4. The sum of digits of a two digit number is 7. The number obtained, on reversing the order of digits
is greater than original number by 9. Find the number.
Answers
ANSWER
Let the original number be
yx
; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in
xy
, i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:
x+y=7....(1)
8x−19y=2....(2)
Multiply the equation (1) by 19 and get
19x+19y=133.
Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.
The required number is 25.
Step-by-step explanation:
The sum of digits of two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the numbers?
When will Lunchclub be active in New Delhi?
Lunchclub is now virtual and finally open to users in New Delhi! Network from home and make relevant connections locally and glob
Let x and y be the digits at tens and ones place respectively.
Let A be the number formed by these digits.
Therefore, A=10x+y……….(1)
According to the question.
x+y=7…………(2)
Let B be the new number formed by reversing the digits.
Therefore, B=10y+x……….(3)
According to the question.
B=27+A
=>(10y+x)=27+(10x+y)
=>(10y+x)-(10x+y)=27
=>9y-9x=27
=>9(y-x)=27
=>y-x=27/9=3…………..(4)
Adding equations (2) and (4).
(x+y)+(y-x)=7+3=10
=>2y=10
=>y=5 and x=7–5=2……….from equation(2)
Hence,the number is A=10x+y=10*2+5=25