Question

The sum of the digits of a two-digit number is 11. The tens digit is one more than four times the units digit. Find the number.
a. 92
b. 82
c. 85
d. 95

Answer 1

Hint: We will assume that the number is 10y + x. Then according to the conditions given in the question, we can write x + y = 11 and y = 4x + 1. We will put the value of y as 4x + 1 in x + y = 11 and then find the value of x from there and then we will find the value of y, hence we will get the number.

Complete step by step solution:
It is given in the question that the sum of the digits of a two-digit number is 11 and that the tens digit is one more than four times the units digit and we have been asked to find the number.
So, let us assume the number to be 10y + x ……… (i)
Now, we have been given that the sum of the digits is equal to 11. So, we get,
x + y = 11 ……… (ii)
Also, it is given that the tens digit is one more than four times the units digit. So, we can write,
y = 4x + 1 ……… (iii)
Now, we will substitute the value of y from equation (iii) in equation (ii). So, we will get,
x + 4x + 1 = 11
5x + 1 = 11
On transposing 1 from LHS to RHS, we get,
5x = 11 – 1
5x = 10
On dividing both the sides by 5, we get,
x = 2
Therefore, we get the value of x as 2. Now, on substituting the value of x = 2 in equation (iii), we get,
y = 4 (2) + 1
y = 8 + 1
y = 9
Hence, we get the value of y as 9. Now, on substituting the values of x = 2 and y = 9 in equation (i), we get the number as,
10 (9) + 2
90 + 2
92
Thus, we get the required number as 92.
Hence, option (a) is the correct answer.

Note: The possible mistakes that the students can make in this question is by writing the formula of the number as y + x instead of 10y + x, this will lead to the wrong answer. Also, for the condition, the tens digit is one more than four times the units digit, the students may write the equation as y + 1 = 4x instead of y = 4x + 1. So, the students must be careful while forming the equations. Also, after finding the values of x and y, the students may interchange those values and substitute it in the formula of the number, as 10 (2) + 9 = 29 and this is not the correct answer.