Please solve the following two questions for me :-?

Question

=>The result of dividing a number of two digits by the number with the digits reversed is 5/6. If the difference of digits is 1, find the number.

=> A number of three digits has the hundred digit four times the unit digit and the sum of three digits is 14. If the three digits are written in the reverse order , the value of number is decreased by by 594. Find the number.

Please solve in steps.

Answer 1

1) Let the digits be x and y and the number be xy.
Reversed number = yx.

Magnitude of the number = 10x + y
Magnitude of reversed number = 10y + x

Given:
y - x = 1
(10x+y)/(10y+x) = 5/6.

=> 6(10x+y) = 5(10y+x)
=> 60x + 6y = 50y + 5x
=> 55x = 44y
We have y - x = 1 => y = x + 1
=> 55x = 44(x+1)
=> 55x = 44x + 44
=> 11x = 44
=> x = 4, y =5

2) Here we are told that the 100's digit is 4 times the 1's digit.
Therefore our only options are (1,4) and (2,8) for (1's digit, 100's digit).

Case(1):
The number is 4X1.
Sum of digits is 14 => Missing digit is 14 - 4 - 1 = 9.
The number is 491.
The difference between this and the reversed number is (491-194)=297. => this case is invalid.

Case(2):
The number is 8X2.
Missing digit = 14 - 8 - 2 = 4.
The number is 842.
Number - reversed number = 842 - 248 = 594.

Therefore, the correct answer is 842.

Answer 2

(1) To solve, I just multiplied 5/6 by whole numbers until I got the answer. You will find it is 45 and 54.

(2) We know that the hundreds digit is either 4 or 8 from the first statement. Likewise, the units digit is 1 or 2. All three add to 14. Let's write our possibilities:

4x1 ==> 4 + x + 1 = 14 ==> x = 9
==> 491
8y2 ==> 8 + y + 2 = 14 ==> y = 4
==>842

Reverse both and subtract:

491 - 194 = 297 ==> not it
842 - 248 = 594 ==> Correct.

Answer 3

It would be cheating to give you the answer (see other answers if you want to cheat), but here's a start:

For the first question: Use variable "a" to stand for one digit; and variable "b" to stand for the other digit. Then:

"a number of two digits" is: 10a + b. (Do you see why? Try an example. if a=5 and b=3, then "a number of two digits" is 10*5 + 3, or 53. It works for any two digits.)

"the number with the digits reversed" is: 10b + a.

"the difference of the digits" is: a&endash;b (or possibly: b&endash;a. It depends on which is bigger, a or b, which you should be able to figure out.

Now you've got some equations, so you can just use the algebra you already know.

For the second problem: Similar thing, but now use a, b and c.

"a number of three digits": 100a + 10b + c
"the hundred digit": a
"the unit digit" c
etc.

Answer 4

If the tens digit is x, the units digit is (x+1). The value of the number is 10x + x +1 = 11x + 1. Reversed, it's worth 10(x+1) + x = 11x + 10. We know the reversed number is greater than the original since their quotient is less than 1

So (11x + 1)/(11x + 10) = 5/6

Cross multiply to get 55x + 50= 66x + 6

Thst's 11x = 44 so x=4 and the other digit is 5

so the number is 45

Answer 5

The first solution is 45.

45 and 54 are both multiples of nine.

45/9 = 5
54/9 = 6

Therefore, 45/54 = 5/6.

Also, the difference between the digits (5 and 4) is equal to one.


The second answer is 842.

8/2 = 4 - This fulfills the first criteria (100s digit is 4x the units digit).

8+4+2 = 14

If you reverse the digits, you get 248. 842-248=594.




God, I love math.

Answer 6

45 / 54 and 842

Answer 7

let the nos. be x and x+1

atp,
[10*x+(x+1)]/[(x+1)*10+x]=5/6

simplifying we get , x=4 and x+1=5

number is 45