A number consists of two digits whose sum is 9 .If the digit are reversed the new number is 3/8 of the first number. Find the number
Answers
Answer:
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Step-by-step explanation:
The sum of the two digits of a two digit number is 9. Let the two digits be x and y
x+y=9 ———Eq-(1)
Let the tens digit be x and units digit be y .
The number is 10x+y
If we reverse the digitas the number we get =10y+x.
Condition given in the problem is that the New number is 3/8 of the original number. If we put this condition into equation it will look like 10y+x=(3/8)(10x+y)
By solving the above equation we get
80y+8x=30x+3y. By rearranging the equation we get
30x+3y=80y+8x.
22x−77y=0 by dividing the left hand and right hand side by 11 we get
2x−7y=0 ————Eq-(2)
Eq - (1)×2 =2x+2y=18
Eq - (2)×1 =2x−7y=0
By subtracting the equation 2 from equation 1 we get
9y=18.
y=18/9=2.
By substituting the value of y in equation 1 we get value of x=7.
The original number is 72, if we interchange the digits we get 27. 27 is 3/8th of 72