If a trader, by means of false measures, gains 20% while buy

Question

If a trader, by means of false measures, gains 20% while buying and again gains 25% while selling. What is his overall gain percentage?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%

GyanOne · Answer

The answer is 50%.

Assume that the cost price of the item is x. Then the trader pays x(1-20/100) = 0.8x for it. Therefore gain made in buying the item = x - 0.8x = 0.2x
Next, he sells it for a 25% gain. So he sells it at 0.8x(1+25/100) = x. Gain made while selling = x - 0.8x = 0.2x

Total gain = 0.2x + 0.2x = 0.4x 
Cost price = 0.8x
Therefore % gain = 0.4x/0.8x = 50%

kostyan5 · Answer

Assume trader started with X amount of money. After buying, he had 1.2X. After selling he had 1.25(1.2X) = 1.5X. So he made 50%.

devinawilliam83 · Answer

The logic i was using was as follows :

original Price (OP) was 100 units @ 1/- . OP= 100/-
Buying price - 120 units for 100/- (he used false measures, hence reducing the quantitiy and not the amount)
selling price - 90 units for 100/-
Gain = SP-BP = (100/90) - (100/120) = 10/36
Gain% is gain/BP = (10/36)/(100/90) = 25%

What is wrong with what I am doing ?Thanks in advance

KarishmaB · Answer

I will tell you the direct method of doing this but first let me explain what's wrong with your method.
Remember that the gain is in terms of money, not in terms of units. 
original Price (OP) was 100 units @ 1/- . OP= $100/-
Buying price - 120 units for $100/- (he used false measures, hence reducing the quantitiy and not the amount)
 The value of 120 units is $120 so his gain is $20/$100 = 25%

selling price - 90 units for 100/-
Gain = SP-BP = (100/90) - (100/120) = 10/36
Gain% is gain/BP = (10/36)/(100/90) = 25%

When he sells, he gains 25% by using false measures.
For $100, he should have given the customer 100 units but he gives only 80 units to get a 25% gain.
His cost price of 80 units is $80 and selling price is $100 so gain = 20/80 * 100 = 25%

So he sells 80 units for $100
He will sell 120 units for $(100/80) * 120 = $150

How much did he pay for these 120 units? Only $100 (again because he used false measures)
Gain = (50/100) *100= 50%

You can also do this directly. There are 2 consecutive gains -> 20% and 25%
Overall gain = a + b + ab/100 = 20 + 25 + 20*25/100 = 50%

Mindreko · Answer

You can also put in a SMART number. Let the number be 100.

20% of 100 = 20, so price is 120.
25% of 120 is 30, so price is 150

Therefore there is a change of 50 units from 100 = 50%

MBAhereIcome · Answer

1.2*1.25 = 1.5
so 50%

skywalker07 · Answer

20% gain -> 25% gain => 1.2 x 1.25 = 1.5. 50% gain

charlie1195 · Answer

Successive profits or losses can be calculated using the formula: 
x + y + (x.y)/100............ (1)

In case of losses, the values will have a negative sign.

For this particular question, x=20; y=25

Putting the values in (1)
20 + 25 + (20.25)/100 
= 50%

If a trader, by means of false measures, gains 20% while buy

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If a trader, by means of false measures, gains 20% while buy

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