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In a two digit number, the digital unit place is 1 more than twice of the digit at ten's place. If the digit at unit's and ten's place be interchanged, then the difference between the new number and original number is less than 1 to that of original number. what is the original number ?
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- 52
- 73
- 25
- 37
Correct Option: D
Let the original number be 10p + q.
So from question,
q = 2p + 1 ...(i)
and (10q + p) - (10p + q ) = (10p + q) - 1
⇒ 9q - 9p = 10p + q -1
⇒ 19p - 8q = 1...(ii)
Putting the value of (i) in equation (ii) we get
19p - 8(2p + 1) = 1
⇒ 19p - 16p - 8 = 1
⇒ 3p = 9
⇒ p = 3
So, q = 2 x 3 + 1 = 7
∴ Original number = 10 x 3 + 7 = 37
