Officer (General) | 28.09.2018/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ If the numerator of fraction is increased by 200% and the denominator is increased by 350% . The resultant fraction is 5/12 . what was the original fraction ?

বর্ণনাঃ

Let numerator of the fraction is X and denominator is Y, then fraction will be X/Y.

Numerator increased 200%, so new numerator would be,

[X + (200 of X)/100] = 3X ----------------------------- (1)

New denominator,

[Y + (350Y)/100 ] = 45Y/10 --------------------------------- (2)

Now, accordibng to question,

3X /(45Y/10) = 5/12

30X / 45Y = 5/12
360X = 225Y

X/Y = 225/360
X/Y = 5/8
So, Original fraction was 5/8.

প্রশ্নঃ In a mixture, the ratio of the milk and water is 6 : 5. when 22 liter mixture is replaced by water, the ratio becomes 9 : 13. Find the quantity of water after replacement.

বর্ণনাঃ

Correct Option: D

Let milk = 6x, water = 5x

According to the question,

 

6x – 12 : 5x – 10 + 22 = 9 : 13

13 (6x – 12) = 9 (5x + 12)

78x – 156 = 45x + 108

78x – 45x = 156 + 108

33x = 264

x = 8

Water after replacement = 5 × 8 – 10 + 22 = 40 + 22 = 52 litre

Hence, option D is correct.

প্রশ্নঃ A man can reach a certain place in 40 hours . If he reduces his speed by 1/15th, he goes 5 km less in that time . Find the total distance covered by him.

বর্ণনাঃ

Correct Option: D

Let Distance = D km, Speed = S km/h
 

After reducing speed,

After solving equation 1 and 2
 

14 Distance = 15 (Distance – 5)

14 Distance = 15 Distance – 75

Distance = 75 km.

Hence, option D is correct.

প্রশ্নঃ A shopkeeper gains 17% after allowing a discount of 10% on the marked price of an article . Find his profit percent if the article is sold at marked price allowing no discount .

বর্ণনাঃ

Let the cost price = Tk.100

Therefore, Selling price = 100×117100= Tk.117100×117100= Tk.117

Therefore, Marked price = 117×10090=130117×10090=130

Therefore, Profit Percentage = (130−100)100×100=30%

প্রশ্নঃ Aalm sold tow vehicles for Tk. 46000 each . If he gained 10% on the first and lost 10% on another , then what is his percentage profit or loss in this transaction ?

বর্ণনাঃ In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut: Loss on total deal, =(Common loss or gain percentage/10)^2=(10/10)^2=1%

প্রশ্নঃ The profit earned after selling an article for Tk. 3,362 is the same as the loss incurred after selling the article for Tk. 2,346. At what selling price will a trader make a 20% profit on this article?

বর্ণনাঃ

Let the cost price of the article be Tk. x.

∴   3362 − x = x − 2346
 

∴  S.P. corresponding to a 20% profit = 1.2 × 2854 =Tk. 3,424.8/-

Hence, option D is correct.

প্রশ্নঃ An article costs Tk. 500 and the marked price is mentioned as Tk. 800. What is the profit % for the seller it he sells and offers a discount of 10% on the marked price ?

বর্ণনাঃ 10% of 800= 800x10/100=80
Profit = (800-80)- 500=720-500=220
So, the profit %= (220x100)/500=44%

প্রশ্নঃ The average of the first and the second of three numbers is 15 more than the average of the second and the third of these numbers .what is the difference between the first and the third of these three numbers?

বর্ণনাঃ Let Ist no = x
2nd no =y
3rd no = z
According to Q.
(x+y)/2 = 15 + (y+z)/2
Multiply above equation by 2
x + y = 30+y+z So,
x-z = 30 Difference of Ist & 3rd no is 30.

প্রশ্নঃ 30 pens and 75 pencils altogether were purchased for Tk. 510 . If the average price of a pencil was Tk. 2 , what was the average price of a pen ?

