# Rajesh sold his scooterto rahim at 8percent losss and rahim,in turn ,sold the same scooter to prem at 5 percent gain. if prem paid rs.14490for the scooter;find: the S.P and C.P of the scooter for rahim and the S.P and C.P of the scooter for rajesh

$Gain\%=\frac{sp-cp}{cp}\times 100\\*Loss\%=\frac{cp-sp}{cp}\times 100\\* Also,\;the\;cp\;for\;Rahim\;is\;equal\;to\;sp\;for\;rajesh\\* sp\;for\;rahim=cp\;for\;prem=14490\\*Let\;sp\;for\;rajesh\;be\;x\\* sp\;for\;rajesh=cp\;for\;rahim=x\\*Let\;cp\;for\;rajesh\;be\;y\\* For\;loss\;of\;8\%\\* 8=\frac{y-x}{x}\times 100\\*On\;simplfying\;we\;get,\\*\Rightarrow x=\frac{100y}{108}\\*For \;5\%\;gain,\\*5=\frac{14490-x}{x}\times 100\\* Now,\;put\;value of\;x\;from\;above\;equation,\;we\;get\\* 5=\frac{14490-\frac{100y}{108}}{\frac{100y}{108}}\\*On\;solving\;this\;we\;get,\\* y=\frac{1564920}{105}=14904\Rightarrow y=14904\\* Now\;put\;value\;of\;y\;in\;x=\frac{100y}{108}\\*\Rightarrow x=13800\\*Hence,\;the\;sp\;=14490\- \;and\;cp\;=13800\-\;of\;the\;scoote\; for\;rahim\;and\;the\;sp\;=13800\-\;and\;cp=14904\-\;of\;the\;scooter\;for\;rajesh.$

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