Question

Raman sells two wristwatches for rs1200 each. on one watch, he gains 20% & on the other he loses 20%. What r the cost prices of each, & what is his total gain or loss percentage

Answer 1

The cost prices are 1440rs. and 960rs. respectively.
The percentage is 0% of his gain or loss......

Answer 2

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For the first wristwatch

SP = ₹ 1200

Gain% = 20%

$\sf{CP = \frac{100}{(100 + gain\%)} \times SP} \\ \\ \: \: \: \: \: \: \: \sf{= Rs \: \: \frac{100}{(100 + 20)} \times 1200}$

$\: \: \: \: \: \: \: \sf{= Rs \: \: [( \frac{100}{120} \times 1200)]} \\ \\ \: \: \: \: \: \: \: \sf{= Rs \: \: 1000}$

For the second wristwatch

SP = ₹ 1200

Loss% = 20%

$\sf{CP = \frac{100}{100 - loss\%} \times SP} \\ \\ \: \: \: \: \: \: \: \sf{= Rs \: \: [\frac{100}{(100 - 20)} \times 1200]}$

$\: \: \: \: \: \: \: \sf{= Rs \: \: ( \frac{100}{80} \times 1200)} \\ \\ \: \: \: \: \: \: \: \sf{= Rs \: \: 1500}$

Total SP of the wristhwatches = ₹ (1200 × 2) = ₹ 2400

Total CP of the wristwatches = ₹ (1000 + 1500) = ₹ 2500

Since CP > SP , there is a loss in the whole transaction

Loss = CP - SP

= ₹ (2500 - 2400)

= ₹ 100

•°• Required Loss percent

$\sf{ = ( \frac{Loss}{CP} \times 100)\% }\\ \\ = \sf{( \frac{100}{2500} \times 100)\%}$

$\sf{ = 4\%}$