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.​

Answer 1

Answer:

$\bf\underline{\underline{\red{Given:-}}}$

• 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.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The gain or loss percent on the whole transaction.

$\bf\underline{\underline{\green{Solution:-}}}$

$\sf Cost \: price \: of \: each \: article = Rs. 8000$

So:-

$\sf Cost \: price \: of \: TV = Rs. 8000$

$\sf Profit\% \: on \: TV = 8\%$

$\sf Profit = 8\% \: of \: 8000$

$\sf = \dfrac{8}{100}\times 8000$

$\sf = 8 \times 80$

$\sf = 640$

$\sf Profit \: on \: TV= Rs. 640$

$\sf Cost \: price \: of \: VSR = Rs. 8000$

$\sf Loss\% \: on \: VSR= 4\%$

$\sf Loss= 4\% \: of \: 8000$

$\sf = \dfrac{4}{100}\times 8000$

$\sf = 4\times 80$

$\sf = 320$

$\sf Loss \: on \: VSR= Rs.320$

$\sf Here:-$

$\sf Profit \: is \: more \: than \: loss$

$\sf Net \: Profit = 640 - 320 = Rs. 320$

Now:-

$\sf Profit\%\: on \: whole\: transaction = \dfrac{Net\: Profit}{ Total \: C.P}\times 100$

$\sf Total \: C.P \: on \: both\: the \: articles = 8000 + 8000 = Rs. 16000$

$\sf Net \: Profit = Rs. 320$

$\sf Profit\%\: on\: whole\: transaction$

$\sf = \dfrac{320}{16000}\times 100$

$\sf = \dfrac{320}{160}$

$\sf = 2\%$

$\underline{\boxed{\purple{\sf \therefore Gain\: on\: whole\: transaction = 2\%}}}$

Answer 2

Given:-

CP of VCR = Rs.8000

CP of TV = Rs.8000

Loss on the VCR = 4%

Profit on the TV = 8%

To find:-

The gain or loss% on the whole transaction.

___________________________________

Answer:-

▪As given, profit on TV = 8% of Rs.8000,

Formula used,

$\tt \frac{Profit \: percent}{100} \times CP$

$\tt = \frac{8}{100} \times 8000$

$\tt\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{Profit = Rs.640}$

▪As given, Loss on VCR = 4% of Rs.8000

Formula used,

$\tt \frac{Loss \: percent}{100} \times CP$

$\tt = \frac{4}{100} \times 8000$

$\tt\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{Loss = Rs.320}$

▪Therefore,

Net gain = Rs.640 - Rs.320 [Since, profit is more than loss]

$\tt\ \: \: \: \: \: \: \: \: \boxed{Net \: gain = Rs.320}$

▪Now,

Total CP = 8000 + 8000 = Rs.16000.

Net gain = Rs.320.

__________________________________

Profit % on whole transaction:

Formula used,

$\tt \frac{Net \: gain}{total \: CP} \times 100$

$\tt = \frac{320}{16000} \times 100$

$\tt \boxed{Gain \: on \: whole \: transaction = 2 \: percent}$