Question

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

A 1
+ 1 B
__________
B 0
__________

Answer 1

Given :  

A 1

+ 1 B

__________

B 0

__________

Concept :

Numbers can be written in general form. Hence, a two digit number ab will be written as ab = 10a + b.

The general form of numbers is helpful in solving puzzles or number games.

Rules to be followed while solving the puzzles:

1.Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter.  

2. The first digit of a number cannot be zero.

Solution  :

On putting B = 9, we get 9 + 1 = 10

Put 0 at one’s place and carry over 1, we get

For A = 7

7 + 1 + 1 = 9

  A 1

+ 1 B

__________

  B 0  

__________

   7 1

+ 1 9

__________

 9  0  

__________

Hence, the values of the letter A is 7 & B is 9 .

Hope this answer will help you….

 

Here are some more questions from this chapter :  

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

A B

x 5

__________

C A B

__________

brainly.in/question/17209680

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

1 2 A

+ 6 A B

__________

A 0 9

__________

brainly.in/question/17209680

Answer 2

Let the two digit number is 10x + y.

Sum of the digits of to digit number is

x + y = 9 ………….. (i)

Number obtained by reversing the order of the digits, we get 10y + x.

Twitching the 10y + x, it is nine times of first number.

∴ 2(10y + x) = 9(10x + 4)

20y + 2x = 90x + 9y

2x – 90x + 20y – 9y = 0

-88x + 11y = 0

88x – 11y = 0

8x – y = 0 ………….. (ii)

By adding eqn. (i) to eqn. (ii)

$x + y = 9 \\ \underline {+ 8x - y = 0} \\ 9x \: \: \: \: \: = 9$

Substituting the value of ‘x’ in eqn. (i),

x + y = 9

1 + y = 9

y = 9 – 1

y = 8

∴ x = 1, y = 8

∴ Two digit number = 10x + y

= 10 × 1 + 8

= 10 + 8

=18

$so \: no. \: are \boxed{18}$