the sum of two digits of a two digits number is 7.on reversing the digits the number obtained is 27 more than the original number find the number.
Answers
Answer:
Step-by-step explanation:
let the units place be x
then the tens digit be 7 - x
number formed by these digits = 10 x t's digit+u's digit
=> 10(7-x)+x
70 x -10 x +x
70 x -9x
when the digits are interchanged than,
t's digit= x
u's digit = 7-x
the new no. formed = 10x + 7-x
= 9 x +7
given that the no. exceeds by 27
new no. - given no.
9x +7 - (70-9x)=27
9 x + 7 - 70 + 9x =27
18x -63= 27
18 x = 63+27
18 x= 90
x = 90/18
=5
the no. = 70- 9x
=> 70-45
=> 25 ans
Answer:
Suppose the two digit original number is 10x+y.
(x is at tens place so multiple by 10 and y is at unit place so left as is, you may multiply it by 1 to get a clear picture but 1y is represented as y only)
The sum of digits of original number is 7 →x+y = 7 —equation(1)
If 27 is added to original number its digits are interchanged .So, 10x + y +27 =10y+ x → 9x +27 = 9y → 9(x+3) = 9(y) → x+3 = y — equation(2)
Substituting value of y from equation (2) in equation (1)
x + x+3 = 7
2x + 3 = 7
2x =4
x= 2
Substituting x= 2 in equation (2)
y= 5
So original number is 10 (2) + 5 i.e. 20 +5 → 25.
In order to check the answer.. 25 is original number and 52 is the number formed by interchanging the digits.
25 +27 = 52.