**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.

**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 16.2**

**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:

1
2 8

+ 6
8 1

-------------

8
0 9

------------

Therefore, A = 8 and B = 1.

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