**Chapter 16 Playing with Numbers Exercise 16.1**

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

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

3 × B = B

⇒ B = D

3 × A = CA

⇒ 3 × 5 = 15

Thus A = 5 and C = 1

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

Question 6.

Solution:

5 × B = B

⇒ B = 0 or 5

5 × A = CA

5 × 5 = 25

Only possible when B = 0

Thus A = 5 and C = 2

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

Question 7.

Solution:

B × 6 = B

6 × 4 = 24 → B = 4 and 2 is carried to

6 × A = BB

⇒ 6 × 7 = 42 + 2 (carried on) = 44

Thus B = 7

Hence A = 7 and B = 4

Question 8.

Solution:

1 + B = 0

1 + 9 = 10 → unit digit is 0 and 1 is carried to A

+ 1 +1 (carried on) = B = 9

A + 2 = 9 ⇒ A = 9 – 2 = 7

Hence A = 7 and B = 9

Question 9.

Solution:

B + 1 = 8 ⇒ B = 8 – 1 = 7

A + B = a number with unit digit 1

A + B = 11

⇒ A + 7 = 11

⇒ A = 11 – 7 = 4 (1 Carried to)

Now 1 carried on + 2 + A = B

3 + A = 7

⇒ A = 7 – 3 = 4

Hence A = 4, B = 7

Question 10.

Solution:

9 = A + B

9 = 1 + 8 or 2 + 7 or 3 + 6 or 4 + 5 or 8 + 1 or 7 + 2 or 6 + 3 or 5 + 4 or 0 + 9 or 9 + 0

Now 0 is required at unit place

2 + A = 10

⇒ A = 10 – 2 = 8

B = 9 – 8 = 1

1 + 6 + 1 (carried on) = A = 8

Hence A = 8 and B = 1