ) 5 : 2 : 10

ব্যাখ্যা

Question: A, B and C start a business. A invests 2 times as much as B invests 5/2 times as much as C invests. Find the ratio of capitals of A, B and C?

Solution:
ধরি,
C বিনিয়োগ করে = x টাকা
B বিনিয়োগ করে = 5x/2 টাকা
A বিনিয়োগ করে = 2 × (5x/2) টাকা
= 5x টাকা
A, B এবং C এর বিনিয়োগের অনুপাত = 5x : (5x/2) : x
= 5 : (5/2) : 1
= 10 : 5 : 2

৩,১৭৩.

A, B and C are three points on the circle. If AB = AC = 7√2 cm and ∠BAC = 90° then the radius is equal to:

ক
7 cm
খ
7√2 cm
গ
14 cm
ঘ
14√2 cm
ঙ
None of these

ব্যাখ্যা

Question: A, B and C are three points on the circle. If AB = AC = 7√2 cm and ∠BAC = 90° then the radius is equal to:

Solution:

Radius = hypotenuse/2
= 14/2
= 7

৩,১৭৪.

Rahim and Karim can finish a work together in 6 hours. If Rahim takes 3 times as long as Karim to finish the job alone, how long will Karim take to finish the job alone?

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

ব্যাখ্যা

Question: Rahim and Karim can finish a work together in 6 hours. If Rahim takes 3 times as long as Karim to finish the job alone, how long will Karim take to finish the job alone?

Solution:
ধরি, করিম একা কাজটি শেষ করতে সময় নেয় = x ঘন্টা
রহিম একা কাজটি শেষ করতে সময় নেয় = 3x ঘন্টা

এখন,
করিমের 1 ঘন্টার কাজের পরিমাণ = 1/x অংশ
রহিমের 1 ঘন্টার কাজের পরিমাণ = 1/(3x) অংশ

তারা একসাথে 1 ঘন্টায় কাজ করতে পারে = (1/x) + 1/(3x)
= (3+1)/(3x)
= 4/(3x) অংশ

একসাথে কাজটি শেষ করতে সময় লাগে = 6 ঘন্টা

অর্থাৎ, 6 ঘন্টায় তারা পুরো 1টি কাজ শেষ করে

তাহলে,
(4/3x) × 6 = 1
⇒ 24/(3x) = 1
⇒ 8/x = 1
⇒ x = 8

∴ করিমের কাজটি একা শেষ করতে 8 ঘন্টা সময় লাগবে।

৩,১৭৫.

Karim and Bablu can build a wooden table in 3 days. Bablu can do it alone in 5 days. How many days would it take Karim to do this job alone?

ক
0.2
খ
7.5
গ
5.0
ঘ
6.4
ঙ
None of these

ব্যাখ্যা

Question: Karim and Bablu can build a wooden table in 3 days. Bablu can do it alone in 5 days. How many days would it take Karim to do this job alone?

Solution:
Let's say Karim's work rate per day = 1/x, where x is the days he takes alone
bablu's work rate per day = 1/5 (as he takes 5 days alone)
Together they take 3 days, so their combined rate = 1/3

ATQ,
(1/x) + (1/5) = 1/3
⇒ (5 + x)/5x = 1/3
⇒ 15 + 3x = 5x
⇒ 15 + 3x - 5x = 0
⇒ 15 - 2x = 0
⇒ 2x = 15
∴ x = 7.5

Therefore, Karim would take 7.5 days to build the table alone.

৩,১৭৬.

A tap can fill a tank in 10 minutes and another can empty it in 6 minutes. If the tank is already two-fifths full and both the tapes are opened together, how long will it take before the tank is either filled completely or emptied completely?

ক
12 min
খ
10 min
গ
8 min
ঘ
6 min

ব্যাখ্যা

Question: A tap can fill a tank in 10 minutes and another can empty it in 6 minutes. If the tank is already two-fifths full and both the tapes are opened together, how long will it take before the tank is either filled completely or emptied completely?

Solution:
Part to be emptied = 2/5 part

Net part emptied in 1 minute = 1/6 - 1/10 = (5 - 3)/30 = 2/30 = 1/15

1/15 part emptied in 1 minute
2/5 part emptied in 15 × (2/5) minute = 6 min

৩,১৭৭.

ক
7/25
খ
7/16
গ
9/25
ঘ
7/13

ব্যাখ্যা

Question:

Solution:

৩,১৭৮.

What is the difference between 0.6 and 0.6%?

ক
0.594
খ
5.94
গ
54
ঘ
60

ব্যাখ্যা

Question: What is the difference between 0.6 and 0.6%?

Solution:
Difference = 0.6 - 0.6%
= 0.6 - 0.006
= 0.594

৩,১৭৯.

Which letter in the alphabet is as far from G as T is from M?

ক
ক) N
খ
খ) O
গ
গ) P
ঘ
ঘ) M

ব্যাখ্যা

a b c d e f G h i j k l m N o p q r s t u v w x y z

৩,১৮০.

Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age?

ক
14 years and 28 years
খ
14 years and 30 years
গ
16 years and 32 years
ঘ
12 years and 28 years

ব্যাখ্যা

Question: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age?

Solution:
Let the age of an younger person be A
age of elder person = (A + 16)

According to the question, we have
3(A - 6) = (A + 16 - 6)
⇒ 3A - 18 = A + 10
⇒ 2A = 28
⇒ A = 14

∴ The younger and elder person age is 14 years old and 30 years old.

৩,১৮১.

The distance between two places A and B is 570 km. A train starts from A at 50 km/h at 6 am and another starts from B at 80 km/h at 7 am towards each other. At what time will they meet?

ক
9 am
খ
10 am
গ
11 am
ঘ
12 am

ব্যাখ্যা

Question: The distance between two places A and B is 570 km. A train starts from A at 50 km/h at 6 am and another starts from B at 80 km/h at 7 am towards each other. At what time will they meet?

Solution:
Let the two trains meet at a distance d km from place A.
Time required by the train starting from A to cover p = p/50 hr
Time taken by the other train starting from B to cover (570 - p) km = (570 - p)/80

But the first train has started 1 hr early. So, it has traveled 50 km in this 1 hr.
Therefore,
(p/50) - 1= (570 - p)/80
⇒ (p - 50)/50 = (570 - p)/80
⇒ 28500 - 50p = 80p - 4000
⇒ 130p = 32500
∴ p = 250

So, they will meet at a distance of 250 km from Place A.
So the time at which they will meet will be (250/50) = 5 hrs [after 6 am]
Hence, they will meet at 11 am.

৩,১৮২.

A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

ক
4.95 kmph
খ
5 kmph
গ
4.75 kmph
ঘ
4.65 kmph

ব্যাখ্যা

Speed downstream = 22/4 = 5.5 kmph
Speed upstream = 22/5 = 4.4 kmph
Speed of the boat in still water = (5.5 + 4.4)/2
= 4.95 kmph.

৩,১৮৩.

If |2x + 5| < 3, then for what values of p and q will p < 3x - 2 < q hold?

ক
p = - 12, q= - 3
খ
p = - 8, q = - 2
গ
p = - 10, q = - 4
ঘ
p = - 14, q = - 5

ব্যাখ্যা

Question: If |2x + 5| < 3, then for what values of p and q will p < 3x - 2 < q hold?

Solution:
Given that,
|2x + 5| < 3
⇒ - 3 < 2x + 5 < 3
⇒ - 3 - 5 < 2x + 5 - 5 < 3 - 5
⇒ - 8 < 2x < -2
⇒ - 4 < x < -1 ; [dividing by 2]
⇒ - 12 < 3x < - 3 ; [Now multiply all parts by 3]
⇒ - 12 - 2 < 3x - 2 < - 3 - 2 ; [Subtract 2 from all parts]
⇒ - 14 < 3x - 2 < - 5

Now comparing with p < 3x - 2 < q, Then we get,
∴ p = - 14 and q = - 5

৩,১৮৪.

