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Bank Math

PrepBank · পাতা ১৩৭ / ১৬১ · ১৩,৬০১–১৩,৭০০ / ১৬,১২৪

১৩,৬০১.
In a class of 40 students, 18 study French, 15 study Spanish, and 7 study both languages. How many students study neither language?
  1. ক
    0
  2. খ
    7
  3. গ
    10
  4. ঘ
    14
ব্যাখ্যা

Question: In a class of 40 students, 18 study French, 15 study Spanish, and 7 study both languages. How many students study neither language?

Solution:
Given that,
Total students = 40
Study French = 18
Study Spanish = 15
Study both = 7

Students studying at least one language = F + S - Both
= 18 + 15 - 7
= 26

Therefore, Students who study neither language = Total students - at least one language
= 40 - 26 = 14

∴ 14 students study neither language.

১৩,৬০২.
An article is sold at a 25% discount, resulting in a 20% profit. If the discount is reduced to 15%, what will be the new profit percentage?
  1. ক
    39%
  2. খ
    22%
  3. গ
    35%
  4. ঘ
    36%
ব্যাখ্যা

Question: An article is sold at a 25% discount, resulting in a 20% profit. If the discount is reduced to 15%, what will be the new profit percentage?

Solution:
Let the cost price (CP) be Tk. 100

With 20% profit:
Selling Price (SP) = CP + 20% profit
= 100 + 20
= Tk. 120

This SP is after 25% discount on Marked Price (MP).
∴ SP = 75% of MP 
⇒ 120 = 0.75 × MP
⇒ MP = 120 / 0.75
= Tk. 160

Now, with reduced discount of 15%:
New Selling Price = 85% of Marked Price
= 0.85 × 160
= Tk. 136

∴ New profit = New Selling Price – Cost Price 
= 136 – 100
= Tk. 36

∴ New profit percentage = (36 / 100) × 100% = 36%

১৩,৬০৩.
A train left Dhaka for Chittagong at 62 km per hour and at the same time another train left Chittagong for Dhaka at 48 km per hour on the same route. How far apart were the two trains one hour before they met?
  1. ক
    ক) 80
  2. খ
    খ) 92
  3. গ
    গ) 100
  4. ঘ
    ঘ) 110
ব্যাখ্যা

ঢাকা থেকে চট্টগ্রামগামী ট্রেনটি 1 ঘন্টায় 62 km. যায়।
চট্টগ্রাম থেকে ঢাকাগামী ট্রেনটি 1 ঘন্টায় 48 km. যায়।
∴ 1 ঘন্টায় দুটি বিপরীতমুখী ট্রেন মোট যায় (62 + 48)
= 110 km. দূরত্ব অতিক্রম করে।
অর্থাৎ মুখোমুখি হওয়ার 1 ঘন্টা আগে তাদের দুরত্ব = 110 km.

১৩,৬০৪.
The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?
  1. ক
    30%
  2. খ
    25%
  3. গ
    20%
  4. ঘ
    35%
ব্যাখ্যা
Question: The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

Solution:
We can let the original length = 4, and the original width = 10.
So the original area is 40.

When the length increases by 25% we have 4 × 1.25 = 5
Thus, for the area to remain 40, the width must be 8.

Since {(8 - 10)/10} × 100 = - 20, we see that 8 is 20 percent less than 10. In other words, the width has to decrease by 20%.
১৩,৬০৫.
In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
  1. ক
    ক) 12
  2. খ
    খ) 13
  3. গ
    গ) 14
  4. ঘ
    ঘ) 15
ব্যাখ্যা
Let n be the number of persons in the party
Number of hands shake = 105
Total number of hands shake is given by nC2
Now,
According to the question,
nC2 = 105
or, n!/(2!×(n−2)!) = 105
or, n × (n−1)/2 = 105
or, n2 − n = 210
or, n2 − n − 210 = 0
or, n = 15,−14

But, we cannot take negative value of n
So, n = 15
১৩,৬০৬.
The population of a town is 40,000. It decreases by 20 per thousand per year. Find out the population after 2 years.
  1. ক
    ক) 38416
  2. খ
    খ) 38226
  3. গ
    গ) 38484
  4. ঘ
    ঘ) 38266
ব্যাখ্যা

R = {(20 × 100)/1000)}
= 2% [percentage is calculated for twenty per thousand]
Population after 2 years
= P(1 - R/100)T
= 40000{1 - (2/100)}2
= 40000{1 - (1/50}2
= 40000(49/50)2
= (40000 × 49 × 49)/(50 × 50)
= 16 × 49 × 49
= 38416.

১৩,৬০৭.
40% of the students passed a computer science test. Of the ones who failed, 12 took a computer science course while 30 did not. What was the total number of students who took the exam?
  1. ক
    70
  2. খ
    60
  3. গ
    120
  4. ঘ
    100
ব্যাখ্যা
Question: 40% of the students passed a computer science test. Of the ones who failed, 12 took a computer science course while 30 did not. What was the total number of students who took the exam?

Solution:
পাস করতে পারে নি (১০০ - ৪০)%
= ৬০%

৬০% পরীক্ষার্থী(যারা অংশগ্রহণ করে পাশ করে নি + যারা অংশগ্রহণ করে নি) = ৩০ + ১২ জন
= ৪২ জন 

এখন,
৬০% পরীক্ষার্থী = ৪২ জন 
১% পরীক্ষার্থী = ৪২/৬০ জন 
১০০%পরীক্ষার্থী =(৪২ × ১০০)/৬০
= ৭০ জন
১৩,৬০৮.
A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-
  1. ক
    80
  2. খ
    160
  3. গ
    120
  4. ঘ
    60
ব্যাখ্যা
Question: A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

Solution:
এখানে ৪% লাভ দেয়া স্টকটি বর্তমানে ৫% লাভ দেয়।

অর্থাৎ,
বর্তমানে ৫ টাকা লাভ করতে বিনিয়োগ করতে হবে ১০০ টাকা 
বর্তমানে ১ টাকা লাভ করতে বিনিয়োগ করতে হবে ১০০/৫ টাকা 
বর্তমানে ৪ টাকা লাভ করতে বিনিয়োগ করতে হবে (১০০ × ৪)/৫ টাকা 
= ৮০ টাকা

∴ স্টকটির বাজারমূল্য ৮০ টাকা।
১৩,৬০৯.
If α and β are the zeros of the polynomial f(x) = x2 - 5x + k such that α - β = 1, find the value of k.
  1. ক
    6
  2. খ
    5
  3. গ
    3
  4. ঘ
    8
ব্যাখ্যা

Question: If α and β are the zeros of the polynomial f(x) = x2 - 5x + k such that α - β = 1, find the value of k.

Solution:
Given,
f(x) = x2 - 5x + k
α - β = 1 .................... (1)
α and β are the zeros of the polynomial.
α + β = - (- 5)
∴ α + β = 5......................... (2)

(1) + (2)
α - β = 1
α + β = 5
2α = 6
∴ α = 3

From equ. (2) 
β = 5 - 3
∴ β = 2

Now, αβ = k
⇒ k = 3 × 2
∴ k = 6

১৩,৬১০.
  1. ক
    7/4
  2. খ
    4/7
  3. গ
    1/3
  4. ঘ
    1/5
১৩,৬১১.
The ratio, in which tea costs Tk. 192 per kg is to be mixed with tea costing Tk. 150 per kg so that the mixed tea when sold for Tk. 194.40 per kg, gives a profit of 20%
  1. ক
    2 : 5
  2. খ
    3 : 5
  3. গ
    5 : 3
  4. ঘ
    5 : 2
ব্যাখ্যা

CP of first tea = Tk. 192 per kg.
CP of Second tea = Tk. 150 per kg.
The mixture is to be sold in Tk. 194.40 per kg, which has included 20% profit. So,
SP of Mixture = Tk. 194.40 per kg.

Let the CP of Mixture be Tk. X per kg. Therefore,
X + 20% of X = SP
6x/5 = 194.40
6X = 194.40 × 5
X = Tk. 162 per kg.

Let N kg of first tea and M kg of second tea be added.

Now, Using Alligation,
We get,
N/M = 12/30
N/M = 2 : 5

.
১৩,৬১২.
At the end of a business conference, all 9 people present shake hands with each other once. How many handshakes will there be altogether?
  1. ক
    ক) 45
  2. খ
    খ) 42
  3. গ
    গ) 36
  4. ঘ
    ঘ) 32
ব্যাখ্যা
Number of handshakes in a conference = n(n - 1)​/2 where n being the number of people.

