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Standard VI
Mathematics
Question

a,b,c(a>c) are three digits from left to right, of a three digits number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digits 4 in its unit place. The other two digits from left to right are
  1. 5 and 4
  2. 4 and 5
  3. 5 and 9
  4. 9 and 5

A
9 and 5
B
5 and 4
C
5 and 9
D
4 and 5
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Solution
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The correct option is B 5 and 9
LetthenumberbewrittenasfollowsPlacevalue⟶HundredsTensUnitsabcReversing⟶cbaUnitsplace:−Givena>c∴Weborrow10andtheresultisc+10−a=4⇒a=c+6−−−−(1)Tensplace:−upperrowbhasbecomeb−1∴Weborrow10andtheresultis(b−1+10)−b=9.Hundredsplace:−ahasbecomea−1∴(a−1)−cistheresult.Substitutingthevalueofafrom(1),theresultwillbec+6−1−c=5∴Theothertwonumbersare5,9(Ans)(i.e.Theresultis594)

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