Solve this:

​Q2. A boy was asked to find the LCM of 3, 5, 12 and another number, But while calculating, he wrote 21 instead of 12 and yet came with correct answer. What could be the fourth number?

Q5. Whcih two digit numbers when added to 27 get reversed?

Q6. Cement mortar was being prepared by mixing cement to sand in the ratio of 1:6 by volume. In a cement mortar of 42 units of volume, how much more cement needs to be added to enrich the mortar to ratio 2: 9?



 

 

Dear Student,

Please find below the solution to the asked query:

2 ) We have numbers , As : 3 , 5 , 12 and we assume forth number = x 

So, L.C.M. ( 3 , 5 , 12 and x  ) :

here 3 and 5 are prime numbers

and

12  = 2 $\times$ 2 $\times$ 3

So, L.C.M.  ( 3 , 5 , 12 and x  ) = 2 $\times$ 2 $\times$ 3 $\times$ 5 $\times$ x                        --- ( 1 )

And as given while calculating he wrote 21 instead of 12 , So

21  = 3 $\times$ 7

So,

So, L.C.M.  ( 3 , 5 , 21 and x  ) =  3 $\times$ 5 $\times$ 7 $\times$ x                         --- ( 2 )

As we get same L.C.M. from equation 1 and 2 and we can see that :  2$\times$ 2 $\times$ 7  are not common in both equations , So

Our forth number could be =  2 $\times$ 2 $\times$ 7 =  28                                ( Ans )


5 ) Let our two digit number = 10 x  + y , So from given condition we get :

10 x  + y + 27 = 10 y  + x , 

9 x  - 9 y = - 27  ,

- 9 ( y - x ) = - 27 ,

y  - x  =  3                                --- ( 1 )

So,  At y  =  4 and x  =  1 we get from equation 1 :

4 - 1 = 3 ,

3 = 3 , Satisfied , So our number  = 10 ( 1) + 4 =  10 + 4 =  14 

And

14 + 27 =  41 , That verified given condition so

Our required number could be  = 14  ,  Here we can find more two digits number by following above process ,Try to find those numbers by yourself .

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