Given, there  are 9 people present in the conference.
So, number of handshakes in the conference = 9(9 - 1)​/2 = 36
১৩,৬১৩.
The area of a triangle with sides 3 cm, 5 cm and 6 cm is?
  1. ক
    ক) 2√3 cm2
  2. খ
    খ) 4√14 cm2
  3. গ
    গ) 2√14 cm2
  4. ঘ
    ঘ) 2√5 cm2
ব্যাখ্যা

অর্ধ পরিসীমা, s = (3+5+6) / 2 = 7
ক্ষেত্রফল = √{s(s-a)(s-b)(s-c)}
= √{7(7-3)(7-5)(7-6)}
= √(7×4×2×1)
= √56
= √(4 x 14)
= 2√14

১৩,৬১৪.
In how many ways a committee of 5 men and 6 women can be formed from 8 men and 10 women?
  1. ক
    ক) 266
  2. খ
    খ) 11,760
  3. গ
    গ) 5020
  4. ঘ
    ঘ) 4580
ব্যাখ্যা
Given that 
Men = 8 
Women = 10

Required number of ways =8C5 × 10C6
                                          = 56 × 210
                                          = 11,760
১৩,৬১৫.
If the average of 5 consecutive integers is 15 then what is the difference between least and the greatest of the 5 integers?
  1. ক
    4
  2. খ
    5
  3. গ
    8
  4. ঘ
    10
  5. ঙ
    None of these
ব্যাখ্যা
প্রশ্ন: If the average of 5 consecutive integers is 15 then what is the difference between least and the greatest of the 5 integers?

সমাধান:
ধরি, পাঁচটি ক্রমিক সংখ্যা x,  x + 1,  x + 2,  x + 3,  x + 4

পাঁচটি ক্রমিক সংখ্যার গড় = 15
পাঁচটি সংখ্যার সমষ্টি = 15 × 5 = 75 

প্রশ্নমতে,
x + x + 1 + x + 2 + x + 3 + x + 4 = 75
⇒ 5x + 10 = 75
⇒ 5x = 65 
∴ x = 13

সবচেয়ে ছোট সংখ্যাটি = 13
সবচেয়ে বড় সংখ্যাটি = 13 + 4 = 17

∴ সবচেয়ে বড় সংখ্যা ও সবচেয়ে ছোট সংখ্যার পার্থক্য = 17 - 13 = 4
১৩,৬১৬.
Which one of the following figure is different from the rest three?
  1. ক
    ক)
  2. খ
    খ)
  3. গ
    গ)
  4. ঘ
    ঘ)
ব্যাখ্যা
প্রশ্ন: Which one of the following figure is different from the rest three?




সমাধান: 
সবগুলো চিত্র আড়াআড়ি (×) দাগ দ্বারা ৪ ভাগে বিভক্ত হয়েছে, কেবলমাত্র গ বা ৩ নং চিত্র ছাড়া।
তাই, গ এর চিত্রটি ভিন্ন। 
১৩,৬১৭.
A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days. How many days will they take if they work together?
  1. ক
    ক) 8 days
  2. খ
    খ) 10 days
  3. গ
    গ) 11 days
  4. ঘ
    ঘ) 12 days
ব্যাখ্যা

3 men's 1 day's work = 1/20;
5 boy's 1 day's work = 1/30.
(3 men + 5 boys)'s 1 day's work = (1/20) + (1/30)
= 5/60
= 1/12.
∴ 3 men and 5 boys will complete the work in 12 days.

১৩,৬১৮.
The average of three consecutive multiples of 7 is 70. What is the largest of these three multiples?
  1. ক
    90
  2. খ
    87
  3. গ
    77
  4. ঘ
    67
  5. ঙ
    None
ব্যাখ্যা

Question: The average of three consecutive multiples of 7 is 70. What is the largest of these three multiples?

Solution:
Let the three consecutive multiples of 7 be 7x, 7x + 7, 7x + 14.

Average = {(7x + (7x + 7) + (7x + 14))}/3
= (21x + 21)/3

As per the question,
(21x + 21)/3 = 70
⇒ 21x + 21 = 210
⇒ 21x = 189
⇒ x = 189/21
∴ x = 9

So, the largest multiple is 7x + 14 = 63 + 14 = 77.

১৩,৬১৯.
Six years ago, Hena was 1/4th of the age she will be after 12 years from now. How old is she now?
  1. ক
    6 years
  2. খ
    8 years
  3. গ
    12 years
  4. ঘ
    24 years
ব্যাখ্যা

Question: Six years ago, Hena was 1/4th of the age she will be after 12 years from now. How old is she now?

Solution:
ধরি
হেনার বর্তমান বয়স = x বছর
6 বছর পূর্বে হেনার বয়স ছিলো = x - 6 বছর
12 বছর পর হেনার বয়স হবে = x + 12 বছর

প্রশ্নমতে
x - 6 = (1/4)(x + 12)
বা, 4x - 24 =  x + 12 
বা, 4x - x = 24 + 12
বা, 3x = 36
∴ x = 12
হেনার বর্তমান বয়স = 12 বছর

১৩,৬২০.
There are 48 books on 3 shelves. If 3 books from third shelf are shifted to the second there will be same number of books on first and third shelves and double the number of books on second shelf. How many books were there on three shelves originally?
  1. ক
    ক) 10, 25,13
  2. খ
    খ) 12, 21,15
  3. গ
    গ) 11, 23, 14
  4. ঘ
    ঘ) 13, 19, 16
  5. ঙ
    ঙ) None
ব্যাখ্যা
Suppose, the first shelf had x books.
So, the third shelf had x+3 books.
And the second shelf had 2x-3 books.
According to the question,
x + x+3 + 2x-3 = 48
4x = 48
x = 12
1st shelf = 12, 2nd shelf = 2×12-3 = 21, 3rd shelf = 12+3 = 15.
১৩,৬২১.
The length of a rectangular plot is 3 folds its width. Half the area of the plot is covered by a playground whose area is 363 square meter. What is the length of the plot?
  1. ক
    ক) 18.50m
  2. খ
    খ) 46.67m
  3. গ
    গ) 17.21m
  4. ঘ
    ঘ) 15.51m
ব্যাখ্যা
Question: The length of a rectangular plot is 3 folds its width. Half the area of the plot is covered by a playground whose area is 363 square meters. What is the length of the plot?

Solution: 
let the width is = x
the length is = 3x

ATQ,
3X2 = 2 × 363
x2 = 242
x = 15.556

the length = 3 × 15.556 = 46.67m
১৩,৬২২.
A jogger is running at a speed of 15 km/hr. In what time he will cross a track of length 400 meters?
  1. ক
    96 sec
  2. খ
    100 sec
  3. গ
    104 sec
  4. ঘ
    110 sec
ব্যাখ্যা
Question: A jogger is running at a speed of 15 km/hr. In what time he will cross a track of length 400 meters?

Solution:
Speed = 15 km/hr = 15 × (5/18) m/s = 75/18 m/s
Distance = 400 meters

∴ Required time = 400/(75/18) sec
= (400 × 18)/75 sec
= 96 sec
১৩,৬২৩.
A train is moving at 120 km/hr. The length of the train is 150 meters. How long it will take to cross a platform of length 100 meters?
  1. ক
    10 seconds
  2. খ
    7.5 seconds
  3. গ
    20 seconds
  4. ঘ
    25 seconds
  5. ঙ
    None of these
ব্যাখ্যা
Question: A train is moving at 120 km/hr. The length of the train is 150 meters. How long it will take to cross a platform of length 100 meters?

Solution:
Speed of train in m/s = 120 × (5/18) m/s = 100/3 m/s
Distance covered to cross the platform is equal to the sum of length of the train and length of the platform.
So, distance= 150 + 100 = 250 meters

Time = distance/speed
= 250 × (3/100)
= 7.5 sec
১৩,৬২৪.
একটি ট্রাপিজিয়ামের ক্ষেত্রফল 25 ব‍র্গফুট। ট্রাপিজিয়ামের দুই বাহুর মধ্যব‍র্তী উচ্চতা 2 ফুট এবং সমান্তরাল দুই বাহুর একটি অপরটি হতে 1 ফুট বেশি হলে বৃহত্তর বাহুর দৈ‍র্ঘ্য কত?
  1. ক
    25 ফুট
  2. খ
    15 ফুট
  3. গ
    13 ফুট
  4. ঘ
    12 ফুট
  5. ঙ
    10 ফুট
ব্যাখ্যা
প্রশ্ন: একটি ট্রাপিজিয়ামের ক্ষেত্রফল 25 ব‍র্গফুট। ট্রাপিজিয়ামের দুই বাহুর মধ্যব‍র্তী উচ্চতা 2 ফুট এবং সমান্তরাল দুই বাহুর একটি অপরটি হতে 1 ফুট বেশি হলে বৃহত্তর বাহুর দৈ‍র্ঘ্য কত?