বর্ণনাঃ According to the question,
30 pens + 75 pencils =Tk. 510
Average price of a pencil =Tk. 2 Price of 75 pencils = 2 × 75 = Tk. 150 ∴ Price of 30 pens = 510 - 150 = Tk. 360 ∴ Average price of pen = 360/30 = Tk. 12

প্রশ্নঃ A boat travel with a speed of 10 km / hr in still water. If the speed of the stream is 3 km / hr then find time taken by boat to travel 52 km downstream .

বর্ণনাঃ Speed downstream = (10 + 3) km/hr = 13 km/hr
Time taken to travel 52 km downstream = 52/13 hours = 4 hours

প্রশ্নঃ The ratio of the speed of boat in still water to the speed of stream is 16 : 5. A boat goes 16.5 km in 45 minute upstream , find the time taken by boat to cover the distance of 17.5 km downstream .

বর্ণনাঃ

Correct Option: B

Let the speed of boat in still water = 16x, speed of stream = 5x

Upstream speed = 16x – 5x = 11x
 

x = 2

speed of boat in still water = 32 km/h, speed of stream = 10 km/h

Downstream speed = 32 + 10 = 42 km/h 

Distance = 17.5 km
 

Hence, option B is correct.
 

প্রশ্নঃ A train 125 m long passes a person , running at 8 km / hr in the same direction in which the train is going in 25 seconds . The speed of the train is :

বর্ণনাঃ Speed of the train relative to man = (125/25) m/sec = 5 m/sec.
[5 x (18/5)] km/hr = 18 km/hr.
Let the speed of the train be 'S' km/hr.
Then, relative speed = (S -8) km/hr.
S - 8 =18 => S = 26 km/hr.

প্রশ্নঃ There are two numbers , 1 st number is 12 more than the 2nd number . The average of the two numbers is 19. If 2 is added in both numbers , find the ratio of the numbers .

বর্ণনাঃ ATQ,
x-y=12
x+y=38
.......................
2x=50 (Adding the equations)
Or, x=25
So, y=13 Then, if 2 is added in both numbers , find the ratio of the numbers= x+2/y+2=27/15=9/5

প্রশ্নঃ Sum of 4 consecutive even numbers is greater than consecutive odd numbers by 81. If the sum of the least odd and even numbers is 59 then find the sum of largest odd and even numbers.

বর্ণনাঃ Let 4 consecutive even numbers be x, x + 2, X + 4 and x + 6 respectively.
3 consecutive odd numbers be y, y+2 and y+ 4
According to question,
[x+x+2+x+4+x+6]−[y+y+2+y+4]=81
=> (4x+12)−(3y+6)=81
4x−3y=81−12+6
4x−3y=75
x+4=59
On solving equations (i) and (ii), we get
X = 36
y = 23
The sum of largest odd and even number = x+6+y+4 = x+y+10 = 36+23+10=69

প্রশ্নঃ A number is as much greater than 36 as is less than 86 . Find the number.

বর্ণনাঃ A number is as much greater than 36 as is less than 86 . Find the number. ATQ, x= (36+86)/2=122/2=61

প্রশ্নঃ X, Y and Z can do a piece of work in 6 hours. X and Y can do the same work in 8 hours and Z can the same work in 12 hours . In how many times will X and Z do the same work?

বর্ণনাঃ X+Y+Z can do 1/6 of job in one hour……1
X+Y can do 1/8 of job in one hour……2
Y+Z can do 1/12 of job in one hour……3
adding 2&3 we get
X+Y+Y+Z=1/8+1/12
X+Z+2Y=5/24…4
subtracting 1 from 4 we get
Y=5/24–1/6=1/24.substituting the value of Y in 4 we have
X+Z+2/24=5/24
X+Z=5/24–2/24=3/24=1/8
hence X&Z will do 1/8 of job in one hour.
So X & Z will do the work in 8 hours.

প্রশ্নঃ If A can do 1 /4 of a work in 3 days and B can do 1 /6 of the same work in 4 days , how much will A get if both work together and are paid Tk. 180 in all ?

বর্ণনাঃ A 3 days = 1/4 of a work
:. 1 day = 1/12
B 4 days = 1/6 of a work
:. 1 day = 1/24
In terms of ration
A :B
2x : x = 180
120 : 60
A will get =Tk. 120