Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is 3, determine the number.

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

Question 15
Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is 3, determine the number.
Number is of the form
Let digit at units place = y
and the digit at tens place = x
Number = 10x + y
Reversed Number = 10y + x
Given that
7 times number is equal to 4 times reverse of number
7 (Number) = 4 (Reversed Number)
7 (10x + y) = 4 (10y + x)
70x + 7y = 40y + 4x
70x 4x = 40y 7y
66x = 33y
x = 33 /66
x = /2
Also,
given that
Difference of digits is 3
So x y = 3
or
y x = 3
Since x = /2
x is smaller than y
So, x y will be negative ( /2 =( )/2)
We can t use x y = 3
Thus, our equations are
x = /2 (1)
y x = 3 (2)
From (2)
y x = 3
Putting x = /2
y /2 = 3
/2 = 3
y = 3 2
y = 6
Putting y = 6 in (1)
x = /2
x = 6/2
x = 3
Hence x = 3, y = 6 is the solution
Number = 10x + y = 10(3) + 6 = 30 + 6 = 36
Number = 36

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.