সমাধান:
ধরি,
সমান্তরাল ক্ষুদ্রতর বাহুর দৈ‍র্ঘ্য = x ফুট
সমান্তরাল বৃহত্তর বাহুর দৈ‍র্ঘ্য = (x + 1) ফুট

আমরা জানি,
ট্রাপিজিয়ামের ক্ষেত্রফল = (1/2) × সমান্তরাল বাহুদ্বয়ের মধ্যবর্তী দূরত্ব × সমান্তরাল বাহুদ্বয়ের সমষ্টি  

প্রশ্নমতে,
(1/2) . 2 . (x + x + 1) = 25
বা, 2x + 1 = 25
বা, 2x = 24
∴ x = 12

∴ বৃহত্তর বাহুর দৈ‍র্ঘ্য = 12 + 1 = 13
১৩,৬২৫.
If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is -
  1. ক
    10 km/hr
  2. খ
    12 km/hr
  3. গ
    13 km/hr
  4. ঘ
    14 km/hr
ব্যাখ্যা
42 minutes = (42/60) hours = (7/10) hour
Rate upstream = 7 km / (7/10) hour = 10 km/hour
Speed of stream = 3 kmph.
Let speed in still water is x km/hr
Then, speed upstream = (x - 3) km/hr.
∴ x - 3 = 10 or x = 13 kmph
১৩,৬২৬.
A solution contains 20% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-
  1. ক
    40%
  2. খ
    20.36%
  3. গ
    40.36%
  4. ঘ
    33.33%
ব্যাখ্যা
Question: A solution contains 20% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-

Solution: 
let, solution is 100 unit
amount of sugar = 100 × 20%
= 100 × (20/100)
= 20 unit 

by doubling, amount of sweet = 40 unit

solution now = 100 + 20 = 120 unit 

percent of sugar = (40 × 100)/120 %
= 33.33%

 
১৩,৬২৭.
An employer pays 3 workers X, Y and Z a total of Tk. 36,600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week? 
  1. ক
    ক) 9,000
  2. খ
    খ) 10,800
  3. গ
    গ) 11,700
  4. ঘ
    ঘ) 12,000
ব্যাখ্যা
X = 125% of Y = 125Y/100 = 5Y/4
⇒ Y = 4X/5
Again,
X = 80% of Z = 80Z/100 = 4Z/5
⇒ Z = 5X/4
X : Y : Z  = X : 4X/5 : 5X/4 = 20 : 16 : 25
Sum of ratio = 20 + 16 + 25 = 61
So, X makes a week = (20/61) × 36600
                               = 20 × 600
                                = 12000 tk.
১৩,৬২৮.
A train with 20m/s velocity and 200m length is crossing a person with 5m/s velocity. If the person is coming towards the train, it will cross the person in - 
  1. ক
    ক) 6 seconds
  2. খ
    খ) 8 seconds
  3. গ
    গ) 7 seconds
  4. ঘ
    ঘ) 10 seconds
ব্যাখ্যা
Question: A train with 20m/s velocity and 200m length is crossing a person with 5m/s velocity. If the person is coming towards the train, it will cross the person in - 

Solution: 
যেহেতু ট্রেন ও ব্যক্তি পরস্পর অভিমুখে আসে তাহলে তাদের আপেক্ষিক বেগ = (২০ + ৫) = ২৫ মি/সে

তাহলে, ব্যক্তিকে অতিক্রম করতে সময় লাগবে = ২০০/২৫ = ৮ সেকেন্ড
১৩,৬২৯.
There are 6 red, 5 blue, and 7 yellow balls in a bag. If a ball is picked at random, what is the probability of having either a red or a blue ball?
  1. ক
    5/18
  2. খ
    1/3
  3. গ
    2/3
  4. ঘ
    11/18
ব্যাখ্যা

Question: There are 6 red, 5 blue, and 7 yellow balls in a bag. If a ball is picked at random, what is the probability of having either a red or a blue ball?

Solution:
ব্যাগে মোট বলের সংখ্যা = 6 + 5 + 7 = 18 টি।

লাল বল পাওয়ার সম্ভাবনা = 6/18
নীল বল পাওয়ার সম্ভাবনা = 5/18

∴ লাল অথবা নীল বল পাওয়ার সম্ভাবনা = (6/18) + (5/18)
​= (6 + 5)/18
​= 11/18

১৩,৬৩০.
A number is doubled and 9 is added. If the resultant is tripled, it becomes 81. What is that number?
  1. ক
    ক) 8
  2. খ
    খ) 9
  3. গ
    গ) 10
  4. ঘ
    ঘ) 11
ব্যাখ্যা
Question: A number is doubled and 9 is added. If the resultant is tripled, it becomes 81. What is that number?

Solution: 
Let
The number be x

Now
3(2x + 9) = 81
⇒ 6x + 27 = 81
⇒ 6x = 81 - 27
⇒ 6x = 54
⇒ x = 54/6
⇒ x = 9

∴ The number is 9
১৩,৬৩১.
A man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son.
  1. ক
    25.7 years
  2. খ
    28 years
  3. গ
    29.3 years
  4. ঘ
    36 years
  5. ঙ
    None of these
ব্যাখ্যা
Question: A man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son.

Solution:
Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 1/3 of P.
(48 - P) = (1/3)P
⇒ 144 - 3P = P
⇒ 4P = 144
∴ P = 36
১৩,৬৩২.
The area of a rectangular classroom is x2 - 25. Which of the following binomials could represent the length and the width of the room.
  1. ক
    ক) (x + 5) (x + 5)
  2. খ
    খ) (x - 5) (x - 5)
  3. গ
    গ) (x + 5) (x - 5)
  4. ঘ
    ঘ) x(x - 25)
ব্যাখ্যা
Given, x2 - 25
= x2 - 52
= (x + 5)(x - 5)
১৩,৬৩৩.
In a social gathering, 12 people shake hands with each other. How many handshakes were there in total?
  1. ক
    30
  2. খ
    66
  3. গ
    84
  4. ঘ
    108
ব্যাখ্যা

Question: In a social gathering, 12 people shake hands with each other. How many handshakes were there in total?

Solution:
একটি হ্যান্ডশেক সম্পন্ন করতে 2 জন ব্যক্তির প্রয়োজন হয়। তাই 12 জন ব্যক্তি থেকে 2 জনকে কতভাবে বাছাই করা যায়, সেটিই হবে মোট হ্যান্ডশেক সংখ্যা।

এখানে মোট ব্যক্তি, n = 12
প্রতিবার হ্যান্ডশেক করতে লাগে, r = 2

সূত্রমতে, মোট হ্যান্ডশেক সংখ্যা = nC2
 = n(n - 1)/2
= 12(12 - 1)/2
= (12 × 11)/2
= 132/2
= 66

১৩,৬৩৪.
If the selling price is tripled, the profit becomes eight times. Find the profit percent.
  1. ক
    25%
  2. খ
    40%
  3. গ
    50%
  4. ঘ
    55%
ব্যাখ্যা
Question: If the selling price is tripled, the profit becomes eight times. Find the profit percent.

Solution:
Let,
The cost price be Tk.100 and sell price be Tk. x,

Then,
The profit is = (x - 100)

Now, The sell price is doubled, then the new sell price is 3x
New profit is = (3x - 100)

ATQ,
8(x - 100) = 3x - 100
⇒ 8x - 800 = 3x - 100
⇒ 8x - 3x = 800 - 100
⇒ 5x = 700
∴ x = 140

Then, the Profit = (140 - 100) = 40
Hence the profit percentage is = (40/100) × 100%
= 40%
১৩,৬৩৫.
In an AP, The 7th term is 3 times of 2nd term. If the 5th term is 11, what is the 20th term?
  1. ক
    ক) 43
  2. খ
    খ) 41
  3. গ
    গ) 39
  4. ঘ
    ঘ) 38
ব্যাখ্যা
Question: In an AP, The 7th term is 3 times of 2nd term. If the 5th term is 11, what is the 20th term?

Solution:
The 2nd term is a + d.
The 7th term is a + 6d 

ATQ,
3(a + d) = a + 6d
⇒ 3a + 3d = a + 6d
⇒ 2a = 3d
∴ a = (3d)/2

The 5th term is  a + 4d = 11
⇒ (3d)/2 + 4d = 11
⇒ 3d + 8d = 22
⇒ 11d = 22
∴ d = 2

∴ a = (3 × 2)/2 = 3

∴ The 20th term is: a + 19d
= 3 + 19 × 2
= 3 + 38
= 41
১৩,৬৩৬.
The difference between two numbers is 5 and the difference between their squares is 65. What is the larger number?
  1. ক
    ক) 13
  2. খ
    খ) 11
  3. গ
    গ) 8
  4. ঘ
    ঘ) 9
ব্যাখ্যা
প্রশ্ন: The difference between two numbers is 5 and the difference between their squares is 65. What is the larger number?

