# Chapter 16 Playing with Numbers

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.

Ex 16.1 Class 8 Maths Question 1.

Solution:

Ex 16.1 Class 8 Maths Question 2.

Solution:

Ex 16.1 Class 8 Maths Question 3.

Solution:

Ex 16.1 Class 8 Maths Question 4.

Solution:

Ex 16.1 Class 8 Maths 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

Ex 16.1 Class 8 Maths 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

Ex 16.1 Class 8 Maths 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

Ex 16.1 Class 8 Maths 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

Ex 16.1 Class 8 Maths 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

Ex 16.1 Class 8 Maths 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