A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

ক
Tk. 75
খ
Tk. 133
গ
Tk. 120
ঘ
Tk. 80

ব্যাখ্যা

Question: A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

Solution:
For an income of tk. 5, investment = tk. 100.
For an income of tk. 4, investment = tk. (100/5) × 4 = tk. 80.
Market value of tk. 100 stock = tk. 80.

৩,১৮৫.

The present ages of Arif, Sumon, and Saddam are in proportions 4 : 7 : 9. Before eight years, the sum of their ages was 56. What are their present ages in years?

ক
16, 28, 36
খ
16, 28, 40
গ
16, 30, 40
ঘ
Insufficient data

ব্যাখ্যা

Question: The present ages of Arif, Sumon, and Saddam are in proportions 4 : 7 : 9. Before eight years, the sum of their ages was 56. What are their present ages in years?

Solution:
Then the Present age of Arif, Sumon, and Saddam would be 4x, 7x, 9x
Age before eight years:
4x - 8, 7x - 8, 9x - 8

According to question
4x - 8 + 7x - 8 + 9x - 8 = 56
⇒ 20x = 80
⇒ x = 80/20
∴ x = 4

Then their present is 4 × 4 = 16; 7 × 4 = 28 and 9 × 4 = 36 respectively.

৩,১৮৬.

A is two years older than B who is twice as old as C. If the average of the ages of A, B and C be 9, the how old is B?

ক
ক) 8 years
খ
খ) 10 years
গ
গ) 12 years
ঘ
ঘ) 18 years

ব্যাখ্যা

Question: A is two years older than B who is twice as old as C. If the average of the ages of A, B and C be 9, the how old is B?

Solution:
তিনজনের বয়সের গড় ৯ বছর
বয়সের সমষ্টি = (৯ × ৩) বছর
= ২৭ বছর

ধরি, C এর বয়স x বছর
B এর বয়স 2x বছর
A এর বয়স 2x + 2

x + 2x + 2x + 2 = 27
⇒ 5x + 2 = 27
⇒ 5x = 25
∴ x = 5

B এর বয়স = 2x
= (2 × 5) বছর
= 10 বছর

৩,১৮৭.

A tap can fill a tank in 6hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

ক
ক) 3hrs 15min
খ
খ) 3hrs 45 min
গ
গ) 4hrs
ঘ
ঘ) 4hrs 15min

ব্যাখ্যা

Time taken by the tap to make the tank half full= 3 hrs.
Remaining part = 1/2
Part filled by 4 taps in 1 hour= (4×1/6) = 2/3
2/3 part is filled in 1 hour.
1/2 part is filled in (3/2×1/2) hr = 3/4 hr = 45 min.
Required time = 3hrs 45 min.

৩,১৮৮.

A reduction of 20% in the price of potato enables a dealer to purchase 25 kg more potato for TK. 25000. What is the reduced price per kg of potato?

ক
220 TK.
খ
200 TK.
গ
270 TK.
ঘ
300 TK.

ব্যাখ্যা

Question: A reduction of 20% in the price of potato enables a dealer to purchase 25 kg more potato for TK. 25000. What is the reduced price per kg of potato?

Solution:
Let, the original price of potato be TK.x kg
After reduction the price becomes = x − 20% of x = (4x/5) per kg
Now,
25000/(4x/5) − 25000/x = 25
or, 25000 × (5/4x) - (25000/x) = 25
or, (31250/x) - (25000/x) = 25
or, (31250 - 25000)/x = 25
or, 6250/x = 25
or, x = 6250/25
∴ x = 250 Tk.
Hence, new price = (4 × 250)/5 = 200 TK. per kg

৩,১৮৯.

