Question

A man sold two radios for 2000 each. On one he gains 16% and on the other he loses 16 %. Find his gain or loss percent in the whole transaction?

Answer 1

selling price of each radios =Rs 2000

let the cost price of first radio be 'x' .

selling price of first radio = Rs 2000

gain on first radio = 16 %

Find the cost price of first radio:
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x + 16% of x = 2000

x + 0.16x = 2000

1.16x = 2000

x = Rs 1724.1

selling price of second radio = Rs2000

loss = 16 %

let the cost price of second radio be 'y'

y - 16 % of y = 2000

y - 0.16y = 2000

0.84y = 2000

y = 2380.9

Find the total cost price of two radios:
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x + y = 1724.1 + 2380.9 = Rs 4105

Find total selling price of two radios:
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= 2000 + 2000 = Rs 4000

loss = 4105 - 4000 = Rs 105

loss % = loss × 100 / total cost price

105 × 100 / 4105 = 2.5%

therefore, there was loss of 2.5% in the whole transaction.

Answer : loss = 2.5 %

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Answer 2

Answer

Let a= 16%

Loss % = (a/10)^2

=(16/10)^2

=256/100

= 2.56% loss