Explanation:

The length of a rectangle is increased by 50%, by what percent would the width have to be decreased to maintain sane area? Correct Answer 33.33 Let, the length of the rectangle be x cm and the breadth of the rectangle y cm Therefore area of the rectangle = x * y = xy cm² as the length is increased by 50% ∴ length = x + 50% of x                   = x + 50/100 *x                   = x + x/2                   = 3x/2 Given that area is constant so, xy = 3x/2 * breadth breadth = 2xy/3x = 2y/3 cm Percentage of increase in breadth = decrease in breadth/original breadth *100                               = (y - 2y/3)/y * 100                               = {(3y - 2y) / 3}/y*100                               = y/3y *100                               = 100/3                               = 33.333% The breadth is decreased by 33.333% (Ans)

Explanation:

Tina rented a rickshaw for Tk. 18 plus Tk. 0.10 per km. ruby rented another rickshaw for Tk. 25 plus Tk. 0.05 per km. If each move d km. and paid exactly the same amount of rental, the d equals. Correct Answer 140 প্রথম Rickshaw এর ক্ষেত্রে মোট ভাড়া = 18 + ( d × 0.10) = 18 + 0.10d টাকা   দ্বিতীয় Rickshaw এর ক্ষেত্রে মোট ভাড়া = 25 + ( d × 0.05) = 25 + 0.5d টাকা   প্রশ্নমতে, 18 + 0.10d = 25 + 0.05d 0.05d = 7  d = 7/0.05     = 7/(5/100)     = (7×100)/5     = 140 কিমি

Explanation:

C is the midpoint of the line segment AE, B and D are on the line segment AE so that AB=BC and CD=DE, what percentage of AC is AD? Correct Answer 150 A হচ্ছে 40%

Explanation:

A line segment is drawn from point (8, -2) to point (4, 6). The coordinates of the midpoint of this line segment are --- Correct Answer (6, 2) Coordinates of the midpoint of a line segment made by joining two points are the averages of the respective coordinates of the two points. So, coordinate of the midpoint is {(8 + 4)/2 , ( - 2 + 6)/2} = (6,2)

Explanation:

How much interest will Tk. 2000 earn at an annul rate of 8% in one year if the interest is compounded every six months? Correct Answer Tk. 163.20 Here, P = 2000 Tk; r = 0.08; n = 1 and m = 2      C = P(1 + r/m)n×m         = 2000(1 + .08/2)1×2         = Tk. 2163.20 Interest is (2163.20 - 2000) = Tk. 163.20

Explanation:

Point P in on line segment AB, which of the following is always true? Correct Answer AB>AP 6c1×1! + 6c2×2! + 6c3×3! + 6c4×4! + 6c5×5! + 6c6×6! = 1956 যেহেতু one or more at a time বলছে তাই নিজেদের মধ্যে ও factorial দিয়ে গুণ হয়েছে।

Explanation:

How many spokes are there in a wheel of a car, if any two spokes form an angle if 15 degree? Correct Answer 24 All the spokes will form a total angle of 360°. Two consecutive spokes form an angle of 15° but every spoke takes part in forming two such angles. So, the number of spokes will be equal to the number of 15° angles formed. So, the number of spokes will be = 360/15 = 24

Explanation:

To avoid paying a toll on a direct road, I drive west 10 miles, south 5 miles, west 30 miles and north 35 miles. What is the length of the toll road? Correct Answer 50 I drive west 10 miles, south 5 miles, west 30 miles, and north 35 miles = west 40 miles, north 30 so we get, (30)² + (40)² = n² or,900 + 1600 = n² or,2500 = n² ∴n = 50 or - 50 Throwing out the negative answer, we get the distance to be 50 miles ans: 50 miles

Explanation:

A train travels at an average speed of 50 miles per hour for 2.5 hour, and then travels at an average speed of 70 miles per hour for 1.5 hours. How far did the train travel in the entire 4 hour? Correct Answer 230 miles The train travelled = 50×2.5 + 70×1.5 = 125 + 105 =  230 miles

Explanation:

The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, the average of the remaining number is : Correct Answer 37.50 Average for 50 number is 38. The total is = 38×50 = 1900 The total of discarded number is = 45 + 55 = 100 Hence the total for 48 number is = 1900 - 100 = 1800 So, The new average is = 1800÷48 = 37.5 ans: 37.5

