Question

a two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 7or by multiplyingthe difference of the digits by 18 and then adding one . find the number

Answer 1

Answer:

Explanation:

Let us assume, x and y are the two digits of the two-digit number

Therefore, the two-digit number is 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

Multiply equation 1 by 3

21y – 6x = 15 -------------3

Subtract equation 2 from equation 3

4y = 12

y = 3

substitute y = 3 in equation 1

7*3 – 2x = 5

21 – 2x = 5

2x = 16

x = 8

Therefore, the two-digit number = 10x + y = 10*8 + 3 = 83

Ans – The required two-digit number = 83.

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