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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