a two digit number is such that the tens digit of the number exceeds twice the units digit by 5 and the number obtained interchanging the digits is 7 more than twice the digits find the number
Answers
Answer: Let xy be the required two-digit number.
Let x be the number which is in unit's digit.
Let y be the number which is in ten's digit.
Therefore the decimal expansion is 10x+y. ------- (1)
Given that the 10's digit exceeds twice the unit digit by 2.
x = 2y + 2. ------- (2).
Also, Given that the number obtained by interchanging the digits is 5 more than the sum of the digits.
10y + x = 3(x + y) + 5
10y + x = 3x + 3y + 5
10y + x - 3x - 3y = 5
7y - 2x = 5
7y - 2(2y + 2) = 5 (from (2))
7y - 4y - 4 = 5
3y - 4 = 5
3y = 9
y = 3 ------ (3)
Substitute (3) in (2), we get
x = 2(3) + 2
x = 6 + 2
x = 8. ----- (4)
On substituting (3) & (4) in (1), we get
The number is 10x + y = 10 * 8 + 3
= 80 + 3
= 83.
Therefore, the required two-digit number is 83.
Hope this helps!
Step-by-step explanation: