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# Ex.8.2 Q5 Comparing Quantities Solutions- NCERT Maths Class 8

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## Question

A VCR and TV were bought for $$\rm{Rs} \,8,000$$ 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.

Video Solution
Comparing Quantities
Ex 8.2 | Question 5

## Text Solution

What is known?

C.P of VCR and TV each $$=\rm{Rs}\, 8000$$

Loss (in %) on VCR $$= 4\%$$

Profit (in %) on TV $$= 8\%$$

What is unknown?

Gain or loss of whole transaction

Reasoning:

S.P of VCR $$+$$ S.P of TV is compared with $$16,000$$ to know gain or loss

Gain% \begin{align}=\frac{\mathrm{Gain}}{\mathrm{C}\mathrm{.P}}\mathrm{ }\!\!\times\!\!\text{ 100}\end{align}

Loss% \begin{align}=\frac{\mathrm{Loss}}{\mathrm{C}\mathrm{.P}}\mathrm{ }\!\!\times\!\!\text{ 100}\end{align}

Steps:

\begin{align}{\rm{ S.P.of\,VCR}} &=\rm{C}{\rm{.}}P. - \text{Loss%} \times\! 8000\\&= 8000 - 4\% \times 8000\\&= 8000 - \frac{4}{{100}} \times 8000\\& = 8000 - 320\\& = {\rm{Rs }}\,7680\\{\rm{ S.P.of \,TV}} &= \!\rm{C.P} \!+ \!\text{Profit%}\! \times \!\rm{C.P}\\& = 8000 + \frac{8}{{100}} \times 8000\\& = 8000 + 640\\& = {\rm{Rs }}\,8640\end{align}

\begin{align}\rm{S.P.of\,VCR}+\text{TV}&=7680+8640\\&=\text{Rs}16320\\\text{C.P.of VCR}+\text{TV}&=8000+8000\\&=\text{Rs }16000\\\end{align}

\begin{align}{\text{Gain}}&={\rm{Rs }}\left( {16320 - 16000} \right)\\&= {\rm{Rs }}\,320\\{\text{Gain}}\%&= \frac{{\text{Gain}}}{{{C}{.P}}}{ \times 100}\\&= \frac{{{320}}}{{{16000}}}{ \times 100}\\&= 2\%\end{align}

The shopkeeper gains $$2\%$$ on the whole transaction

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