A piece of wire 91 cm long is bent in the form of an isosceles triangle. If the ratio of one of the equal sides to the base is 5 : 3, then what is the length of the base?

ক
ক) 14 cm
খ
খ) 18 cm
গ
গ) 21 cm
ঘ
ঘ) 24 cm

ব্যাখ্যা

Question: A piece of wire 91 cm long is bent in the form of an isosceles triangle. If the ratio of one of the equal sides to the base is 5 : 3, then what is the length of the base?

Solution:
Given,
Ratio of one of the equal sides to the base is 5 : 3
Therefore, the sides are 5x, 3x, 5x.

91 cm piece of wire is bent to form an isosceles triangle.
Thus perimeter of triangle is 91 cm.

ATQ,
∴ 13x = 91
⇒ x = 7
Thus the length of the base = 3 × 7 = 21 cm.

৩,১৯০.

The average of a and b is 30, and the average of b and c is 40. If b = 36 than find the value of (a + c).

ক
60
খ
64
গ
68
ঘ
72

ব্যাখ্যা

Question: The average of a and b is 30, and the average of b and c is 40. If b = 36 than find the value of (a + c).

Solution:
Given b = 36

Average of a and b = 30
a + b = 30 × 2
⇒ a + b = 60
⇒ a + 36 = 60
⇒ a = 60 - 36
∴ a = 24

Average of b and c = 40
b + c = 40 × 2
⇒ b + c = 80
⇒ c = 80 - 36
∴ c = 44

Now,
a + c = 24 + 44 = 68

৩,১৯১.

One million two thousand and two is written as-

ক
ক) 102002
খ
খ) 1002002
গ
গ) 100202
ঘ
ঘ) None

ব্যাখ্যা

Question: One million two thousand and two is written as-

Solution:
১ মিলিয়ন = ১০ লাখ

১ মিলিয়িন ২ হাজার ২
= ১০ লাখ ২ হাজার ২
= ১০০২০০২

৩,১৯২.

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
makes a profit of 25%
খ
A neither losses nor gains
গ
A makes a profit of 11%
ঘ
B loses 15%

ব্যাখ্যা

Question: 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 -

Solution:
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%

৩,১৯৩.

The sum of three consecutive even integers is 42 more than the first number. What is the middle number?

ক
18
খ
20
গ
22
ঘ
None

ব্যাখ্যা

Question: The sum of three consecutive even integers is 42 more than the first number. What is the middle number?

Solution:
Let,
denote the three consecutive even integers as x, x + 2 and x + 4

ATQ,
x + (x + 2) + (x + 4) = x + 42
⇒ 3x + 6 = x + 42
⇒ 2x + 6 = 42
⇒ 2x = 36
∴ x = 18

The three consecutive even integers are 18, 20, and 22
∴ The middle number is 20

৩,১৯৪.

The number 2 - 0.5 is how many times the number 1 - 0.5?

ক
2
খ
2.5
গ
3
ঘ
3.5

ব্যাখ্যা

Question: The number 2 - 0.5 is how many times the number 1 - 0.5?

Solution:
Let,
2 - 0.5 is x times the number 1 - 0.5

So,
(2 - 0.5) = x × (1 - 0.5)
⇒ 1.5 = x × 0.5
⇒ x = 1.5/0.5
∴ x = 3

৩,১৯৫.

If 2x - 7 ≤ 11, then-

ক
x ≤ 3
খ
x ≥ - 3
গ
x ≤ 6
ঘ
x ≥ 9
ঙ
None of them

ব্যাখ্যা

Question: If 2x - 7 ≤ 11, then-

Solution:
Given,
⇒ 2x - 7 ≤ 11
⇒ 2x - 7 + 7 ≤ 11 + 7
⇒ 2x ≤ 18
∴ x ≤ 9

৩,১৯৬.

A mechanic repairs 4 cars in 5/3 hours. How many cars can he repair in 50 minutes?

