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The sum of the digits of …

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The sum of the digits of a two digit number is 14.If the number formed by reversing the digits is less than the original number by 18.Find the original numbers .

Posted by Yash Thadani 7 years ago

CBSE > Class 08 > Mathematics

1 answers

Aashka Shah 7 years ago

Let x = the 10's digit
Let y = the units
:
10x + y = the original two digit number
:
The sum of the digits of a two-digit number is 14.
x + y = 14
:
"If the digits are reversed, the number is 18 less than the original number."
Rev no. = orig no. - 18
10y + x = 10x + y - 18
10y - y = 10x - x - 18
9y = 9x - 18
simplify, divide by 9
y = x - 2
:
In the sum equation replace y with (x-2)
x + (x-2) = 14
2x = 14 + 2
2x = 16
x = 8
obviously y = 6
:
86 is the original number
:
:
Check solution in the statement:
"If the digits are reversed, the number is 18 less than the original number."
68 = 86 - 18

ANSWER

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