সমাধান:
ধরি,
বৃহত্তম সংখ্যাটি = x 
ক্ষুদ্রতম সংখ্যাটি = y 

প্রশ্নমতে,
x - y = 5 ..............(1)
x2 - y2 = 65 ..............(2)

(2)নং সমীকরণ হতে পাই,
x2 - y2 = 65
(x + y)(x - y) = 65
(x + y) × 5 = 65 
x + y = 13.................(3) 

(1) + (3)⇒
x - y + x + y = 5 + 13
2x = 18
x = 9
১৩,৬৩৭.
A man completes 5/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?
  1. ক
    ক) 4
  2. খ
    খ) 3
  3. গ
    গ) 6
  4. ঘ
    ঘ) 2
ব্যাখ্যা
Work done = 5/8
Balance work =(1 - 5/8) = 3/8
Let the required number of days be x.
Then,(5/8 : 3/8) :: 10 : x
⇒ 5/8 × x = 3/8 × 10
⇒ x = 3/8 × 10 × 8/5
⇒ x = 6.
১৩,৬৩৮.
25% of the candidates failed in English and 35% failed in Math. If 15% failed in both subjects, what percentage passed both English and Math?
  1. ক
    30%
  2. খ
    45%
  3. গ
    55%
  4. ঘ
    60%
ব্যাখ্যা
Question: 25% of the candidates failed in English and 35% failed in Math. If 15% failed in both subjects, what percentage passed both English and Math?
(২৫% প্রার্থীর ইংরেজি পরীক্ষায় এবং ৩৫% গণিত পরীক্ষায় ফেল হয়েছে। ১৫% প্রার্থী উভয় বিষয়েই ফেল করেছে, তাহলে কত শতাংশ প্রার্থী ইংরেজি ও গণিত উভয় বিষয়েই পাস করেছে?)

Solution:
ইংরেজি এবং গণিত উভয় বিষয়ে ফেল করেছেন = 15%
শুধুমাত্র ইংরেজিতে ফেল করেছেন = (25 - 15)% = 10%
শুধুমাত্র গণিতে ফেল করেছেন = (35 - 15)% = 20%

∴ এক বা দুটি বিষয়ে ফেল করা প্রার্থী সংখ্যা = 15% + 10% + 20% 
= 45%

∴ উভয় বিষয়েই পাশ করা প্রার্থী সংখ্যা = (100 - 45)% = 55%
১৩,৬৩৯.
The product of three consecutive natural numbers is always divisible by
  1. ক
    ক) 6
  2. খ
    খ) 7
  3. গ
    গ) 13
  4. ঘ
    ঘ) 11
ব্যাখ্যা
Let n, n + 1, n + 2 be three consecutive natural numbers and P(n) be their product.

We have,
n= 1 ⇒ n(n + 1)(n + 2) =1 × 2 × 3 = 6, which is divisible by 3 and 6.
n= 2 ⇒ n(n + 1)(n + 2) =2 × 3 × 4 = 24, which is divisible by 3, 8 and 6.
n= 3 ⇒ n(n + 1)(n + 2) =3 × 4 × 5 = 60, which is divisible by 3 and 6.
n= 4 ⇒n(n + 1)(n + 2) =4 × 5 × 6 = 120, which is divisible by 3, 8 and 6.

Hence, n(n + 1)(n + 2) is divisible by 3 and 6 for all  n∈ N.
১৩,৬৪০.
On a certain map of India the actual distance of 1450 km between two cities Teknaf and Tetulia is shown as 5 cm. What scale is used to draw the map?
  1. ক
    ক) 1 : 29 × 106
  2. খ
    খ) 3 : 29 × 106
  3. গ
    গ) 5 : 29 × 106
  4. ঘ
    ঘ) 1.5 : 29 × 106
ব্যাখ্যা
cm on the map represents 1450 km
∴ 1 cm on the map represents (1450/5 km = 290 km
Hence,
the scale is 1 cm : 290 km
= 1cm : 29 × 106cm
= 1 : 29 × 106
১৩,৬৪১.
১০০০ টাকা ১২% চক্রবৃদ্ধি মুনাফা হারে বিনিয়োগ করলে ২ বছর পরে লাভসহ কত হবে?
  1. ক
    ক) ১২৫৪.৪০ টাকা
  2. খ
    খ) ১২৪৪.৫০ টাকা
  3. গ
    গ) ১২৬৪.৪০ টাকা
  4. ঘ
    ঘ) ১৩৫৫.৪০ টাকা
ব্যাখ্যা
প্রশ্ন: ১০০০ টাকা ১২% চক্রবৃদ্ধি মুনাফা হারে বিনিয়োগ করলে ২ বছর পরে লাভসহ কত হবে?

সমাধান:
দেওয়া আছে,
মুনাফার হার, r = ১২% = ১২/১০০ = ০.১২ 
মূলধন, P = ১০০০ টাকা 
সময়, n = ২ বছর 

আমরা জানি, 
চক্রবৃদ্ধি মূলধন, C = P( ১ + r)n টাকা 
= ১০০০(১ + ০.১২)২ টাকা 
= ১০০০ × ১.১২ × ১.১২ টাকা 
= ১২৫৪.৪০ টাকা 

∴ ২ বছর পর লাভসহ ১২৫৪.৪০ টাকা হবে। 
১৩,৬৪২.
Raju swims 26 km downstream in same time as 14 km upstream. What is his speed in still water if speed of stream is 3 km/hr?
  1. ক
    10 km/hr
  2. খ
    11 km/hr
  3. গ
    9 km/hr
  4. ঘ
    12 km/hr
  5. ঙ
    8 km/hr
ব্যাখ্যা

Question: Raju swims 26 km downstream in same time as 14 km upstream. What is his speed in still water if speed of stream is 3 km/hr?

Solution:
Let Raju's speed in still water = x km/hr
Speed of stream = 3 km/hr

∴ Downstream speed = x + 3 km/hr
∴ Upstream speed = x - 3 km/hr

Given that, 
Time taken to swim 26 km downstream = Time taken to swim 14 km upstream
⇒ 26/(x + 3) = 14/(x − 3)  ; [Time = Distance / Speed]
⇒ 26(x - 3) = 14(x + 3)
⇒ 26x - 78 = 14x + 42
⇒ 26x - 14x = 42 + 78
⇒ 12x = 120
⇒ x = 120/12
∴ x = 10

So Raju's speed in still water is 10 km/hr.

১৩,৬৪৩.
A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of the total marks in Bangla How much does he score in Bangla?
  1. ক
    62
  2. খ
    66
  3. গ
    68
  4. ঘ
    72
ব্যাখ্যা
Question: A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of the total marks in Bangla How much does he score in Bangla?

Solution:
৮ টি বিষয়ে মোট নম্বর = 8 × 100 = 800
সে নম্বর পেয়েছে = 800 এর 55%
= 800 এর 55/100
= 440

সে বাংলায় নম্বর পেয়েছে = 440 এর 15%
= 440 এর 15/100
= 66
১৩,৬৪৪.
যদি x = - 3 হয় এবং y = 2 হয়, তবে xy2 = কত?
  1. ক
    36
  2. খ
    - 36
  3. গ
    - 12
  4. ঘ
    12
ব্যাখ্যা
প্রশ্ন: যদি x = -3 হয় এবং y = 2 হয়, তবে xy2 = কত?

সমাধান:
দেওয়া আছে,
x = - 3
এবং y = 2

∴ xy2 = - 3 × 22
= - 3 × 4
= - 12
১৩,৬৪৫.
A can do a piece of work in 10 days and B can do the same piece of work in 15 days. A and B together complete the same piece of work and get Tk. 600 as the combined wages. A's share of the wages will be- 
  1. ক
    Tk. 300
  2. খ
    Tk. 260
  3. গ
    Tk. 360
  4. ঘ
    Tk. 460
ব্যাখ্যা

Question: A can do a piece of work in 10 days and B can do the same piece of work in 15 days. A and B together complete the same piece of work and get Tk. 600 as the combined wages. A's share of the wages will be-

Solution:
A এর 1 দিনের কাজ = 1/10
B এর 1 দিনের কাজ = 1/15

(A + B) একত্রে 1 দিনের কাজ = (1/10) + (1/15)
= (3 + 2)/30
= 5/30
= 1/6

∴ (A + B) এর 1 দিনের কাজের অনুপাত = (1/10) : (1/15) = 3 : 2

∴ A এর শেয়ার = {(3/5) × 600} = 360 টাকা

১৩,৬৪৬.
The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by-
  1. ক
    10%
  2. খ
    12%
  3. গ
    20%
  4. ঘ
    25% 
ব্যাখ্যা

Question: The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by-

Solution:
২৫% বৃদ্ধিতে দাম = (১০০ + ২৫) = ১২৫টাকা।
 
১২৫ টাকায় চিনি খাওয়া কমে = ১২৫ - ১০০ = ২৫ টাকা
∴ ১ টাকায় চিনি খাওয়া কমে = ২৫/১২৫ টাকা
∴ ১০০ টাকায় চিনি খাওয়া কমে = (২৫ × ১০০)/১২৫
= ২০ টাকা
 
অর্থাৎ, শতকরা ২০% কমিয়েছিল

১৩,৬৪৭.
The simplified value of
 
  1. ক
    2
  2. খ
    3
  3. গ
    4
  4. ঘ
    6
ব্যাখ্যা
Question: The simplified value of
 

