Problem Solving

goyalsau wrote:Gautam has different brands of Laptop in his show room. They are Acer, IBM, Compaq and Toshiba. Gautam found that he has sold Acer & Compaq at same selling price. He made 12% profit in Acer but suffered 10% loss in Compaq. If the total cost price of Acer & Compaq is Rs.84000, find how much money Gautam has gained or lost in the transaction?

Rs. 1680 loss
Rs. 730 loss
Rs. 1680 gain
Rs. 1344 loss
Rs. 672 gain

Say cost price of Acer is Rs. A and that of Compaq is Rs. C.
Therefore (A + C) = 84000 ......................................................... (i)

Now he made 12% profit in Acer but suffered 10% loss in Compaq.
Thus selling price of Acer = A + 12% of A = (1.12)A
and selling price of Compaq = C - 10% of C = (0.9)C

Total selling price = (1.12)A + (0.9)C
=> Total selling price - Total cost price = (0.12)A - (0.1)C .......... (ii)

According to the question, selling price of Acer and Compaq is same.
=> (1.12)A = (0.9)C
=> A = (0.9/1.12)C

Put this value of A in (i) : [(0.9/1.12) + 1]*C = 84000
=> C = 84000*(56/101)
=> A = 84000*(56/101)*(45/56) = 84000*(45/101)

From (ii), we have,

• Total selling price - Total cost price = (0.12)A - (0.1)C
  = (0.12)*84000*(45/101) - (0.1)*84000*(56/101)
  = (84000/101)*[(12*45)/100 - (10*56)/100]
  = (84000/101)*[(3*9)/5 - (1*28)/5]
  = (84000/101)*[(27 - 28)/5]
  = -(16800/101)
  ≈ -168

Thus the selling price is less by Rs. 168 => Loss of Rs. 168

Either I've done a calculation mistake or the option A and C should remove the rightmost zero.