## In a certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3. If the digits are interchanged and the r

Question

In a certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3. If the digits are interchanged and the resulting number is divided by the sum of its digits, then the quotient is 4 and the remainder is 9. Find the number

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2021-09-04T17:44:20+00:00
2021-09-04T17:44:20+00:00 2 Answers
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## Answers ( )

TheNumber[Accordingtoquestion].## ☞

GIVEN:–Inacertainnumberisdividedbythesumofitstwodigits,thequotientis“6”andreminderis“3”.Ifthedigitsareinterchangedandtheresultingnumberisdividedbythesumofitsdigits,thenthequotientis“4”andreminderis“9”.☞FORMULA:–☞CALCULATION:–(╬)SupposetheoriginalNumbers,unitdigitbe“x”tensdigitbe“y”TheOriginalNumber=“(10y+x)”(╬)Accordingtoquestion,(10y+x)isdividedby(x+y)andweget“6”asaquotientand“3”asareminder.Dividend=(10y+x)Divisor=(x+y)Quotient=6Reminder=3———(1)

☞Again,Ifthedigitsareinterchanged,weget“(10x+y)”asanumberand“(10x+y)”isdividedby“(x+y)”resulting“4”asaQuotientand“9”asareminder.Dividend=(10x+y)Divisor=(x+y)Quotient=4Reminder=9———(2)

☞Now,wesolvetheEquations“(1)and(2)”,seetheattachmentpictureforsolvationofEquations“(1)and(2)”☞weget,“x=5”and“y=7”.☞Therefore,TheoriginalNumberis,=>Dividend=Divisor×Quotient+Remainder:Hence,Thecertainnumber=10x+yThe certain number=10×7+5The certain number=70+5The certain number=75