Explanation:

A cricketer has a certain average for 9 innings. In the 10th innings he scores 100 runs, thus increasing his average by 8 runs. His new average is : Correct Answer 28 Let, initial average = x So, total runs = 9x And total runs scored in 10 innings = 9x + 100 So, new average = (9x + 100)/10 Since average increase by 8 ATQ, x + 8 = (9x + 100)/10 10x + 80 = 9x + 100 x = 20 New average 20 + 8 = 28 (Ans)

Explanation:

Masud has twice as much money as Selim has and Selim has 50% more money than what Bashir has. If the average money with them is Tk. 110, then Masud has : Correct Answer 180 Let Bashir has = x tk Then selim has = 3x/2 tk Then Masud has = 3x tk Now ratio of Masud: Selim: Bashir = 6:3:2 They have total = 110 × 3 = 330 Taka Then Masud share is 6/11 × 330 = 180 tk

Explanation:

A man spends 75% of his income. his income is increased by 20% and he increased his expenditure by 10%. His savings are increased by : Correct Answer 50% Let income = 100 Expenditure : 75 So, saving (100 - 75) = 25 New income = 100 + 20% of 100 = 120 New expenditure = 75 + 10% of 75 = 82.5 New saving = 120 82.5 = 37.5 Increase of saving = 37.5 25 = 12.5 % increase in saving = (12.5/25) × 100 = 50% (ans)

Explanation:

The difference of two numbers is 7 and their product is 60 , then one of the two numbers must be - Correct Answer 5 x - y = 7; x = (y + 7) xy = 60 or,(y + 7).y = 60 or,y2 + 7y - 60 = 0(y + 12) (y - 5) = 0So,Y = - 12,5So,the two number is 12 and 5

Explanation:

A man donated 5% of his income to a charitable organization and deposited 20% of the remainder in a bank. if he now has Tk. 1919 left, then his income is : Correct Answer Tk 2525 Let total income is x 5% for Charitable organisation is 5% of x = 5x/100 = 0.05 x Balance available ( x - 0.05x) = 0.95x 20% deposited in bank = 20% of 0.095x = (20 × 0.95x)/100 = .19 x Now left ( 0.95x - 0.19x) = 0.76x ATQ, 0.76x = 1919 x = 1919/ 0.76 x = 2525 (ans)

Explanation:

A woman had 50 ducks . All but 8 died. How many ducks are still alive? Correct Answer 8 All but 8 মানে ৮টি বাদে বাকি সব।

Explanation:

If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15% the gain is : Correct Answer 13.33% Let CP = 100 And Marked price = x SP = x - 10% of x x - 10% of x = 120 x - 10x/100 = 120 9x/100 = 120 9x = 1200 X = 133.33 If 15% Commission was given, then SP = 133.33 - 15% of 133.33 SP = 133.33 - 20 SP = 113.33 Gain = 113.33 - 100 = 13.33% (ans)

Explanation:

An ambulance travels 10 miles at a speed of 50 miles per hour. how fast must the ambulance travel on the return trip if the round trip travel time is 20 minutes? Correct Answer 75 mph Given, Distance = 10 miles, speed = 50 miles per hour Time taken = distance ÷ speed = 10÷ 50 = 1/5 hour = 1/5×60 = 12 mins Total time = 20 mins Time for returned trip = 20 - 12 = 8 min 8 mins = 8/60 = 2/15 hours Speed = distance ÷ time = 10 ÷ 2/15 = 10 × 15/2 = 150/2 = 75 mph (ans)

Explanation:

The owner of Aarong starts to calculate the percentage of customers who purchase Tagas. if 40% of the total customers who visit the store actually purchase goods and 15% of them purchase tagas, then what percentage of Aarong's customers are Taga buyers? Correct Answer 6% Let the total Customers number = 100 Then Customers who actually purchase goods = 40 And Customers who purchase tagas = 40 × 15/100 = 6 Required percentage = 6%

Explanation:

Reza's average in four tests is 80% . what marks does he need in his fifth test to raise his average to 84% . Correct Answer 100% ধরি, প্রথম 4টি exam এর যোগফল x এবং 5th exam এ পাওয়া marks y xy = 80x = 4x80and,x + y5 = 84So,Y = 5x84 - x অথাৎ 100%

