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Q.

A trader marks his goods at 20% above the cost price. He sold half the stock at the marked price one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is

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a

4.5%

b

2%

c

13.5%

d

15% 

answer is A.

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Detailed Solution

Given that a trader marks his goods at 20% above the cost price. He sold half the stock at the marked price one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price.
Let the CP be x. M.P=120%×CP
⇒M.P=120%×x
⇒M.P=1.2x
Gain while selling half stocks of goods,
Gain =0.5(MP-CP)
⇒Gain =0.5(1.2x-x)
⇒Gain = 0.1x
Gain while selling remaining one quarter stocks of goods,
Gain = 0.25 [(80% of MP) - CP]
⇒Gain =0.25[(80%×1.2x)-x]
⇒Gain=-0.01x
Gain while selling remaining stocks of goods,
Gain = 0.25 [(60% of MP) - CP]
Gain =0.25[(60%×1.2x)-x] ⇒Gain=-0.07x
Net gain =(0.1-0.01-0.07)x
⇒Net gain =0.02x
Gain %=gainCP×100 ⇒Gain %=0.02xx×100 ⇒Gain%=2%
Thus, the total gain is 2%.
Therefore, the correct option is 1.
 
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A trader marks his goods at 20% above the cost price. He sold half the stock at the marked price one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is