A 2 digit number obtained by either multiplying the sum of digit by 8 and then subtracting 5 or by multiplying the difference of digits by 16 and adding 3. find the number
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Let us assume x and y are the two digits of the 2 digit-number
Therefore, the two-digit number = 10x + y
Given:
10x + y = 8 (x + y) – 5
10x + y = 8x + 8y – 5
7y – 2x = 5 ---------------1
Also given:
10x + y = 16 (x – y) + 3
10x + y = 16x – 16y + 3
17y – 6x = 3 ------------ 2
Adding equation 1 and equation 2
24y – 8x = 8
3y – x = 1
x = 3y – 1 ---------------3
Substitute the value of x in equation 1
7y – 2 (3y - 1) = 5
7y – 6y + 2 = 5
y = 3
Therefore, x = 3y – 1 = 3*3 – 1 = 8
Therefore, the two-digit number = 10x + y = (10 * 8) + 3 = 83Similar questions
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