3. The digit in the tens place of a two-digit number is three times that in the units. If the digits are
reversed, the new number will be 36 less than the original number. Find the original number,
Answers
Step-by-step explanation:
Method 1: Let the number be 10x+y.
x=3y …(1)
10x+y-36 = 10y+x, or
9x=9y+36, or
x=y+4 …(2)
Equate (1) and (2),
3y = y+4, or
y = 2 and x = 6.
So the number is 62.
Method 2: Consider the numbers 31, 62, 93.
Subtract 36 from each of the above numbers : -5, 26, 44.
The number is 62 which gets reversed to 26 when you subtract 36 from it.
Answer : 62.
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We know, that any 2 digit number, can be represented on the form of 10a+b.
We also know, that the tens’ place is 3 times bigger than the ones’ place. Thus a=3b. So 10a+b=10∗3b+b=31b.
Now we also know, that the two digit number reversed is 36 less than the original number. So 10b+a=31b−36. We still know, that a=3b, so 10b+3b=31b−36⇔13b=31b−36⇔36=18b⇔2=b
Now all we have to is insert 2, and we get that the number is 10*(3*2) + 2, which would be 62.
If the number is TU, its value is 10T + U
We know T = 3U, so the value of the number is 31U.
Reversing the digits to UT, the value is 10U + T, which is 13U
31U - 13U = 36
18U = 36
U = 2
T = 3U = 6
The number is 62.
Of course this problem can also be solved by “guess and check,”. Since the tens digit is three times the ones digit, the only possible numbers are 31, 62, and 93. Pretty easy to check that neither 31–13 nor 93–39 is 36. The number is 62, because 62–26=36.
Let the number be xy = 10x + y = 31y, since x = 3y
Now yx = 13 y
so, 31y-13y = 36, y = 2, so, x = 6. Hence the original no. is 62
62–26 = 36, proved.
Let n be the digit in the one’s place in the original number. Then the ten’s place would be 3n. So:
10(3n)+n -36=10n+(3n)
31n-36=13n
18n=36
n=2
3n=6
The original number is 62
62–26=36
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Let number be ab = 10a + b
a = 3b
(10a + b) - (10b +a) = 36
Hence 9(a - b) = 36
a - b = 4
Substituting a = 3b into a - b = 4
2b = 4
b = 2 and a = 6
Check 62 - 26 = 36
If a is in the 10’s position and b in the units position, then a =3b and further,
10b + a = 10a+b - 36, so 12b =30b - 36 or
18b = 36 So b = 2, making a= 6
So the 2 digit number is 62
the number =3x×10+x=31x
Reversed number=x ×10+3x=10x+3x=13x
31x-13x=36
18x=36
x=2
3x=6
The number is 62
X = 3Y
10Y + X + 36 = 10X + Y
9Y + 36 = 9X
Y + 4 = X
So, Y + 4 = 3Y
4 = 2Y, Y= 2, X = 6
Original number is 26
62
Reverse of this is
26
Difference between two numbers is
62–26=36
Possible choices are 31,62,93
31–13=18
62–26=36
62 is the answer