Explanation:

The price of desktop computer is discounted by 20%, and reduced price is then discounted by 20%. The series of successive discount is equivalent to a single discount of : Correct Answer 36% Let the price of desktop computer be 100 Then after first discount price becomes 80 Then again it is discounted by 20% So the Price Becomes = 80 (80 × 20/100) = 64 So a single discount will be = (100 64) = 36%. (ans)

Explanation:

Which fraction is the largest? Correct Answer 4/5 Generally উপরে নিচের Difference যত less হয় fraction তত large । তবে পার্থক্য একই হলে, যে ক্ষেত্রে ব্যবহৃত সংখ্যা বড় সেই fraction বড়। যেমন 4/5 ও 9/10 এর মধ্যে 9/10>4/5।

Explanation:

The sum of principal and simple interest of a certain amount of money would be Tk. 460 after three years from now and Tk. 500 after five years from now. What is the related interest rate? Correct Answer 5% (5 - 3) = 2 years interest = (500 - 460) = 40 tk 1 years interest = 40/2 = 20 tk 3 year's interest 20 × 3 = 60 tk Principle amount = (460 - 60) = 400 tk Interest rate = (60×100)/(400×3) = 5% (ans)

Explanation:

Humayra borrowed Tk. 240, free of interest, to pay for her new hair band. If she pays back 20% of the amount each month and has already paid back Tk. 120. how many months have passed since she took the loan? Correct Answer 2.5 months As She pays 20% of the amount each month So, 20% of 240 = 20/100 × 240 = 48 tk She paid back 120 tk So, remaining (240 - 120) = 120 48 tk pays back in 1 month So, 120 tk pays back in 120/48 = 2.5 months (ans)

Explanation:

the average age of 12 children is 20 years. If the age of one more child is added, the average decreased by 1. What is the age of child added later? Correct Answer 7 Average of 12 is 20 Total = 12 × 20 = 240 Let the age of one more is x So, total 240 + x Average of 13 is (240 + x)/13 ATQ (240 + x)/13 = 19 or, 240 + x = 13 × 19 or, 240 + x = 247 ∴ x = 7 (ans)

Explanation:

Of the 120 households in an area, 55 have cars, 35 have motor bikes, and 20 have both cars and motor bikes. How many of the households in the area have neither cares nor motor bikes? Correct Answer 50 Given total = 120, n(C) = 55, n( B) = 35 and n (C U B) = 20, none = ? Total = n(c) + n(B) n(CUB) + none 120 = 55 + 35 - 20 + none None = 50 (ans)

Explanation:

The length of a rectangle is 3 times of its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches? Correct Answer 75 Given Width of the rectangle = 5 inches So length = 3 × 5 = 15 inches Area of a rectangle is = 5 × 15 = 75 sq. Inch (ans)

Explanation:

If P is the center of the given circle, what fraction of the circle is shaded? Correct Answer 1/6 Area covered by any angle to center of a corcle is <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mi>θ</mi><msup><mn>360</mn><mo>∘</mo></msup></mfrac><mo>×</mo><msup><mi>πr</mi><mn>2</mn></msup><mspace linebreak = "newline"/><mo> = </mo><mfrac><msup><mn>60</mn><mo>∘</mo></msup><msup><mn>360</mn><mo>∘</mo></msup></mfrac><mo>×</mo><msup><mi>πr</mi><mn>2</mn></msup><mspace linebreak = "newline"/><mo> = </mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>×</mo><msup><mi>πr</mi><mn>2</mn></msup></math>

Explanation:

ABCD is a square, EFGH is a rectangle, AB=3, EF=4, FG=6. Determine the area of the region outside of ABCD and inside of EFGH. Correct Answer 15 Area of the square = <math xmlns = "http://www.w3.org/1998/Math/MathML"><msup><mn>3</mn><mn>2</mn></msup><mo> = </mo><mn>9</mn></math>Area of the rechangle = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><mn>6</mn><mo> = </mo><mn>24</mn></math><math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Area of region outside of ABCD & inside of EFGH = 24 - 9 = 15

Explanation:

