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

Solution:

Each letter in the given puzzle must stand for just one digit. 

The operation performed here is multiplication.

• The multiplication of 6 and B gives a number whose one’s digit is B again. It is possible only when B = 0, 2, 4, 6, or 8
• If B = 0, then the product will be 0. Therefore, this value of B is not possible.
• If B = 2, then B × 6 = 12, and 1 will be a carry for the next step. 6A + 1 = BB = 22 ⇒ 6A = 21 and hence, any integer value of A is not possible.
• If B = 6, then B × 6 = 36, and 3 will be a carry for the next step. 6A + 3 = BB = 66 ⇒ 6A = 63 and hence, any integer value of A is not possible.
• If B = 8, then B × 6 = 48, and 4 will be a carry for the next step. 6A + 4 = BB = 88 ⇒ 6A = 84 and hence, A = 14. However, A is a single-digit number.Therefore, this value of A is not possible.
• If B = 4, then B × 6 = 24, and 2 will be a carry for the next step. 6A + 2 = BB = 44 ⇒ 6A = 42 and hence, A = 7

The multiplication is as follows.

Hence, the values of A and B are 7 and 4 respectively.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 16

Video Solution:

Find the values of the letters in the following and give reasons for the steps involved. A B × 6 = B B B

Class 8 Maths NCERT Solutions - Chapter 16 Exercise 16.1 Question 7

Summary:

The values of the letters A and B are 7 and 4 respectively.

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