Question

A number consists of 2 digits whose sum is 7.If 9 is added to the number,the digits are reversed.The original number is

Answer 1

Answer:

A number consists of two digits whose sum is 5. If 9 is subtracted from it the digits are reversed. What is the number?

3-in-1 protection for moms-to-be helps protect baby too.

The number is 32.

10a+b−9=10b+a

⟹(10a+b−9)−(a+b)=(10b+a)−(a+b)

⟹9b9=9a−99

→b=a−1

a+b=5⟹b=5−a

⟹(5−a)+(a+1)=(a−1)+(a+1)

⟹2a2=62

→a=3

b=5−a⟹b=5−3

→b=2

answer:32

Proof:

32−9=23

Q.E.D.

Give Amazon a try.

Let the tens digit be a and ones digit be b.

Then a + b = 5 (equation 1) and

10a + b — 9 = 10b + a (equation 2)

9a — 9 = 9b

a — 1 = b

a — b = 1 (equation 3)

But a + b = 5 (equation 1)

Adding equation 3 and equation 1 gives

2a = 6, which means a = 3 and b = 2

In other words, the number is 32

Let the number be 10x+y.

x+y = 5 …(1)

10x+y-9 = 10y+x, or

9x-9y=9, or

x-y= 1 …(2)

Add (1) and (2)

2x = 6 or x = 3 and so y = 2.

The number is 32.

Take control of your diabetes.

A number has two digits whose sum is 9. If 27 is added to the number, the digits get interchanged. What is the number?

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, are the digits reversed? What is that number?

A number consists of two digits. The sum of the digits is 6. If 18 is subtracted from the number, its digits are interchanged. What is the number?

Starting from the lowest possible 2-digit number, your answer is 32.

3+2 = 5; and 32 - 9 = 23

By subtracting nine from any number having at least two digits which are consecutive in descending order (eg. 187 to 178; 76 to 67, etc.) the tens and ones digits will reverse as long as hundreds digit is unaffected.

I’ve used this like a mnemonic a few times. But it doesn’t for numbers like 309 (300) or 10 (1).

Well, we have 3 possible 2-digit numbers where the sum of the digits is 5: 50, 41, and 32. 50 - 9 = 41, so THAT one doesn’t work. 41 - 9 = 32, so THAT one doesn’t work. (Ahhhh, 3rd try lucky?????) 32 - 9 = 23. Success!!!

Answer: 32

32

3 +2=5

32 -9= 23

ie. Digits reversed

32