If x+2y=4, and x/y=2 then determine the value of x and y. Correct Answer 2, 1 <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>y</mi></mfrac><mo> = </mo><mn>2</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>x</mi><mo> = </mo><mn>2</mn><mi>y</mi><mspace linebreak = "newline"/><mo>∴</mo><mi>x</mi><mo> + </mo><mn>2</mn><mi>y</mi><mo> = </mo><mi>x</mi><mo> + </mo><mi>x</mi><mo> = </mo><mn>4</mn><mspace linebreak = "newline"/><mo>⇒</mo><mn>2</mn><mi>y</mi><mo> = </mo><mn>4</mn><mspace linebreak = "newline"/><mo>⇒</mo><mi>x</mi><mo> = </mo><mn>2</mn><mspace linebreak = "newline"/><mo>∴</mo><mi>y</mi><mo> = </mo><mn>1</mn></math>

Explanation:

2 bats and 2 balls cost Tk. 300. 5 bats and 5 balls cost Tk. 750.3 balls and 3 bats cost ---- Correct Answer Tk. 450 2 bats & 2 balls cost Tk. 300 <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> 1 " " 1 " " = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mn>300</mn><mn>2</mn></mfrac><mo> = </mo><mn>150</mn></math> Tk.<math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> 3 " " 3 " " = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>150</mn><mo>×</mo><mn>3</mn><mo> = </mo><mn>450</mn></math> Tk.

Explanation:

After x years Sujan will be y years old. After z years Sujan will be--- Correct Answer y-x+z Present age of Sujan = y - x yearsAfter z years Sujan will be y - x + z years old

Explanation:

A man invests Tk. 9,00,000 in a share earning Tk. 9 as dividend per share, when a share of face value of Tk.100 is selling for Tk. 150. What is his annual income? Correct Answer Tk. 81,000 Total number of shares = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>9</mn><mo>,</mo><mn>00</mn><mo>,</mo><mn>000</mn></mrow><mn>100</mn></mfrac><mo> = </mo><mn>9</mn><mo>,</mo><mn>000</mn></math><math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Total annual income = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>k</mi><mo>.</mo><mo> </mo><mn>9</mn><mo>,</mo><mn>000</mn><mo>×</mo><mn>9</mn><mspace linebreak = "newline"/><mo> = </mo><mo> </mo><mi>T</mi><mi>k</mi><mo>.</mo><mo> </mo><mn>81</mn><mo>,</mo><mn>000</mn></math>[Annual income শুধু dividend থেকে আসে। So selling price দিয়ে হিসাব করলে হবে না।]

Explanation:

The interest charged on a loan is Tk. p per Tk. 1,000 for the first month and Tk. q per Tk. 1,000 for each month after the first month. How much interest will be charged during the first three months on a loan of Tk. 10,000? Correct Answer 10p+20q For the first month interest of Tk 10000 = 10pFor the second & third month interest of Tk 10000 = 10q + 10q = 20qTotal interest = 10p + 20q

Explanation:

A 40 feet long rope is cut into two pieces. If one piece is longer than the other by 18 feet, what is the length, in feet, of the shorter piece? Correct Answer 11 feet Let, length of one piece be x. Then, another pieces lengh = x + 10Shorter piece = x + x + 10 = 402x = 22x = 11

Explanation:

A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80% of the remaining rolls were sold between noon and closing time. How many dozen rolls had been sold when the bakery closed yesterday? Correct Answer 4 dozen Sold by noon = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mn>40</mn><mn>2</mn></mfrac><mo> = </mo><mn>20</mn><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>s</mi></math>80% of remaining = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>×</mo><mn>80</mn><mo>%</mo><mo> = </mo><mn>16</mn><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>s</mi></math> sold between noon & closing time<math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> After closing <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>20</mn><mo> - </mo><mn>16</mn></mrow></mfenced><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> = </mo><mn>4</mn><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>s</mi><mo> </mo><mi>a</mi><mi>r</mi><mi>e</mi><mo> </mo><mi>u</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>l</mi><mi>d</mi><mo>.</mo></math>

Explanation:

The sum of 5 consecutive integers is 105. The sum of the first 2 is ----- Correct Answer 39 x + (x - 1) + (x + 2) + (x + 3) + (x + 4) = 1055x + 10 = 1055x = 95x = 19x + (x - 1)19 + 20 = 39

Explanation:

