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A man sold two pipes for Rs. 12 each. On one he gained 20% and on the other he lost 20% . What is his gain /loss in the whole transaction?

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Rs . 25

Rs . 12

Rs . 15

Rs . 24

answer is D.

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Detailed Solution

Concept- We will take the cost price of both pipes as

C P_{1}

and C

P_{2}

.find

C P_{1}

using formula for gain% as gain of 20% is given for pipe 1.now ,find

C P_{2}

.using the formula of loss % as loss of 20% is given on

P_{2}

.Now compare total selling price and cost price to find out gain /loss
First we will find the cost price pipe 1,

Gain = SP - CP

P 1, gain is 20 % and SP = Rs . 12

Gain percentages = (\frac{gain}{percentage}) \times 100

(\frac{SP - C P_{1}}{C P_{1}}) \times 100

20 = (\frac{12 - C P_{1}}{C P_{1}}) \times 100

Applying cross multiplication property

C P_{1} = (\frac{12 - CP 1}{20}) \times 100

C P_{1} = (12 - C P_{1}) \times 5

C P_{1} + 5 C P_{1} = 60 \to 6 C P_{1} = 60

So, C P_{1} = Rs . 10

Now cost price of pipe 2, CP2 as P2 encounter a loss of 20%
Loss=cost price-selling price=CP2-SP

loss % = \frac{loss}{cost price} \times 100

loss % = (\frac{C P_{2} - SP}{C P_{2}}) \times 100

20 = (\frac{C P_{2} - 12}{C P_{2}}) \times 100

Applying cross multiplication property,

C P_{2} = (\frac{C P_{2} - 12}{20}) \times 100

(C P_{2} - 12) 5

5 C P_{2} - 60

5 C P_{2} - C P_{2} = 60

4CP2=60→CP2

= \frac{60}{4} = Rs . 15

total cost price=CP1+CP2

= Rs . 10 + Rs . 15 = Rs . 25

total selling price=SP of 2 pipes
=

12 + 12 = Rs . 24

Hence, the correct option is 4.

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