Question

the sum of the digit of a two digit number is 7 if the digits are reversed the new number increased by 3 less than 4 times the original number find the number

Answer 1

Let original No. Be X = ab where ab are 2 digits.
Now Acc. to question.
a+b= 7
and if ab are reversed like
Let a no. Y formed when ab are reversed to ba then
Y = ba.
then Y= 4X-3 acc. to Question.
Y + 3 = 4X
thus
sum a + b = 7 possible a and b are
a = 1 , b = 6
a = 2, b = 5
a = 3, b = 4

Now then is ab is the no. when a = 1 ,b= 6
then ba = 61
thus Y = 4X result is correct.
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Now then if a = 2 and b = 5 ab = 25 and ba = 52 thus
X = 2Y + 2 .
result is absured.
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Now for a = 3 and b = 4 hence
ab = 34 and ba = 43.
result is absured.
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Thus by applying all conditions only a= 1 and b = 6 satisfy thus the given no. is ⏩ 16 ⏪
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