ক
2
খ
21/3
গ
22/3
ঘ
25/6
ঙ
None of these

ব্যাখ্যা

Question: A mechanic repairs 4 cars in 5/3 hours. How many cars can he repair in 50 minutes?

Solution:
Here,
5/3 hours = (5/3) × 60 minutes
= 100 minutes

In 100 minutes he repairs = 4 cars
In 1 minutes he repairs = 4/100 cars
So, In 50 minutes he repairs = (4 × 50)/100 cars
= 2 cars

৩,১৯৭.

If sec²θ + tan²θ = 7, then the value of θ when 0° ≤ θ ≤ 90° is?

ক
30°
খ
45°
গ
60°
ঘ
90°

ব্যাখ্যা

Question: If sec²θ + tan²θ = 7, then the value of θ when 0° ≤ θ ≤ 90° is?

Solution:
sec²θ + tan²θ = 7
⇒ 1 + tan²θ + tan²θ = 7 - 1
⇒ 2tan²θ = 6
⇒ tan²θ = 3
⇒ tanθ = √3
⇒ tanθ = tan60°
∴ θ = 60°

৩,১৯৮.

Rahim borrowed Tk. 800 at 6% per annum and Karim borrowed Tk. 600 at 10% per annum. After how much time, will they both have equal debts?

ক
ক) 50/3 yr
খ
খ) 83/3 yr
গ
গ) 44/3 yr
ঘ
ঘ) 20/3 yr

ব্যাখ্যা

Question: Rahim borrowed Tk. 800 at 6% per annum and Karim borrowed Tk. 600 at 10% per annum. After how much time, will they both have equal debts?

Solution:
ধরি,
ক বছর পর তাদের টাকা মুনাফা আসলে একই হবে।

ক বছরে রহিমের মুনাফা আসল = ৮০০ + {(৮০০ × ক × ৬)/১০০}
ক বছরে করিমের মুনাফা আসল = ৬০০ +{(৬০০ × ক × ১০)/১০০}

প্রশ্নমতে,
৮০০ + {(৮০০ × ক × ৬)/১০০} = ৬০০ +{(৬০০ × ক × ১০)/১০০}
৮০০ + ৪৮ক = ৬০০ + ৬০ক
৬০ক - ৪৮ক = ৮০০ - ৬০০
১২ক = ২০০
ক = ২০০/১২
= ৫০/৩ বছর

৩,১৯৯.

If a² - 4a + 1 = 0, then the value of a³ + 1/a³ = ?

ক
64
খ
76
গ
52
ঘ
48

ব্যাখ্যা

Question: If a² - 4a + 1 = 0, then the value of a³ + 1/a³ = ?

Solution:
Given that,
a² - 4a + 1 = 0
⇒ a² + 1 = 4a
⇒ (a²/a) + 1/a = 4a/a
∴ a + 1/a = 4

Now,
a³ + 1/a³
= (a + 1/a)³ - 3 × a × (1/a) (a + 1/a)
= 4³ - (3 × 4)
= 64 - 12
= 52

৩,২০০.

A man paid tax on 12000 Taka at the rate of 20%. He paid the tax in 10 equal payments. what is the amount of each payment?

ক
Tk. 220
খ
Tk. 240
গ
Tk. 280
ঘ
Tk. 290

ব্যাখ্যা

Question: A man paid tax on 12000 Taka at the rate of 20%. He paid the tax in 10 equal payments. what is the amount of each payment?

Solution:
100 টাকায় কর দেয় = 20 টাকা
∴ 1 টাকায় কর দেয় = 20/100 = 1/5 টাকা
∴ 12000 টাকায় কর দেয় (20× 12000)/100 = 2400 টাকা

∴ মোট কর = 2400 টাকা

10টি সমান কিস্তিতে পরিশোধ করে।

∴ প্রতি কিস্তিতে পরিশোধ = 2400/10 = 240 টাকা