# A sum of rs.3000 is to be given in the form of 63 prizes.if the prize money is either rs.100 or rs.25 find the number of prizes of each type

Dear Student,

$Lettheno.ofprizesbearingRs100=x\phantom{\rule{0ex}{0ex}}Then,no.ofprizesbearingRs25=63-x\phantom{\rule{0ex}{0ex}}ValueofRs100prizes=Rs100x\phantom{\rule{0ex}{0ex}}ValueofRs25prizes=Rs\left[25\right(63-x\left)\right]=Rs(1575-25x)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Accordingtoquestion:\phantom{\rule{0ex}{0ex}}100x+1575-25x=3000\phantom{\rule{0ex}{0ex}}\Rightarrow 75x=1425\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{1425}{75}=19\phantom{\rule{0ex}{0ex}}So,no.ofprizesbearingRs100=x=19\phantom{\rule{0ex}{0ex}}No.ofprizesbearingRs25=63-x=63-19=44$

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