1. Question:Hari purchased 25 kg of wheat at Tk 4 per kg and 35 kg of wheat at tk 4.50 per kg. He sold the mixture at taka 4.25 per kg. Find his gain or loss. 

    Answer
    Loss Tk 2.50






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  2. Question:a grocer purchased 80 kg of rice at tk 13.50 per kg and mixed with 112 kg rice at tk 16 per kg. At what rate per kg should he sell the mixture to gain 16%? 

    Answer
    Tk 17.40 per kg






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  3. Question:Find the unit's digit in the product `(256 xx 27 xx 159 xx 182)`. 

    Answer
    Product of units the given numbers = `(6 xx 7 xx 9 xx 2) = 756`
      `:.` unit digit in the given product is `6`.






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  4. Question:2.Find the unit,s digit in the product` (3^67 xx 6^39 xx 7^53)` 

    Answer
    sol.Clearly ,unit digit in `3^4` is 1.
          
         :. unit digit in `3^64` is 1.
          
         :. unit digit in `3^67` is 7. [unit digit in `1 xx 3 xx 3 xx 3` is 7]
           
          clearly unit digit in every power of 6 is 6.
           
          :.unit digit in `6^39` is 6.
           
           clearly unit digit in `7^4` is 1.
         
           :. unit digit in `7^72`is 1.
           
           :. unit digit in `7^53`is 7. [unit digit in `1 xx 7` is 7]
            
           :.unit digit in given product =unit digit in`(7 xx 6 xx 7) = 4`






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  5. Question:4.which of the following are prime numbers.? (i)191 (ii) 241 (iii)337 (iv) 391 

    Answer
    Sol.(i) ,14>√191.
    prime numbers less than 14 are 2.3,5,7,11,13.
    191 is not divisible by any of them .
    So 191 is a prime number.
    
    (ii) Clearly,16>√241.
     prime numbers less than 16 are 2,3,5,7,11,13.
      241 is not divisible by any of them. 
    :.241 is a prime number.
     (iii) Clearly,19>√337.
     prime numbers less than 19 are 2,3,5,7,11,13,17.
    337 is not disivible by any of them.
    :. 337 is a prime number.
    (iv)Clearly,20>√391.
     prime number less than 20 are 2,3,5,7,11,13,17,19.
    We find than 391 is divisible by 17.
    :. 391 is not prime.






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