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

Rajasthan Board RBSE Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.1 Textbook Exercise Questions and Answers.

RBSE Class 8 Maths Solutions Chapter 16 Playing with Numbers Ex 16.1

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

Question 1.

Answer:

∵ A + 5 = 2
∴ A + 5 = 12 or 22 or 32 etc.
∴ A = 12 - 5 = 7
or 22 - 5 = 17
∴ A = 7 (∵ A = 17 is not possible)

Hence, A = 7, B = 6

Question 2.

Answer:

Thus, A = 5, B = 4 and C = 1

Question 3.

Answer:
Since the ones digit of A × A = A, so it must be 1, 5 or 6.
∵ 1 × 1 = 1
5 × 5 = 25
6 × 6 = 36
Now, taking the value of ‘A’ as 1, 5 or 6.
When : A = 1;
11 = 9A
When : A = 5
75 = 9A
When : A = 6
96 = 9A

Thus, A = 6 is correct answer.

Question 4.

Answer:
Addition in ones column:
Here, B + 7 is ‘A’ that is a number whose one digit is ‘A’.
Let us put the values of ‘B’ starting from 0.
If B = 0, then A = 7 ∴ 7 + 3 ≠ 6
If B = 1, then A = 8 ∴ 8 + 3 ≠ 6
If B = 2, then A = 9 ∴ 9 + 3 ≠ 6
If B = 5, then A = 2 ∴ (2 + 3) + 1 = 6

So, B = 5 and A = 2 satisfying die given condition.

Question 5.

Answer:
∵ The ones digit of B × 3 is B, it must be B = 0 or B = 5.
Now, If A = 1, then

Thus B = 0, A = 5 and C = 1

Question 6.

Answer:
Since the ones digit of B × 5 is B
∴ B must be 0 or 5.
When B = 0 and A = 5

A = 7, B = 5, C = 3 (Satisfied the condition)
Hence, (A = 5, B = 0, C = 2)
or (A = 7, B = 5, C = 3)

Question 7.

Answer:
Here the possible products are 222, 444 or 888.
When B = 4, then

Thus A = 7 and B = 4.

Question 8.

Answer:
If we do the addition in the ones column i.e. (1 + B), we get 0.
∴ B should be 9.
Thus, A must be 7.

Thus, B = 9 and A = 7

Question 9.

Answer:
If we do the addition in the ones column i.e. (B + 1), then we get 8.
∴ B should be 7 and A should be 4.

So, the given condition is satisfied.
Hence, A = 4 and B = 7

Question 10.

Answer:
Here addition of ones column gives the value 9.
∴ A + B should be (1, 8) or (8, 1)
If A = 1 and B = 8, then

Thus A = 8 and B = 1
Satisfy the given condition.