A VCR and TV were bought for Rs 8000 each. The shopkeeper made a loss of\[4\% \] on the VCR and a profit of \[8\% \]on the TV. Find the gain or loss percent on the whole transaction.

Question

A VCR and TV were bought for Rs 8000 each. The shopkeeper made a loss of$$4\% $$ on the VCR and a profit of $$8\% $$on the TV. Find the gain or loss percent on the whole transaction.

Vedantu Content Team · Accepted Answer

Hint: First calculate the loss of $$4\% $$ on the VCR and then a profit of$$8\% $$ on the TV. A loss will be taken in negative while profit will be taken in positive and so profit or loss price can be calculated as $$\dfrac{{profit/loss}}{{100}} \times CP$$, calculate the total summation of profit and loss and hence if the final result is positive then the profit will be obtained to shopkeeper otherwise he will suffer from a loss, now to calculate profit/loss percentage, we use $$(\dfrac{{profit/loss}}{{T.C.P}}) \times 100$$, to get our answer.Complete step by step Answer:As per the given the value of a VCR and TV were bought for$$Rs.8000$$ each and the shopkeeper made a loss of $$4\% $$ on the VCR and a profit of$$8\% $$ on the TV.Hence, calculating the loss of $$4\% $$ on the VCR is given as,The cost price of a VCR is Rs 8000So, calculate loss for VCR as $$4\% $$ of Rs 8000 , We use $$n\% ofA = \dfrac{n}{{100}} \times A$$,$$   = (\dfrac{4}{{100}})8000   \\   = Rs.320   \\  $$Now, calculating the profit for TV as of $$8\% $$ of Rs 8000,Using $$n\% ofA = \dfrac{n}{{100}} \times A$$, we get,$$   = (\dfrac{8}{{100}})8000   \\   = Rs.640   \\  $$A loss will be taken in negative while profit will be taken in positive,Hence, the net loss and profit can be shown as,$$  net = 640 - 320   \\   = Rs.320   \\  $$So, we can see that the profit has been occurred and now in order to calculate profit percentage,We use,$$(\dfrac{{profit/loss}}{{T.C.P}}) \times 100\% $$On substituting values we get,$$ = (\dfrac{{320}}{{8000 + 8000}}) \times 100\% $$On simplification we get,$$ = \dfrac{{320}}{{16000}} \times 100\% $$On cancelation we get,$$ = 2\% $$Hence, the gain percent on the whole transaction is of $$2\% $$.Note: Calculate the profit percentage as $$(\dfrac{{profit}}{{T.C.P}}) \times 100$$ ,T.C.P is total cost price of an item. Calculate the loss and profit for each item carefully and also remember the convention to use without any mistake. Loss is always taken as negative, so don’t forget that and solve it accordingly.