A fan is sold at a profit of 15%. If the selling price had been Rs 48 more, the profit would have been 18%. Show how will you find the cost price of the fan?
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Let SP = x
CP = (100/100+Gain%)*SP
CP = (100/100+15)*x
CP = (100/115)* x. First equation.(1).
48 more SP = x+48
SP = (100+Gain%/100)*CP
x+48 = (100+18/100)*CP
x+48 = (118/100)*CP
x+48 = (118CP/100)
x = 118CP/100 - 48
x = 118CP-4800/100 (LCM)... Second equation (2).
Use 2nd equation in 1st
1st equation
CP = (100/115) * (118CP - 4800/100)
Cancle 100 on both side
CP = ( 118CP - 4800/115)
LCM of 115 on both sides
115 CP = 118CP - 4800
4800 = 118CP - 115CP
4800 = 3CP
CP = 4800/3
CP = 1600
CP = (100/100+Gain%)*SP
CP = (100/100+15)*x
CP = (100/115)* x. First equation.(1).
48 more SP = x+48
SP = (100+Gain%/100)*CP
x+48 = (100+18/100)*CP
x+48 = (118/100)*CP
x+48 = (118CP/100)
x = 118CP/100 - 48
x = 118CP-4800/100 (LCM)... Second equation (2).
Use 2nd equation in 1st
1st equation
CP = (100/115) * (118CP - 4800/100)
Cancle 100 on both side
CP = ( 118CP - 4800/115)
LCM of 115 on both sides
115 CP = 118CP - 4800
4800 = 118CP - 115CP
4800 = 3CP
CP = 4800/3
CP = 1600
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