George sells a CDs at a profit of 20% and a DVDs at a loss of 20%. If

Solution

• Profit % on CDs \(= 20\)%
• Loss % on DVDs \(= 20\)%
• Overall Profit \(= 10\)%
• Selling Price of CDs \(= $ 36\)

• Cost Price of CDs \(* (1 + \frac{1}{5}) = $ 36\)
• Cost Price of CDs \(= $ 30\)
• Let the Cost Price of DVDs \(= D\)

o Loss on DVDs \(= -D*\frac{1}{5} = -\frac{D}{5}\)

• Overall Profit \(= (36-30) + \frac{D}{5} = 6 - \frac{D}{5}\)

• % \(Profit = (6 - \frac{D}{5})/(D+30)\)

• \(\frac{(30 - D)}{5(D+30)} = \frac{1}{10}\)

• \(60 - 2D = D + 30\)

• \(D = 10\)

• Note: We have been asked the SP of DVDs, so don’t mark Option B as you answer, otherwise all the hard work will be a BIG waste.

• SP of DVDs \(= 10( 1-\frac{1}{5}) = $ 8\)

• Hence the correct answer is Option A.

Method 2

• Let CP of CDs be \(C\) and CP of DVDs be \(D\).
• Thus, we can write


o (Profit from C – Loss from D)= Overall Profit*(Sum of CP of C and D)
o \((C*\frac{1}{5} – D*\frac{1}{5}) = \frac{1}{10}*(C+D)\)
o \(\frac{(C-D)}{(C+D)} = \frac{1}{5}\)
o \(D = \frac{C}{3}\)

• We need to find the SP of DVDs \(= D*(1-\frac{1}{5}) = \frac{4D}{5}\)


o As \(D = \frac{C}{3}\)
o SP of DVDs \(= \frac{4D}{5} = \frac{4C}{15}\)

• Cost Price of CDs \(* (1 + \frac{1}{5}) = $ 36\)
• Cost Price of CDs \(= $ 30\)
• Thus, \(SP = 4 * \frac{30}{15} = $8\)