(e) If a two-digit number is divided by the sum of the digits, the quotient is 9. But the number obtained by reducing the digit at the tens place by four times the digit at the units place, leaves the remainder 5 when divided by the sum of the original number. Find the original number.
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Answer:
72
Step-by-step explanation:
Let the tens digit be x
Let the units digit be y
The required number is 10x+y
The sum of the digits is x+y
Given, (10x+y)/(x+y) = 8
=> 10x+y = 8(x+y)
=> 10x+y = 8x+8y
=> 10x-8x = 8y-y
=> 2x = 7y
=> 2x-7y = 0 ------------(1)
Given, x-3y = 1
=> 2x-6y=2 -------------(2)
Solving (1) and (2), we get x=7 and y=2
The answer is 72
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