If 5x + 2y = 10 and x + 8y = 46, then 3x + 5y equals : Correct Answer 28 Given 5x + 2y = 10 and x + 8y = 46 By solving we get x = - 6/19 and y = 110/19 Now 3x + 5y = 3( - 6/19) + 5(110/19) = - 18/19 + 550/19 = 532/19 = 28 (ans)

Explanation:

An overnight express firm charges Tk. 2 per kg for the first 10 kg of packet weight and Tk. 1 for each kg of or fraction of kg over 10 kg of packet weight. How much will it charge to ship a package which weighs 17.5 kg? Correct Answer 28 10 × 2 = 20 tk 7.5 × 1 = 7. 5 = 8 tk [ Because fraction kgs will also charge 1 tk] Total cost = 20 + 8 = 28 tk (ans)

Explanation:

If the side of a square decreases by 30%, then the area of the square decreases by : Correct Answer 51% Suppose the of the square = a The area of the square = a2 Now the sides are reduced by 30% . So its new side = 7a/10 New area = 49a2/100 So by reducing the diagonals of the square by 30%, the area becomes (a2 49a2/100)*100/a2 = 51% of the original. (ans)

Explanation:

How many of the integers between 150 and 160 are prime numbers? Correct Answer 2 between 150 and 160 there are 2  prime numbers.  151 and 157

Explanation:

City B is 4 miles east of City A. City C is 3 miles north of City B. City D is 8 miles east of City C and City E is 6 miles north of City D. What is the distance from City A to City E? Correct Answer 15 miles AR = AB + BR = 4 + 8 = 12 RE = RD + DE = 3 + 6 = 9 AE2 = AR2 + RE2 AE = √144 + 81 = 15

Explanation:

There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. how many possible selections of 4 books form this shelf include at least 1 paperback book? Correct Answer 55 Selections of 4 books out of 8: 8C4 = 70; Selections of 4 hardback books out of 6 (so none paperback): 6C4 = 15; At least One paperback = {total} - {none} = 70 - 15 = 55. (ans)

Explanation:

(-5)(4)(2) (-1/2) (3/4) = ? Correct Answer 15 ( - 5)(4)(2)( - 1/2) (3/4) = (−5) ×4 ×2 ×(−1) ×3 / (2 ×4) = 15 (ans)

Explanation:

If it takes 50 workers 4 hours to dig a hole, how long should it take 30 workers to dig the same hole? Correct Answer 6 hrs, 40 mins Here, 4 hours = 240 minutes Now,  50 workers can dig the hole in 240 minutes So, 30 workers can dig the hole in 240×50/30 = 400 minutes = 6 hours 40 minutes

Explanation:

Of the fruits that arrive at the cannery, 20 percent by weight is rejected before processing. Of the fruit that is processed, 15 percent by weight is rejected before canning. Of the fruit that arrives at the cannery. what percent by weight is canned? Correct Answer 68% Let Fruits arrived at cannery = 100 Selected for processing = 100 20 = 80 Percentage of canned fruits = 80 (80 × 15/100) = 68% (ans)

Explanation:

When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time? Correct Answer 1/3 We need to determine the probability that a coin lands on the same side for all 3 tosses of the coin. This means that the 3 - toss outcome will be either H - H - H or T - T - T. P(T - T - T) = 1/2 x 1/2 x 1/2 = 1/8 P(H - H - H) = 1/2 x 1/2 x 1/2 = 1/8 Thus, the probability that the coin lands on the same side each time is 1/8 + 1/8 = 2/8 = 1/4. (ans)

Explanation:

At a selling price of Tk. 275 a book yield 25% profit. What selling price will yield the profit of 10%? Correct Answer 242 Let the actual price be A. Then,  A + 25% of A = 275 or,  A + 0.25A = 275 or,  1.25A = 275 or,  A = 275/1.25 = 220 TK. So, selling price at 10% profit = 220 + 10% of 220 = 220 + 22 = 242 TK

Explanation:

If x percent of 40 is y, Then 10x equals : Correct Answer 25y x% of 40 = y x = 100y/40 10x = 25y

Explanation:

If 40% of all women are voters and 52% of the population are women, what percent of the population are women voters? Correct Answer 20.8 মনে করি, মোট জনসংখ্যা = 100 জন Women দের সংখ্যা = 52 জন Women দের ভোটার সংখ্যা = 52×(40/100) = 20.8