Solution:
১৩,৬৪৮.
What is the next number in the series 1, 4, 9, 16.......?
  1. ক
    ক) 25
  2. খ
    খ) 23
  3. গ
    গ) 21
  4. ঘ
    ঘ) 31
ব্যাখ্যা
এখানে,
12 = 1
22 = 4
32 = 9 
42 = 16 
52 = 25
১৩,৬৪৯.
If x : 7.5 = 7 : 17.5, then the value of x is-
  1. ক
    ক) 1
  2. খ
    খ) 2.5
  3. গ
    গ) 3
  4. ঘ
    ঘ) 3.5
  5. ঙ
    ঙ) 4
ব্যাখ্যা

x:7.5 = 7:17.5
⇒ 17.5x = 7.5×7
⇒ x = (7.5×7)/17.5
= 3

১৩,৬৫০.
What is the height of a right cylinder with radius 5 in and volume 150Π in3 ?
  1. ক
    ক) 5 in
  2. খ
    খ) 6 in
  3. গ
    গ) 7 in
  4. ঘ
    ঘ) 8 in
ব্যাখ্যা

দেওয়া আছে, সিলিন্ডারের ব্যাসার্ধ 5 ইঞ্চি এবং আয়তন 150π ঘন ইঞ্চি। 
আমরা জানি,
সিলিন্ডারের আয়তন = πr2h
প্রশ্নমতে, πr2h = 150π
      ⇒ π52h = 150π [যেহেতু, r = 5 ইঞ্চি]
      ⇒ 25πh = 150π
               ∴ h = 6 in

১৩,৬৫১.
If x2 + yz + zx + xy is divided by x + y, the result is-
  1. ক
    (x - y)
  2. খ
    (x - z)
  3. গ
    (x + y)
  4. ঘ
    (x + z)
ব্যাখ্যা

Question: If x2 + yz + zx + xy is divided by x + y, the result is-

Solution:
x2 + yz + zx + xy
= x2 + xy + zx + yz
= x(x + y) + z(x + y)
= (x + y)(x + z)

∴ divided by (x + y) the result = (x + y)(x + z)/(x +y) = (x + z)

১৩,৬৫২.
If log10000x = - 1/4, then the value of x = ?
  1. ক
    1
  2. খ
    1/10
  3. গ
    1/100
  4. ঘ
    1/1000
  5. ঙ
    1/10000
ব্যাখ্যা
log10000x = - 1/4
or, x = 10000-1/4
or, x = (104)-1/4
or, x = 10-1
∴ x = 1/10
১৩,৬৫৩.
An employer pays 3 workers X, Y and Z a total of TK. 36600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?
  1. ক
    9000
  2. খ
    10800
  3. গ
    11700
  4. ঘ
    12000
ব্যাখ্যা
Question: An employer pays 3 workers X, Y and Z a total of TK. 36600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?

Solution:
X = 125% of Y
⇒ X = 125Y/100
⇒ X/Y = 125/100
∴ X : Y = 5 : 4 = 5 × 4 : 4 × 4 = 20 : 16

X = 80% of Z
⇒ X = 80Z/100
⇒ X/Z = 80/100
∴ X : Z = 4 : 5 = 4 × 5 : 5 × 5 = 20 : 25

∴ X : Y : Z = 20 : 16 : 25

X makes the week = (20/61) × 36600
= 12000
১৩,৬৫৪.
HCF of two number is 4 and the sum of those two numbers is 36. Find how many such pair of number is possible.
  1. ক
    ক) 1
  2. খ
    খ) 2
  3. গ
    গ) 3
  4. ঘ
    ঘ) 4
ব্যাখ্যা
HCF of two number is 4
Let, those numbers be 4x and 4y where x and y are prime to each other Accordingly,
4x + 4y = 36
⇒ 4(x + y) = 36
⇒ (x + y) = 9
Now,
9 = 8 + 1
9 = 7 + 2
9 = 6 + 3
9 = 5 + 4
In all these cases only (8, 1); (7, 2); and (5, 4) are prime to each other.
So, such three pair is possible
∴ Such three pair of number is possible.
 
To find the pairs we only can take those pair, which are prime to each other. 
We can't take those pair, which are not prime to each other. 
For example: In this problem, 9 can be represent as 6 + 3 = 9 
But, 6 & 3 are not prime to each other. 
So, it can't be a possible pair.
১৩,৬৫৫.
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
  1. ক
    3/4
  2. খ
    1/6
  3. গ
    2/5
  4. ঘ
    3/5
ব্যাখ্যা
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

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

Now,
E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

∴ n(E) = 27
∴P(E) = n(E)/n(S)
= 27/36
= 3/4
১৩,৬৫৬.
The numbers 2, 3, 5 and x have an average equal to 4. What is the value of x?
  1. ক
    ক) 4
  2. খ
    খ) 6
  3. গ
    গ) 8
  4. ঘ
    ঘ) 10
ব্যাখ্যা

(2 + 3 + 5 + x)/4 = 4
Or, 2 + 3 + 5 + x = 4×4
Or, x = 16 - 10 = 6

১৩,৬৫৭.
A train takes 10 seconds to cross a pole and 20 seconds to cross a platform of length 200m. What is the length of the train?
  1. ক
    ক) 400m
  2. খ
    খ) 600m
  3. গ
    গ) 200m
  4. ঘ
    ঘ) 800m
ব্যাখ্যা
l/10 = (200 + l)/20
2l - l = 200
l = 200m
১৩,৬৫৮.
A fruit seller purchases guavas at the rate of 2 guavas for 1 taka and sells them at the rate of 5 guavas for 3 taka. What is his gain percentage?
  1. ক
    22% 
  2. খ
    18% 
  3. গ
    15%
  4. ঘ
    20%
  5. ঙ
    None
ব্যাখ্যা

Question: A fruit seller purchases guavas at the rate of 2 guavas for 1 taka and sells them at the rate of 5 guavas for 3 taka. What is his gain percentage?

Solution:
2 guavas cost 1 tk
So 1 lemon costs 1/2 tk

For comparing,
let's calculate CP (Cost Price) for 10 guavas
∴ CP of 10 guavas = 10 × (1/2) = 5 tk

Now,
Let's find the selling price (SP) of guavas:
5 guavas cost 3 tk
∴ 10 guavas will cost = (10/5) × 3 = 6 tk

∴ Gain = SP - CP = 6 - 5 = 1 tk
∴ Gain percentage = (Gain/CP) × 100
= (1/5) × 100
= 20%

১৩,৬৫৯.
A question paper has two parts, A and B, each containing 5 questions. If a student has to choose 3 from part A and 2 from part B, in how many ways can he choose the questions?
  1. ক
    80
  2. খ
    90
  3. গ
    100
  4. ঘ
    120
ব্যাখ্যা
Question: A question paper has two parts, A and B, each containing 5 questions. If a student has to choose 3 from part A and 2 from part B, in how many ways can he choose the questions?

Solution:
ways to choose 3 from part A = 5C3
ways to choose 2 from part B = 5C2

Choose 3 from part A and 2 from part B = 5C3 × 5C2
= {5!/(3! 2!)} × {5!/(2! 3!)}
= 10 × 10
= 100
১৩,৬৬০.
10 people can do a work in 4 days working 6 hours a day. If 5 new people join the team to complete the work in 2 days, they have to work per day for -
  1. ক
    ক) 8 hours
  2. খ
    খ) 9 hours
  3. গ
    গ) 10 hours
  4. ঘ
    ঘ) 11 hours
ব্যাখ্যা
Question: 10 people can do a work in 4 days working 6 hours a day. If 5 new people join the team to complete the work in 2 days, they have to work per day for -

Solution: 
প্রশ্নের প্রথম অংশ - ১০ জন লোক একটি কাজ দৈনিক ৬ ঘন্টা কাজ করে ৪ দিনে শেষ করে।
এখানে, 
লোক, M1 = 10,
কাজ, W1 = 1,
দিন, D1 = 4,
সময়, H1 = 6.

প্রশ্নের দ্বিতীয় অংশ থেকে - যদি অতিরিক্ত ৫ জন লোক যুক্ত করা হয় তাহলে একই কাজ ২ দিনে শেষ করতে সবার প্রতিদিন কতক্ষণ কাজ করতে হবে?
এখানে,
লোক, M2 = 10 + 5 = 15,
কাজ, W2 = 1,
দিন, D2 = 2,
সময়, H2 = ?

আমরা জানি,
M1 × W2 × D1 × H1 = M2 × W1 × D2 × H2
H2 = (M1 × W2 × D1 × H1)/ (M2 × W1 × D2)
= (10 × 1 × 4 × 6)/(15 × 1 × 2)
= 240/30
= 8 hours
১৩,৬৬১.
The ratio between the speeds of two trains, Train P and Train Q, is 7:9. If Train Q covers a distance of 270 km in 3 hours, find the speed of Train P in km/h.
  1. ক
    60 km/h
  2. খ
    70 km/h
  3. গ
    80 km/h
  4. ঘ
    90 km/h
ব্যাখ্যা

Question: The ratio between the speeds of two trains, Train P and Train Q, is 7:9. If Train Q covers a distance of 270 km in 3 hours, find the speed of Train P in km/h.

