Q. 14

<span lang="EN-US

Answer :

Let the hundred’s digit be x

Unit’s = x + 1 and ten’s digit = x – 1


The number formed = 100 x + 10 (x – 2) + x + 1


= 100x + 10x – 20 + x + 1


= 111x – 19


After changing the numbers cyclically the first case would be


Unit’s digit = x – 2, ten’s digit = x and hundred’s digit = x + 1


The number formed = 100 (x + 1) + 10 x + x – 2


= 100x + 100 + 10x + x – 2


= 111x + 98


On changing the digits cyclically for the second time


Unit digit = x, ten’s digit =x + 1 and hundred’s digit = x – 2 and the number formed is


100 (x – 2) + 10 (x + 1) + x


= 100 x – 200 + 10x + 10 + x


= 111x – 190


As per the conditions in the question


111x – 19 + 111x + 198 + 111x – 190 = 2664


333x – 11 = 2664


333x = 2664 + 11




Hence the original number = 111 x – 19 = 111 x 8 – 119 = 888 – 119


Original Number = 769


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the LCM and KC Sinha - Mathematics

Find the LCM and KC Sinha - Mathematics

Find LCM and HCF KC Sinha - Mathematics

Find LCM and HCF KC Sinha - Mathematics

Find the LCM and KC Sinha - Mathematics

Find the LCM and KC Sinha - Mathematics