1.

A number consisting 2 digits exceeds 4 time the sum of the digits by 3. If 27 is added to the number, the digits are reversed. find number.

Answer»

Let tens digit be x and units digit be y

Then number =10x+y

Since the number is 4 times the sum of digits

Hence 10x+y=4(x+y) i. e. 6x=3y. Or 2x=y……(i)

Also when 27 is added the digits are reversed

Number when digits are reversed =10y+x

Hence 10x+y+27=10y+x

9x+27=9y. Or x+3=y………..(ii)

From (i) and (ii) we get

x+3=2x hence x=3. and y=2x=6

and number =36



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