গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ The difference between the place value and the face value of 6 in the numeral 856973 is --

বর্ণনাঃ

ব্যাখাঃ  (Place value of 6)  - ( face value of 6)   =(6000 - 6)  = 5994

প্রশ্নঃ The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is :

বর্ণনাঃ

Hints: Let the numbers be 2x  and 3x

Then,their L.C.M = 6x

So, 6x = 48 

x = 8 

The numbers are 16 and 24 

Hence, required sum = (16+24) =40

প্রশ্নঃ The value of (1+.1+.01+.001) is :

বর্ণনাঃ

Hints:  1.000 + 0.100 + 0.010 + 0.001 = (+) 1.111

প্রশ্নঃ What mathematical operation come at the place of '?' in the equation : 2?6-12/4+2=11.

বর্ণনাঃ

Hints: =2×6-12÷4+2= 2 × 6 - 3 + 2 = 12 - 3 + 2 = 11

answer : ×

প্রশ্নঃ A boy was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was :

বর্ণনাঃ

Hints: Let the number be x

x ×52 = x ×25 + 324

27x =324 

x = 12 

প্রশ্নঃ Three-fifth the square of a certain number is 126.15. What is the number?

বর্ণনাঃ

Hints: Let,  the certain number be x

3/5 × x² = 126.15

x² =126.15 ×( 5/3)

x² =210.25

x = 14.5 

প্রশ্নঃ The average of 2, 7, 6 and x is 5 and the average of 18, 1, 6, x and y is 10. What is the value of y?

বর্ণনাঃ

Hints:  (2+7+6+x) / 4 = 5

    15 + x = 20 

x= 20- 15 

x = 5 

and,  (18+1+6+x+y)/5 =10

18 +1+6+5+y =50

y =20

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

বর্ণনাঃ

Hints: Let the number  be x

x-36 = 86 - x

2x = 122

x = 122 ÷ 2 = 61

প্রশ্নঃ A two-digit number becomes five-sixth of itself when its digits are reversed. Two digits differ by one. The number is :

বর্ণনাঃ

Hints: When the digits are reversed, the number become  5/6 th of itself,  lesser. So the units place digit is smaller.

Let, units place digit is x, so 10th place is x+1,  as the two digits differ by 1.

5/6 { 10(x+1) +x} = 10x +x +1 

5 (11x +10) =6(11x +1)

55x +50 =66x +6 

11x =44

x =4 

The number is = 10(4+1) = 10×5+4 =54

প্রশ্নঃ The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years older than P, what will be the ratio of the ages of P and Q after 4 years?

বর্ণনাঃ

Hints: Let P age and Q age be 6x years and 7x years

Then, 7x - 6x =4 

 x = 4 

So the required ratio will be  (6x+4)/(7x+4) = 28/32 = 7/8 

প্রশ্নঃ The difference between a number and its two-fifth is 510. What is 10 percent of that number?

বর্ণনাঃ

Hints: Let the number be x

Then, x- 2x/5 =510

(5x-2x) /5 =510

3x = 510×5

x = 850

So, 10% of 850 = 85

প্রশ্নঃ The profit earned by selling an article for Tk. 832 is equal to the loss incurred when the same article is sold for Tk. 448. What should be the sale price for making 50% profit?

বর্ণনাঃ

Hints: Let, cost price be TK x

Then, (832 -x) /x ×100 = (x-448)/x ×100

832 - x = x- 448

2x = 1280

x = 640

Profit = 50% of TK 640 = Tk.( 50/100)×640 = TK 320

So, the required sales price is (640 + 320)  Tk. = Tk. 960

প্রশ্নঃ The ratio of three numbers is 3 : 4 : 7 and their product is 18144. The numbers are :

বর্ণনাঃ

Hints: Let the number be x

So, the three numbers will be  3x, 4x, and 7x

Now, 3x × 4x × 7x = 18144

 84x³ = 18144

x³ = 216

x³ = 6³

x = 6

Hence, the numbers are 18, 24, 42 

প্রশ্নঃ P and Q started a business investing Tk. 85,000 and Tk. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?

বর্ণনাঃ

Hints: required ratio = 85000 : 15000 = 85 : 15 = 17 : 3 

প্রশ্নঃ A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?

বর্ণনাঃ

Hints: A and B in 1 day together work ( 1/10 + 1/15) portion = (3+2)/30 = 5/30 =1/6

Together they finish in 6 days. 

প্রশ্নঃ Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many will the tank be filled?

বর্ণনাঃ

Hints:  Pipe A, B, and C can fill the tank in 1 hour

( 1/5 +1/10 + 1/30)  portion

= (12+6+2)/6o portion

=  20/60 portion

= 1/3 portion

All three pipes will fill the tank in 3 hours. 

প্রশ্নঃ An athlete runs 200 metres race in 24 seconds. His speed is :

বর্ণনাঃ

Hints: His speed = 200/24 metre per second

         = (200/24) × 18/5 km/hr

       = 30 km/hr 

প্রশ্নঃ How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length?

বর্ণনাঃ

Hints: To convert km/hr  into m/s,  multiply with 5/18

So, 72km/hr = (72×5)/ 18 m/s = 20 m/s

Time required to cross the bridge = (110+132)/20 seconds = 12.1 seconds 

প্রশ্নঃ In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is :

বর্ণনাঃ

Hints : Speed in still water  = 1/2 (11+5) km/hr = 8 km/hr 

প্রশ্নঃ Reena took a loan of Tk. 1200 with simple interest for as many years as the rate of interest. If she paid Tk. 432 as interest at the end of the loan period, what was the rate of interest?

বর্ণনাঃ

Hints : Let, rate = R% and time = R years

Then,  ( 1200×R×R)/100 = 432  [ I= pnr]

  12R²  = 432 

R² = 36 

R = 6 

প্রশ্নঃ At what rate of compound interest per annum will a sum of Tk. 1200 become Tk. 1348.32 in 2 years?

বর্ণনাঃ

Hints : Let ,  Rate will be R%

Compound Interest formula

C= P (1+r)ⁿ

1348.32 = 1200 (1 +r) ²

1348.32/1200 = (1+r)²

R = 6% 

প্রশ্নঃ The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Tk. 800 per sq. metre.

বর্ণনাঃ

Hints: Length = 5.5m  and  width  = 3.75 m

Area = 5.5×3.75 sq.m = 20.625 sq.m

Cost of paying  =800×20.625 = 16500 Tk.

প্রশ্নঃ In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by :

বর্ণনাঃ

Hints:  Distance covered by B in 9 sec = (100/45)×9 m = 20 m

A beats B by 20 metres

প্রশ্নঃ A man buys Tk. 50 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?

বর্ণনাঃ

Hints: Dividend on 1 share = (50×10%) Tk

      = 50 ×(10/100) = 5 Tk. 

Tk. 12.5 is an income on an investment of Tk. 100

Tk. 5 is an income on an investment of Tk (100×5) / 12.5 = 40