সমাধান:
ধরি,
ট্রেন P এবং ট্রেন Q এর গতিবেগ হলো যথাক্রমে 7x কিমি/ঘন্টা এবং 9x কিমি/ঘন্টা।

ট্রেন Q এর গতিবেগ = দূরত্ব / সময়
= 270 কিমি / 3 ঘন্টা
= 90 কিমি/ঘন্টা।

প্রশ্নমতে,
9x = 90 
⇒ x = 90 / 9
⇒ x = 10

∴ ট্রেন P এর গতিবেগ = 7x
= (7 × 10) কিমি/ঘন্টা
= 70 কিমি/ঘন্টা।
∴ ট্রেন P এর গতিবেগ হলো 70 কিমি/ঘন্টা।

১৩,৬৬২.
If speed is increased by 4 miles per hour, it takes 4 hour less to cover a distance of 32 km. Find the previous speed. 
  1. ক
    ক) 8 kmph
  2. খ
    খ) 4 kmph
  3. গ
    গ) 12 kmph
  4. ঘ
    ঘ) 2 kmph
ব্যাখ্যা
ধরি
প্রকৃত বেগ = x kmph 
নতুন বেগ = x + 4 kmph 

এখানে
(32/x) - {32/(x + 4)} = 4 
{32(x + 4) - 32x}/{x(x + 4)} = 4 
(32x + 128 - 32x)/(x2 + 4x) = 4
128/(x2 + 4x) = 4
x2 + 4x = 128/4
x2 + 4x = 32
x2 + 8x - 4x - 32 = 0
x(x + 8) - 4 (x + 8) = 0
(x + 8)(x - 4) = 0
হয় 
x + 8 = 0
x = - 8 [গ্রহণযোগ্য নয় ]
অথবা 
x - 4 = 0
x = 4
১৩,৬৬৩.
The ratio of water and alcohol in two different containers is 2 : 3 and 4 : 5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7 : 5?
  1. ক
    ক) 7:3
  2. খ
    খ) 5:3
  3. গ
    গ) 8:5
  4. ঘ
    ঘ) 2:7
  5. ঙ
    ঙ) 3:5
ব্যাখ্যা

W1 : A1 W2 : A2 …… WN : AN
2 : 3 4 : 5 …… 5 : 7
W1/(W1+A1) = 2/5 ; W2/(W2+A2) = 4/9; WN/(WN+AN) = 5/12
= 72/180
= 80/180
= 75/180



=> 5 : 3
Therefore, the ratio is 5 : 3

১৩,৬৬৪.
Walking 3/5 of his normal speed, Sami is 20 minutes late in reaching his coaching. The usual time taken by him to cover the distance between his home and coaching ?
  1. ক
    30 minutes
  2. খ
    25 minutes
  3. গ
    35 minutes
  4. ঘ
    20 minutes
ব্যাখ্যা
Question: Walking 3/5 of his normal speed, Sami is 20 minutes late in reaching his coaching. The usual time taken by him to cover the distance between his home and coaching ?

Solution:
Let,
Distance y meter and speed x meter/min.
usual time taken y/x min

According to the question,
(y/3x/5) - (y/x) = 20
⇒ (y/x) {(5/3) - 1} = 20
⇒ (y/x) (2/3) = 20
∴ (y/x) = 30
 
∴ The usual time taken by Sami to reach his coaching = 30 minutes
১৩,৬৬৫.
A mobile phone is sold for Tk. 9,600, and the seller makes a profit of 25% on the cost price. What will be the new selling price if he reduces the profit to 10%?
  1. ক
    7575 Tk.
  2. খ
    8448 Tk.
  3. গ
    1056 Tk.
  4. ঘ
    8652 Tk.
ব্যাখ্যা

Question: A mobile phone is sold for Tk. 9,600, and the seller makes a profit of 25% on the cost price. What will be the new selling price if he reduces the profit to 10%?

Solution:
At 25% profit,
Selling Price = 125% of Cost Price
∴ Cost Price = (100/125) × Selling Price
= (100/125) × 9,600
= 7,680 Tk.

Now, if the seller wants 10% profit,
∴ New Selling Price = 7,680 + (10% of 7,680)
= 7,680 + {(10/100) × 7,680}
= 7,680 + 768
= 8,448 Tk.

১৩,৬৬৬.
2 - [2 - {2 - 2 (2 + 2)}] = ?
  1. ক
    ক) -4
  2. খ
    খ) 6
  3. গ
    গ) 4
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

2 - [2 - {2 - 2(2 + 2)}]
= 2 - [2 - {2 - 2 × 4}]
= 2 - [2 - {2 - 8}]
= 2 - [2 + 6]
= 2 - 8 
= -6 

১৩,৬৬৭.
If n(U) = 150, n(A) = 55, n(B) = 48, and n(A ∩ B) = 18, then what is n(A ∪ B)'?
  1. ক
    85
  2. খ
    47
  3. গ
    83
  4. ঘ
    65
  5. ঙ
    55
ব্যাখ্যা

Question: If n(U) = 150, n(A) = 55, n(B) = 48, and n(A ∩ B) = 18, then what is n(A ∪ B)'?

Solution:
Given that,
n(U) = 150
n(A) = 55
n(B) = 48
n(A ∩ B) = 18

We know, n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
⇒ n(A ∪ B) = 55 + 48 - 18
⇒ n(A ∪ B) = 103 - 18
⇒ n(A ∪ B) = 85

Now, n(A ∪ B)' = n(U) - n(A ∪ B)
⇒ n(A ∪ B)' = 150 - 85
∴ n(A ∪ B)' = 65

১৩,৬৬৮.
A and B undertake to do a piece of work for Tk. 18,750. A can do it in 20 days and B can do it in 30 days. With the help of C, they finished it in 8 days. How much C should be paid for his work in proportion?
  1. ক
    ক) Tk. 6,050
  2. খ
    খ) Tk. 6,250
  3. গ
    গ) Tk. 6,750
  4. ঘ
    ঘ) Tk. 6,850
ব্যাখ্যা
A and B undertake to do a piece of work for Rs. 18,750

A can do it in 20 days and B can do it in 30 days.

Concept used:
Total work = LCM of the time taken by workers alone
Share of the amount is in the ratio of efficiency

Calculation:
LCM of 20 and 30 is 60 i.e total work
So, efficiency of A and B is 60/20 = 3, 60/30 = 2
Efficiency of A + B + C = 60/8 = 7.5
Efficiency of C = 7.5 - 3 - 2 = 2.5

Share of C = (18750/7.5) × 2.5
⇒ 18750/3
⇒ 6250

∴ C should be paid Tk. 6250 for his work in proportion

১৩,৬৬৯.
Find the difference between compound profit and simple profit of Tk. 12000 in 2 years at the profit of 20% per annum.
  1. ক
    Tk 440
  2. খ
    Tk 480
  3. গ
    Tk 520
  4. ঘ
    Tk 600
ব্যাখ্যা
Question: Find the difference between compound profit and simple profit of Tk. 12000 in 2 years at the profit of 20% per annum.

Solution:
Given that,
P = 12000 Tk
r = 20%
= 20/100
= 1/5
t = 2 years

We know,
The compound profit = P (1 + r)n - P
= 12000 (1 + 1/5)2- 12000
= (12000 × 36/25)- 12000
= 17280 - 12000
= 5280 Tk
and
Simple profit I = Prn
= 12000 × 1/5 × 2
= 4800

∴ The different between compound profit and simple profit = (5280 - 4800) Tk
= Tk 480
১৩,৬৭০.
The area of a trapezium is 84 square cm. The lengths of its parallel sides are 14 cm and 10 cm. What is the distance between the parallel sides?
  1. ক
    6 cm
  2. খ
    7 cm
  3. গ
    8 cm
  4. ঘ
    9 cm
ব্যাখ্যা
Question: The area of a trapezium is 84 square cm. The lengths of its parallel sides are 14 cm and 10 cm. What is the distance between the parallel sides?

Solution:
We know,
The area of a trapezium = (1/2) × Sum of the lengths of the parallel sides × Distance between the parallel sides.

Let, the distance between the parallel sides be = d.

Then,
d = (2 × Area of the trapezium)/Sum of the lengths of the parallel sides
= (2 × 84)/(14 + 10)
= 168/24
= 7 cm

Thus, the distance between the parallel sides 7 cm.
১৩,৬৭১.
A sum of money triples itself in 5 years at simple interest. What is the rate of interest per annum?
  1. ক
    30%
  2. খ
    40%
  3. গ
    50%
  4. ঘ
    60%
ব্যাখ্যা
Question: A sum of money triples itself in 5 years at simple interest. What is the rate of interest per annum?

