the sum of the digits of a two-digit number is 7 if the digits are reversed the new number increased by 3 less than 4 times the original number find the original number
Answers
Let the Orignal number be xy
We can write this two digit number as,
xy = 10x + y [ because x is in tens place and y is in ones place]
If we reverse the digits the place value of X becomes one and that of y becomes tens.
yx = 10y + x
Now,
According to the question ,
Sum of the digits = 7
=> x + y = 7
=> x + y - 7 = 0 .........(eq. 01)
If numbers are reversed the new number is 3 less than 4 times the orignal number.
=> 10y + x + 3= 4( 10x + y )
=> 10y + x + 3 = 40x + 4y
=> 6y - 39x + 3 = 0 .......(eq. 02)
Now, we will solve eq.01 and eq.02 by substitution method.
=> 6y - 39x + 3 = 0
=> y =( 39x - 3 )/6
we shall put this value in equation 01 ,
=> x + y = 7
=> x + (39 x - 3)/6 = 7
=> 6x + 39x - 3 = 42
=> 45x = 45
=> x = 1
Now we shall substitute this value in eq.01,
x + y = 7
=> 1 + y = 7
=> y = 6
Therefore, the numbers are 16 (orignal) and 61 (new).(Ans)
VERIFICATION :-
We can verify it numerically by substituting values in eq. 02
LHS = 6y - 39 x + 3
=> 6 × 6 - 39 × 1 + 3
=> 36 - 39 + 3
=> 39 - 39 = 0 = RHS
Hence, our answer is correct.
Answer:
Step-by-step explanation:
