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. 

Loss Tk 2.50

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%? 

Tk 17.40 per kg

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

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

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

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`

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

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.

Question:5.Which of the following numbers is not disivible by 2.
 3567516,9130525,7870832,1371594 

Sol.Clearly,the unit,s digit of 913o525 is 5,which is not divisible by 2.
So,9130525 is not disivible by 2.
Each of the numbers has a unit digit disivible by 2.
So, each one other than 9130525 is disivible by 2.

Question:6.Which of the following numbers is divisible by 3.

(i)541326   (ii) 5967013 

Sol.(i) Sum of digit in 541326 is 21,which is divisible by 3.
So,541326 is divisible by 3.
  (ii) Sum of digits in 5967013 is 31,which is not divisible by 3.
  Hence,5967013 is not divisible  by 3.

Question:Divisiblity By 9:A number is divisible by 9,if the sum of its digits is divisible by 9.

7.Which of the following numbers is divisible by 9.
 (i)19725462 (ii) 36870521 

Sol.(i) Sum of digits in 19725462 is 36,which is divisible by 9.
        So,the given number is divisible by 9.
(ii)Sum of digits in 36870521 is 32, which is not divisible by 9.
      So,the given is not divisible by 9.

Question:Divisiblity by 4:A number is divisible by 4,if the  number formed by the last two digits is divisible by 4.

8.Which of the following numbers is divisible by 4.?
  (i) 67920594  (ii) 618703572 

Sol.(i) The number formed by the last 2 digits in the given number is 94,
which is not divisible by 4.
 :. 67920594 is not divisible by 4.

(ii) The number formed by the last 2 digits in the given number is 72,which is divisible by 4.
:. 618703572 is divisible by 4.

Question:Divisiblity by 8: A number is divisible by 8,if the number formed by the last 3 digits of the given number is divisible by 8.

9.Which of the following numbers is divisible by 8.
  (i) 98016542  (ii) 106598304 

Sol.(i) The number formed by the last 3 digits of the given number is 542.
 which is not divisible by 8.
:. 98016542 is not divisible by 8.

(ii)The number formed by the last 3 digits of the given number is
 304, which is divisible by 8.
:. 106598304 is divisible by 8.