NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1 are the part of NCERT Solutions for Class 8 Maths. Here you can find the NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1.

Ex 16.1 Class 8 Maths Question 1.

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

Solution:
1. There are two letters A and B, whose values are required to be found.
Observe the addition in the ones column, i.e., from A + 5 we get 2, i.e., the number whose ones digit is 2.
For this to happen, A must be 7. (∵ A + 5 = 7 + 5 = 12)
So, for the addition in tens column, we have
1 + 3 + 2 = B ⇒ B = 6
So, the puzzle has been decoded as:

3 7
+ 2 5
-----------
6 2
----------

∴ The values of A and B are 7 and 6, respectively.

2. There are three letters A, B and C, whose values are required to be found.
Observe the addition in the ones column, i.e., from A + 8 we get 3, i.e., the number whose ones digit is 3.
For this to happen, A must be 5. (∵ A + 8 = 5 + 8 = 13)
So, for the addition in tens column, we have 1 + 4 + 9 = B ⇒ B = 14
∴ Clearly, B is 4 and C is 1.
So, the puzzle has been decoded as:

4 5
+ 9 8
-----------
1 4 3
----------

∴ The values of A, B and C are 5, 4 and 1, respectively.

3. Since the ones digit of A × A is A, it must be that A = Either 1 or 5 or 6.

When A = 1, then

    1 1
×      1
-----------
    1 1
----------

So, we cannot take A = 1.

When A = 5, then

    1 5
×      5
-----------
    7 5
----------

So, we cannot take A = 5.

When A = 6, then

    1 6
×      6
-----------
    9 6
----------

So, the value A = 6 is correct.

So, the puzzle has been decoded as:

    1 6
×      6
-----------
    9 6
----------

4. There are two letters A and B, whose values are required to be found.
Observe the addition in the given puzzle, i.e., from B + 7 we get A and from A + 3 we get 6.
Let us take the possible values of A and B,

0 + 7 = 7 that is, A = 7 but 7 + 3 ≠ 6, so, rejected

1 + 7 = 8 that is, A = 8 but 8 + 3 ≠ 6, so, rejected

2 + 7 = 9 that is, A = 9 but 9 + 3 ≠ 6, so, rejected

3 + 7 = 10 that is, A = 0 but 1 + 0 + 3 ≠ 6, so, rejected

4 + 7 = 11 that is, A = 1 but 1 + 1 + 3 ≠ 6, so, rejected

5 + 7 = 12 that is, A = 2 but 1 + 2 + 3 = 6 (Correct)

Thus, A = 2 and B = 5 are the correct values.

So, the puzzle has been decoded as:

2 5
+ 3 7
-----------
6 2
----------

Therefore, A = 2 and B = 5.

5. There are three letters A, B and C, whose values are required to be found.
Since the ones digit of 3 × B = B, it must be B = 0. So, the puzzle becomes:

6. There are three letters A, B and C, whose values are required to be found. Since the ones digit of 5 × B = B, it must be that B = Either 0 or 5. If B = 0, then the puzzle becomes:

7. There are two letters A and B, whose values are required to be found.

    A B
×      6
-----------
B B B
----------
The possible values of BBB are 111, 222, 333, etc.
Let us divide these numbers by 6.
111 ÷ 6 = 18, remainder 3. So, 111 is rejected.
222 ÷ 6 = 37, remainder 0. So, the quotient 37 is not of the form A2. Thus,
222 is also rejected.
333 ÷ 6 = 55, remainder 3. So, 333 is rejected.
444 ÷ 6 = 74, remainder 0. The quotient 74 is of the form A4.
So, the puzzle has been decoded as:

    7 4
×      6
-----------
4 4 4
----------
Thus, A = 7 and B = 4 works out correctly.
So, the answer is A = 7 and B = 4.

8. There are two letters A and B, whose values are required to be found.
Observe the addition in the ones column: from 1 + B we get 0, that is, a number whose ones digit is 0.
For this to happen, the value of B should be 9. So, the puzzle becomes:

A 1
+ 1 9
-----------
9 0
----------
But 90 – 19 = 71, so, A1 = 71 ⇒ A = 7.
Thus, A = 7 and B = 9 is the correct answer.

9. There are two letters A and B, whose values are required to be found.
Observe the addition in the ones column, i.e., from B + 1 we get 8, that is, a number whose ones digit is 8.
For this to happen, the value of B should be 7. So, the puzzle becomes:

2 A 7
+ A 7 1
-------------
7 1 8
------------
Now, observe the addition in the tens column, i.e., from A + 7 we get 1, that is, a number whose ones digit is 1.
For this to happen, the value of A should be 4. So, the puzzle has been decoded as:

2 4 7
+ 4 7 1
-------------
7 1 8
------------
Therefore, the values of A and B are 4 and 7, respectively.

10. There are two letters A and B, whose values are required to be found.
Observe the addition in the tens column: from 2 + A we get 0, that is, a number whose ones digit is 0.
For this to happen, the value of A should be 8. So, the puzzle becomes:

1 2 8
+ 6 8 B
-------------
8 0 9
------------
Now, observe the addition in the ones column: from 8 + B we get 9. For this to happen, we must have B = 1. Therefore, the puzzle has been decoded as: