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 B and 5 is giving a number whose one’s digit is B again. This is possible when B = 5 or B = 0 only.
• If B = 5, the product, B × 5 = 5 × 5 = 25, 2 will be a carry for the next step. We have, 5 × A + 2 = CA, which is possible for A = 2 or 7

The multiplication is as follows:

• If B = 0, the product, B × 5 = 0 × 5 = 0. There will not be any carry in this step.
• In the next step, 5 × A = CA. It can happen only when A = 5 or A = 0
• However, A cannot be 0 as AB is a two-digit number. Hence, A can be 5 only. 
• Hence, when B = 0, A = 5 we get 5 × A = CA = 5 × 5 = 25 which dentoes that C = 2.

Hence, there are 3 possible values of A, B, and C.
(i) 5, 0, and 2 respectively
(ii) 2, 5, and 1 respectively
(iii)7, 5, and 3 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. AB × 5 = CAB

Class 8 Maths NCERT Solutions - Chapter 16 Exercise 16.1 Question 6

Summary:

There are 3 possible values of A, B, and C: (i)5, 0, and 2 respectively, (ii)2, 5, and 1 respectively, (iii)7, 5, and 3 respectively

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