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Sample mathematics questions from some contents

Content 01: Numbers, Fraction and Ratio

Follow the rule and solve the math accordingly:

Rule: Finding Mean and Mode

- Mean: গড় / Average হল Example: Mean of 2, 3 and 7 is 4. We found the answer by [(2+3+7)/3]
- Mode: এক সেট সংখার মধ্যে জেতা সবচেয়ে বেশি বার আসে এটা হল

Example: Find the mode of 2, 3, 4, 5, 5, 6

Answer: 5 (because 5 appeared two times in the set)

Content 02: Percentage

Problem: Express 0.5% as a decimal.

Solution: 0.3% = (0.5/100) = 0.005

উপরোক্ত প্রবলেম গুলো আমরা এভাবেই সমাধান করব।

Content 03: Profit and Loss

Rule: Finding selling price (বিক্রয় মূল্য) when there is a gain.

Formula:

Selling Price = [(100+Gain %)/100] * Cost Price (ক্রয় মূল্য)

Example: Find selling price when cost price is Tk. 50 and gain is 10%

Solution: Using the formula, we can write

[(100+10)/100]* 50 = (110/100)*50 = Tk. 55 (ans)

Content 04: Interest

Formula for finding simple interest rate = (P*R*T)/100 , where P = Principle amount, R = Rate of interest and T = time ( in years)

Problem: Find simple interest on Tk. 3125 at 15 percent per annum for 73 days

Solution: Here Principle amount (P) is 3125, Rate of interest (R ) is 15 percent and T is (73/365)= 0.2

Thus, simple interest = (3125*15*0.2)/100 = 93.75 (answer)

Content 05: Ratio/ Proportions

Exercise: Divide Tk. 455 in the ratio of 4:5

Solution: দুই ratio র যোগফল হল 9 । তাই, ratioর প্রথম অংশে 455 র 4/9 অংশ বের করতে হবে এবং পরে 455 র 5/9 অংশ বের করতে হবে।

So, 455*(4/9) = 202.22 and 455*(5/9) = 252.77 .

Answer: 202.22 and 252.77

Content 06: Mixture/ Solution

Exercise: A rice seller mixes two varieties of rice, one costing Tk. 35 per bag and another costing Tk. 45 per bag in the ratio of 3:2. If the rice seller sells mixed variety at Tk. 41.60 per bag then what will be his gain/loss?

Solution:

Suppose the rice seller purchases 3 kg and 2 kg of rice of 1^{st} and 2^{nd} kind respectively. So, in total he is selling 5 kg

Cost Price = Tk. (3*35+2*45) = Tk. 195

His selling price is = Tk. (5* 41.60) = Tk. 208

Thus Gain = (13/195)*100 = 6.66 % (answer)

Content 07: Average

Problem: Find the average of first 20 natural numbers

Solution: For such kind of problems we need to use the following formula

Average = (1^{st} term + last term )/2 = (1+20)/2 = 10.5

Content 08: Age

Problem: Sum of ages of a father and a son is 50 years. 5 years ago father’s age was 5 times than the age of the son. Find out the present age of the father and the son.

Solution: এরকমের অঙ্ক আমরা x ধরে করব।

Let , age of the son is x years.

It is given that the sum of father and son is 50 years.

Thus, x+ Father’s age = 50

So, Father’s age = 50 – x

It is given that 5 years ago father’s age was 5 times then the age of the son.

Therefore, we can write

7(x-5) = (50-x-5)

Solving this, we get

X= 10

So, son’s age is 10 and father’s age is (50-10) = 40 (Answer)

Content 09: Distance

Problem: Covnert 30 km/hr into meters / sec.

Solution: Formula for such kind of problem is

X km/hr = x*(5/18) m/sec

Thus, 8.33 m/sec (ans)

Content 10: Geometry

Rule: Triangle er তিনটি কোণের যোগফল 180 ডিগ্রি।

Problem: Suppose the values of two angles of a triangle are 30 degree and 60 degree respectively. What is the value of other angle?

Ans: 90 degree ( as sum of three angles are 180 degree)

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