A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting by 5 or by multiplying the difference of digits by 16 and adding 3.Find the number
Answers
Answer:
Explanation:
Let the two digit number be 10x + y where x is the tens digit and y is the ones digit.
Now, according to the question.
10x + y = 8(x + y) - 5
10x + y = 8x + 8y - 5
10x - 8x + y - 8y = - 5
2x - 7y = - 5 .................(1)
And,
10x + y = 16(x - y) + 3
10x + y = 16x - 16y + 3
10x - 16x + y + 16y = 3
- 6x + 17y = 3 ................(2)
Now, multiplying the equation (1) by 17 and (2) by 7, we get
34x - 119y = - 85 ...............(3)
- 42x + 119y = 21 ..............(4)
Now, adding (3) and (4), we get
34x - 119y = - 85
- 42x + 119y = 21
_________________
- 8x = - 64
_________________
⇒ 8x = 64
x = 64/8
x = 8
So, tens digit is 8.
Substituting the value of x = 8 in (1), we get
2x - 7y = - 5
2*8 - 7y = - 5
16 - 7y = - 5
- 7y = - 5 - 16
- 7y = - 21
7y = 21
y = 21/7
y = 3
Ones digit is 3.
So, the required number is 83.
Answer.
Answer:
Two-digit number = 83
Explanation:
Let us assume, x and y are
the two digits of the two-digit number
Therefore, the two-digit
number is 10x + y
Given,
10x + y = 8(x
+ y) – 5
10x + y = 8x
+ 8y – 5
7y – 2x = 5
----------------1
Also given,
10x + y = 16(x
– y) + 3
10x + y =
16x – 16y + 3
17y – 6x = 3
--------------------2
Multiply
equation 1 by 3
21y – 6x =
15 -------------3
Subtract
equation 2 from equation 3
4y = 12
y = 3
substitute y
= 3 in equation 1
7*3 – 2x = 5
21 – 2x = 5
2x = 16
x = 8
Therefore,
the two-digit number = 10x + y = 10*8 + 3 = 83
Ans – The required
two-digit number = 83