NCERT Solution For Class 8 Maths Chapter – 16 Playing with numbers Exercise – 16.1

Q1. Find the values of the letters in each of the following and give reasons for the steps involved.

(i)

       3     A

    + 2      5

     ———–

       B        2

 

Solution:-

 

Say A = 7 and we get

7 + 5 = 12

In which one’s place is 2.

Therefore , A = 7

And putting 2 and carry over 1 , we get

B = 6

Hence A = 7  and B = 6

 

2. 4     A

   + 9     8

     CB    3

 

Solution:-

 

If A = 5 and we get

8 + 5 = 13 in which ones place is 3.

Therefore, A = 5 and carry over 1 then

B = 4 and C = 1

Hence , A = 5 B = 4 and  C = 1

 

3. 1      A

     X      A

      9      A

 

Solution:-

 

On putting A = 1 , 2 , 3,4,5,6,7 and so on and we get,

A X A = 6 X 6 =  36 in which ones place is 6.

 

4. A      B

  +  3       7

       6       A

 

Solution:-

 

Here we observe that B = 5 so that 7 + 5 – 12

Putting 2 at ones place and carry over 1 and A = 2, we get

2 + 3 + 1 = 6

Hence A = 2 and B = 5

 

 

5. A      B

      X       3

      CA    B

 

Solution:-

 

Here on pitting B = 0 we get 0 x 3 = 0

And A = 5 , then  5 x 3 = 15

A = 5 and C = 1

Hence A = 5 B = 0 and C = 1

 

 

6. A     B

     X     5

   CA    B

 

 

Solution:-

 

On putting B = 0 , we get 0 x 5 = 0 and A = 5

Then 5 x 5 = 25

A = 5 , C = 2

Hence A = 5 , B = 0 and C = 2

 

7. A    B

      X    6

BB   B

 

 

Solution:-

 

Here the product of B and 6 must be same as ones place digit as B.

6 x 1 = 6,  6 x 2 = 12,   6 x 3 = 18,   6 x 4 = 24

On putting B = 4 ,  we get the ones digit 4 and remaining two B’s value should be 44.

Therefore, for 6 x 7 = 42 + 2 = 44

Hence A = 7 and B = 4

 

 

8. A    1

  + 1    B

      B    0

 

Solution:-

 

On putting B = 9 we get 9 + 1 = 10

Putting  0 at ones place and carry over 1, we get for A = 7

7 + 1 + 1= 9

Hence A = 7 and B = 9.

 

9. 2     A      B

  + A     B      1

     B     1       8

 

 

Solution:-

 

On putting B = 7 we get 7 + 1 = 8

Now A = 4 then 4 + 7 = 11

Putting 1 at tens place and carry over 1, we get

2 + 4  + 1 = 7

Hence A = 4 and B = 7

 

10. 1    2   A

         6    A   B

      —————

          A   0    9

 

 

Solution:-

 

Putting A = 8 and B – 1 we get,

8 + 1 = 9

Now , again we add 2 + 8 = 10

Tens place digit is ‘0’ and carry over 1. Now 1 + 6 + 1 = 8 = A

Hence A = 8 and B = 1