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.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/

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Note:

If we don’t know that y is greater or x greater

We solve using both equations

Check Example 13

 

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Transcript

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

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.