Number System Ques 15
Question
The ten’s digit of a three digit number $X$ is 3 . If the digits of $X$ are interchanged and the number thus formed is 396 more than the previous one. The sum of unit digit and hundred digit is 14, then what is the number?
(1) 480
(2) 539
(3) 593
(4) 935
(5) Other than those given as options
(IBPS Bank PO/MT CWE-VII (Prelim Exam) 15.10.2017)
Show Answer
Answer: (2)
Solution: (2)
Unit’s digit $=x$
$\therefore$ Hundred’s digit $=14-x$
$\therefore$ Original number $=(14-x) \times 100+3 \times 10+x$ $=1400-100 x+30+x$ $=1430-99 x$
New number after interchanging the digits. $=100 x+3 \times 10+14-x$ $=99 x+44$
$\therefore 99 x+44-1430+99 x=396$
$\Rightarrow 198 x-1386=396$
$\Rightarrow 198 x=1386+396=1782$
$\Rightarrow x=\frac{1782}{198}=9$
$\therefore$ Hundred’s digit $=14-9=5$
$\therefore$ Required number $=539$
OR
Ten’s digit $=3$;
Sum of unit’s and hundred’s digit $=14$.
Of the given options
Original number $=539$
New number after interchanging the digits $=935$
Difference $=935-539=396$
BETA
