Question

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

Answer 1

Hint: First we will find the multiplication of A with A itself gives a number whose one digit is A again and this happens only when A is 1, 5 or 6. Then we will consider the cases, first take \[{\text{A}} = 1\], \[{\text{A}} = 5\] and \[{\text{A}} = 6\], whichever satisfies the given product conditions.

Complete step by step solution: We are given that

We know that the basic idea of multiplication is repeated addition.

The multiplication of A with A itself gives a number whose one digit is A again and this happens only when A is 1, 5 or 6.

First, we will take \[{\text{A}} = 1\], so the multiplication will be \[11 \times 1 = 11\].
However, the tens digit is given as 9.

Therefore, \[{\text{A}} = 1\] is not possible.

Now, we will take \[{\text{A}} = 5\], so the multiplication will be \[15 \times 1 = 75\] and as the tens digit is given as 9.

Therefore, \[{\text{A}} = 5\] is not possible.

We will now take \[{\text{A}} = 6\], so the multiplication will be \[16 \times 1 = 96\], where the tens digit is the same as 9.

Thus, \[{\text{A}} = 6\] is true.

We have the multiplication as follows.

This implies that the value of A is 6.

Note: In solving these types of questions, you need to know that a product is the result of multiplication or an expression that identifies factors to be multiplied. One needs to know that the number, which is a carry-over will be added to the first column of the given product or else the solution will be wrong. We can also find the product by adding the number that many times, which is time-consuming.