Solution:
Let,
Principal amount = P
Sum of amount = 3P
∴ Interest, I = 3P - P = 2P
Time, n = 5 years
Rate of interest = r

r = I/(Pn)
= (2P)/(P × 5)
= (2/5) × 100%
= 40%
১৩,৬৭২.
There is 90% increase in an amount in 9 years at simple interest. What will be the compound interest of Tk. 15,000 after 4 years at the same rate?
  1. ক
    6962
  2. খ
    6269
  3. গ
    6988
  4. ঘ
    5867
ব্যাখ্যা
If principal is Tk. 100
∴ Interest = 90% of Tk. 100 = Tk. 90
We know, interest, I = Pnr
Therefore, rate of interest, r = I/(Pn)
∴ Rate of Interest = 90 / (100 × 9) = 1/10 = (1/10) × 100%  = 10%
Compound interest = 15,000 × (1 + 10/100)4 - 15,000 = 6961.50 ≈ 6962
১৩,৬৭৩.
Solution set of inequality: 2x + 5 < 5x - 4 is
  1. ক
    (- ∞, - 3)
  2. খ
    (- ∞, 3)
  3. গ
    [- 3, + ∞)
  4. ঘ
    (3, + ∞)
ব্যাখ্যা

Question: Solution set of inequality: 2x + 5 < 5x - 4 is

Solution: 
Given that, 
2x + 5 < 5x - 4
⇒ 2x + 5 + 4 < 5x - 4 + 4
⇒ 2x + 9 < 5x
⇒ 2x + 9 - 2x < 5x - 2x
⇒ 3x > 9
∴ x > 3
This can also be written as x > 3

So the set of inequality is (3, + ∞)

১৩,৬৭৪.
A bag contains Tk. 410 in the form of Tk. 5, Tk. 2, and Tk. 1 coins. The number of coins is in the ratio 4: 6: 9. So, find the number of 2 Taka’s coins -
  1. ক
    40
  2. খ
    50
  3. গ
    60
  4. ঘ
    70
ব্যাখ্যা

ATQ,
if the ratio of coins = 4: 6: 9
That means if Tk. 5 coins are 4, Tk. 2 coins are 6, and then Tk. 1 coins are 9.

According to the given ratio, the ratio of amounts = 5 × 4 : 6 × 2: 9 × 1 = 20 : 12 : 9
The sum of the ratios of the amounts = 20 + 12 + 9
= Tk. 41

But ATQ,
it is Tk. 410, which means multiply each ratio by 10
i.e., new ratio = 40 : 60 : 90
Now, 40 × 5 : 60 × 2 : 90 × 1 = 200 : 120 : 90

The total amount in the form of two rupees coins = 120
So, the two rupees coins = 120/2
= 60.

১৩,৬৭৫.
Two pipes A and B can fill a cistern in 12 minutes and 15 minutes respectively while a third pipes C can empty the full cistern in 6 minutes. A and B are kept open for 5 minutes in the beginning and then C is also opened. In what time is the cistern emptied? 
  1. ক
    ক) 40minutes
  2. খ
    খ) 42minutes
  3. গ
    গ) 45minutes
  4. ঘ
    ঘ) 48minutes
ব্যাখ্যা
Part filled in 5 min = 5 × {(1/15) + (1/12)}
                              = 5 × {(4 + 5)/60}
                              = 5× (9/60)
                              = 3/4

Part emptied in 1 minute when all the pipes are opened = (1/6) - {(1/15) + (1/12)}
                                                                                          = (10 - 4 - 5)/60
                                                                                          = 1/60
Now,
1​/60 part is emptied in 1 minute.
3/4 part is emptied in =60 ×(3/4) = 45minutes
১৩,৬৭৬.
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
  1. ক
    ক) 100
  2. খ
    খ) 150
  3. গ
    গ) 250
  4. ঘ
    ঘ) 260
  5. ঙ
    ঙ) 416
ব্যাখ্যা

Let the number of boys and girls be 8x and 5x.
Total number of students = 13x
= 13 × 32
= 416.

১৩,৬৭৭.
Two Motorists drove their cars at a speed of 45 km per hour and 50 km per hour respectively. One car took 10 minutes longer than the other to travel a distance. Find the distance travelled.
  1. ক
    60 km
  2. খ
    70 km
  3. গ
    65 km
  4. ঘ
    75 km
ব্যাখ্যা
Question: Two Motorists drove their cars at a speed of 45 km per hour and 50 km per hour respectively. One car took 10 minutes longer than the other to travel a distance. Find the distance travelled.

Solution:
let, the distance is x km

(x/45) - (x/50) = 10/60
⇒ (20x - 18x)/900 = 1/6
⇒ 2x = 150
∴ x = 75 km
১৩,৬৭৮.
Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
  1. ক
    1 hr 12 mins
  2. খ
    2 hr
  3. গ
    1 hr
  4. ঘ
    1 hr 42 mins
  5. ঙ
    None of these
ব্যাখ্যা
Question:  Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?

Solution:
New speed =6/7 of usual speed
Speed and time are inversely proportional.
Hence new time = 7/6 of usual time
Hence, 
7/6 of usual time - usual time = 12 minutes
⇒ 1/6 of usual time = 12 minutes
∴ usual time = 12 × 6 = 72 minutes = 1 hour 12 minutes
১৩,৬৭৯.
Jui is now twice as old as Azim is, but 6 years ago, she was 5 times as old as Azim was. How old is Jui now?
  1. ক
    10 years
  2. খ
    16 years
  3. গ
    20 years
  4. ঘ
    24 years
  5. ঙ
    None
ব্যাখ্যা
প্রশ্ন: Jui is now twice as old as Azim is, but 6 years ago, she was 5 times as old as Azim was. How old is Jui now?

সমাধান:
ধরি,
আজিমের বয়স = x বছর
তাহলে, জুইয়ের বয়স = 2x বছর

প্রশ্নমতে,
2x - 6 = 5(x - 6)
⇒ 5x - 30 = 2x - 6
⇒ 5x - 2x = 30 - 6
⇒ 3x = 24
⇒ x = 24/3
∴ x = 8

∴ জুইয়ের বর্তমান বয়স = 2 × 8 বছর
= 16 বছর
১৩,৬৮০.
A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 
  1. ক
    ক) 3 days
  2. খ
    খ) 4 days
  3. গ
    গ) 5 days
  4. ঘ
    ঘ) 6 days
ব্যাখ্যা
Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days  

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days
১৩,৬৮১.
If the rate of interest is 10% per annum and is compounded half yearly, the principal of Tk. 4000 in 3/2 years will amount to -
  1. ক
    ক) Tk. 4630.00
  2. খ
    খ) Tk. 4630.50
  3. গ
    গ) Tk. 4631.50
  4. ঘ
    ঘ) Tk. 4632.00
ব্যাখ্যা

Given, P = 4000
Interest rate per year = 10%, so per half year = 5%
Time = 3/2 years or 3 half year

C = 4000 × 105/100 × 105/100 × 105/100
= 4630.50

১৩,৬৮২.
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?
  1. ক
    9:00 a.m.
  2. খ
    7:00 a.m.
  3. গ
    6:00 a.m.
  4. ঘ
    4:00 a.m.
ব্যাখ্যা
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?

Solution:
To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: (1/2) ÷ (1/8) = (1/2) × 8 = 4
As it quadruples every hour then container was one-eighth full at 10:00 a.m - 1 hour = 9:00 a.m.
১৩,৬৮৩.
Nazrul saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent did he save in the transaction?
  1. ক
    8%
  2. খ
    (100/9)%
  3. গ
    (100/11)%
  4. ঘ
    None of these
ব্যাখ্যা
Question: Nazrul saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent did he save in the transaction?

Solution: 
cost price = 25 + 2.5 = 27.5 taka

Approximate save = (2.5/27.5) × 100%
= (100/11)%
১৩,৬৮৪.
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?
  1. ক
    ক) 40
  2. খ
    খ) 49
  3. গ
    গ) 100
  4. ঘ
    ঘ) 120
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
= 49.

১৩,৬৮৫.
An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest? 
  1. ক
    ক) 10%
  2. খ
    খ) 20%
  3. গ
    গ) 30%
  4. ঘ
    ঘ) 40%
ব্যাখ্যা
Question: An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest? 

solution:
let the rate be R%

Then,
625 {1 + R/(2 × 100)} 2 × 2 = 1296
⇒ (1 + R/200)4 = 1296/625
⇒ (1 + R/200)4 = (6/5)4
⇒ (1 + R/200) = 6/5
⇒ R/200 = 1/5
⇒ R = 40
∴ R = 40%
১৩,৬৮৬.
In one hour, a boat goes 10 km/hr along the stream and 4 km/hr against the stream. The speed of the boat in still water (in km/hr) is- 
  1. ক
    5 km/h
  2. খ
    8 km/h
  3. গ
    6 km/h
  4. ঘ
    7 km/h
ব্যাখ্যা

Question: In one hour, a boat goes 10 km/hr along the stream and 4 km/hr against the stream. The speed of the boat in still water (in km/hr) is-

Solution:
Speed in still water = (10 + 4)/2 kmph
= 14/2 kmph
= 7 kmph.

So, the speed of the boat in still water is 7 km/h.

১৩,৬৮৭.
Out of 9 persons, 8 persons spent Tk. 30 each for their meals. The ninth one spent Tk. 20 more than the average expenditure of all the nine. How many total money spent by all of them?
  1. ক
    Tk. 262.50
  2. খ
    Tk. 282
  3. গ
    Tk. 294
  4. ঘ
    Tk. 292.50
ব্যাখ্যা
Question: Out of 9 persons, 8 persons spent Tk. 30 each for their meals. The ninth one spent Tk. 20 more than the average expenditure of all the nine. How many total money spent by all of them?

