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.

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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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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 = 33𝑦/66 x = 𝑦/2 Also, given that Difference of digits is 3 So x – y = 3 or y – x = 3 Since x = 𝑦/2 x is smaller than y So, x – y will be negative (𝑦/2−𝑦=(−𝑦)/2) ∴ We can’t use x – y = 3 Thus, our equations are x = 𝑦/2 …(1) y – x = 3 …(2) From (2) y – x = 3 Putting x = 𝑦/2 y – 𝑦/2 = 3 𝑦/2 = 3 y = 3 × 2 y = 6 Putting y = 6 in (1) x = 𝑦/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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