 Hi and welcome to the session. Let us discuss the following question. Question says find the values of the letters in the following and give reasons for the steps involved. Let us now move on to the solution. Now first of all we will rewrite the given puzzle that is 1a multiplied by a gives 9a. Now we need to find the value of letter a. Now clearly you can see unit's digit of a multiplied by a is a itself. Now clearly you can see here unit's digit or we can say 1's digit of 0 multiplied by 0 is 0. Similarly 1's digit of 1 multiplied by 1 is 1 and 1's digit of 5 multiplied by 5 is 5 itself. Similarly unit's digit of 6 multiplied by 6 is 6 itself. So possible values of a are 0, 1, 5 or 6. Now we know that first digit of a number cannot be 0. Now here a is the first digit of this number. So value of a can't be 0. So possible values of a are 1, 5 and 6. And we can write since the 1's digit of a multiplied by a is a it must be that a is equal to 1, a is equal to 5 or a is equal to 6. Now clearly you can see product of 1, a and a is greater than 90. We know that a cannot be equal to 0 so product of 1, a and a is greater than 90. Now we can write is a is equal to 1 then product 1, a multiplied by a is 11. Clearly you can say for a equal to 1 product of 1, a and a is given by 11 multiplied by 1 which is further equal to 11 only. Now 11 is less than the product 9a so a cannot be equal to 1. Now we can write but 11 is less than 9a so a cannot be equal to 1. Now let us consider another possibility that is a is equal to 5. Now if a is equal to 5 then the product that is 1a multiplied by a is 75. We know that if we substitute 5 for a then we get 15 multiplied by 5 as the product and 15 multiplied by 5 is equal to 75. Now 75 is again less than the product 9a. Now we can write but 75 is less than 9a. So a cannot be equal to 5. Now consider last possibility that is a is equal to 6. Now if a is equal to 6 then 1a multiplied by a is 96. Now this value is equal to the product 9a. But value of a is 6. Now we can solve the puzzle as 16 multiplied by 6 gives 96 and required value of a is 6. This is our required answer. This completes the session. Hope you understood the solution. Take care and bye for now.