Solution: 
Let, the average expenditure be Tk. x.

ATQ,
9x = (8 × 30) + (x + 20)
⇒ 9x = 240 + x + 20
⇒ 9x - x = 260
⇒ 8x = 260
∴ x = 32.5

Total money spent = 9x = 9 × 32.5 = Tk. 292.50
১৩,৬৮৮.
If 0 < x < 1, which of the following expressions is greatest?
  1. ক
    1/√x
  2. খ
    √x
  3. গ
    (1/π)x
  4. ঘ
    x3
  5. ঙ
    x4
ব্যাখ্যা
Question: If 0 < x < 1, which of the following expressions is greatest?

Solution:
Since x is > 0 and x < 1, it has to be a decimal/fraction.
Take a value that is a perfect square, as some options have a root value. Let's take x = 0.25

A) 1/√x = 1/√0.25 = 1/0.5 = 2
B) √x = √0.25 = 0.5
C) (1/π)x = 0.25/(22/7) = 0.08
D) x3 = (0.25)3 = 0.015
E) x4 = (0.25)4 = 0.004

So, If 0 < x < 1, then the expressions 1/√x is greatest.
১৩,৬৮৯.
A man buys a cycle for Tk.1400 and sells it at a loss of 15%. What is the selling price of the cycle?
  1. ক
    ক) Tk.1290
  2. খ
    খ) Tk.1190
  3. গ
    গ) Tk.1090
  4. ঘ
    ঘ) Tk.1390
ব্যাখ্যা
S.P. = 85% of Tk.1400 
      = Tk. (85 × 1400)/100
      = Tk.1190
১৩,৬৯০.
What is the solution of the inequality,
- 12 < 4x - 8 ≤ 20 ?
  1. ক
    [- 1, 9)
  2. খ
    [- 1, 7]
  3. গ
    [- 3, 9]
  4. ঘ
    (- 1, 7]
ব্যাখ্যা

Question: What is the solution of the inequality, 
- 12 < 4x - 8 ≤ 20 ?
​
​Solution:
- 12 < 4x - 8 ≤ 20
⇒ - 12 + 8 < 4x - 8 + 8 ≤ 20 + 8
⇒ - 4 < 4x ≤ 28
⇒ - 4/4 < 4x/4 ≤ 28/4
⇒ - 1 < x ≤ 7

ব্যবধি আকারে লিখলে হয়: (- 1, 7]

(- 1, 7] বলতে বোঝায় যে, - 1 এর চেয়ে বড় এবং 7 বা তার চেয়ে ছোট সব বাস্তব সংখ্যা এই সমাধানের অন্তর্ভুক্ত।

১৩,৬৯১.
The ratio of two numbers is 1 : 3 and their L.C.M is 75. What is the sum of the numbers?
  1. ক
    ক) 90
  2. খ
    খ) 100
  3. গ
    গ) 115
  4. ঘ
    ঘ) 120
ব্যাখ্যা
Question: The ratio of two numbers is 1 : 3 and their L.C.M is 75. What is the sum of the numbers?

Solution:  
Let the numbers are x and 3x 
So, L.C.M of x and 3x is 3x
ATQ,
3x = 75
∴ x = 25
So, the sum of the numbers
= (x + 3x)
= 4x
= 4 × 25
= 100
১৩,৬৯২.
The largest prime factor of {3√(24)6} - 1 is-
  1. ক
    ক) 23
  2. খ
    খ) 17
  3. গ
    গ) 5
  4. ঘ
    ঘ) 3
ব্যাখ্যা
Question: The largest prime factor of {3√(24)6} - 1 is-

Solution:
{3√(24)6} - 1
= (24)6/3 - 1
= (24)2 - 1
= (24 + 1) (24 - 1)
= 17 × 15
= 17 × 3 × 5

So, the largest prime factor is 17
১৩,৬৯৩.
A man walking at the rate of 5 km/hr. crosses a bridge in 15 minutes. The length of the bridge (in metres) is:
  1. ক
    680m
  2. খ
    850m
  3. গ
    1056m
  4. ঘ
    1250m
ব্যাখ্যা
Question: A man walking at the rate of 5 km/hr. crosses a bridge in 15 minutes. The length of the bridge (in metres) is:

Solution:
Speed of the man = 5km/hr
= 5 × (1000/60)m/min
= 250/3 m/min

Now,
Time taken to cross the bridge = 15 minutes
Length of the bridge = speed × time
= (250/3) × 15m
= 1250m
১৩,৬৯৪.
P is a prime number and Q is not divisible by P. What will be the L.C.M of P and Q?
  1. ক
    PQ/(P-Q)
  2. খ
    PQ
  3. গ
    P/Q
  4. ঘ
    Q/P
  5. ঙ
    (P+Q)/(P-Q)
ব্যাখ্যা
অবিভাজ্য কোন সংখ্যাদ্বয়ের ল.সা.গু ঐ সংখ্যাদ্বয়ের গুনফলের সমান।
১৩,৬৯৫.
A and B can complete a task together in 6 days. A can do it alone in 8 days. How many days would it take B to do this task alone?
  1. ক
    20 days
  2. খ
    12 days
  3. গ
    18 days
  4. ঘ
    24 days
ব্যাখ্যা
Question: A and B can complete a task together in 6 days. A can do it alone in 8 days. How many days would it take B to do this task alone?

Solution:
A's 1 day's work 1/8
A and B's 1 day's work 1/6

∴ B's 1 day's work = (1/6) - (1/8) = (4 - 3)/24 = 1/24

1/24 part of task done by B in 1 day
∴ Full task done by B in (24/1) = 24 days

Therefore, B will complete the full task in 24 days.
১৩,৬৯৬.
Questions (36-60) : Choose the correct answer.
৩৬) A garden of 100 m length and 60m width has a walkway of 2 m width on every side. What is the area of the garden, in square meter, excluding the walkway?
  1. ক
    ক) 5684
  2. খ
    খ) 6000
  3. গ
    গ) 5376
  4. ঘ
    ঘ) 5123
ব্যাখ্যা

The area of the garden, excluding the walkway, is = {(100 - 2×2) × (60 - 2×2)}
= 96×56
= 5376 m2

১৩,৬৯৭.
A train 300 meters long passes a bridge 700 meters long in 40 seconds. How long will it take to pass a platform that is 500 meters long?
  1. ক
    48 seconds
  2. খ
    52 seconds
  3. গ
    36 seconds
  4. ঘ
    32 seconds
ব্যাখ্যা

Question: A train 300 meters long passes a bridge 700 meters long in 40 seconds. How long will it take to pass a platform that is 500 meters long?

Solution:
Total distance to pass bridge = 300 + 700 meters
= 1000 meters

∴ Train's speed = Distance/Time
= 1000/40 = 25 m/s

Total distance to pass the platform,
= Length of train + Length of platform
= 300 + 500
= 800 meters

∴ Required time to pass the platform = Distance/Speed
= 800/25
= 32 seconds

১৩,৬৯৮.
Find the probability that a leap year has 52 Sundays.
  1. ক
    3/8
  2. খ
    5/7
  3. গ
    3/13
  4. ঘ
    5/14
ব্যাখ্যা
Question: Find the probability that a leap year has 52 Sundays.

Solution:
A leap year can have 52 Sundays or 53 Sundays.
In a leap year, there are 366 days out of which there are 52 complete weeks & remaining 2 days.

Now, these two days can be (Sat, Sun) (Sun, Mon) (Mon, Tue) (Tue, Wed) (Wed, Thur) (Thur, Friday) (Friday, Sat).
So there are total 7 cases out of which (Sat, Sun) (Sun, Mon) are two favorable cases.
So, P(53 Sundays) = 2/7

Now,
P(52 Sundays) + P(53 Sundays) = 1
So, P(52 Sundays) = 1 - P(53 Sundays) = 1 - (2/7) = 5/7
১৩,৬৯৯.
A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.
  1. ক
    10 m
  2. খ
    15 m
  3. গ
    20 m
  4. ঘ
    25 m
ব্যাখ্যা

Question: A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

Solution:

By observing the figure, AB is the pole.

In triangle ABC,
⇒ AB/AC = sin30°
⇒ AB/30 = 1/2
⇒ AB = 15

Therefore, the height of the pole is 15 m.

১৩,৭০০.
Samir is twice as old as Babul was two years ago. If the difference between their ages is 2 years, how old is Samir now?
  1. ক
    ক) 8 years
  2. খ
    খ) 6 years
  3. গ
    গ) 10 years
  4. ঘ
    ঘ) 12 years
ব্যাখ্যা

Let, Samir’s age is = x
So Babul’s age is = x - 2

ATQ,
x - 2 = 2(x - 2 - 2)
Or, x - 2 = 2x - 8
∴ x = 6