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Question

A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding to find the numbers how many such numbers are there

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Solution

Sol:
Let the two digit number be 10x + y.

Two digit number is obtained by multiplying sum of the digits by 8 and adding 1
⇒ 10x + y = 8(x + y) + 1
⇒ 2x - 7y = 1 ---------------- (1) Two digit number is obtained by multiplying the difference of the digits by 13 and adding 2 ⇒10x + y = 13(x - y) + 2 ⇒ 3x - 14y = -2 ----------- (2) Solving equations 1 and 2, we get x = 4 and y = 1.

Therefore, the two digit number is 10(4)+1 = 41

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