# Ex.8.2 Q7 Comparing Quantities Solution - NCERT Maths Class 8

## Question

A milkman sold two of his buffaloes for $$\rm{Rs}\, 20,000$$ each. On one he made a gain of $$5\%$$ and on the other a loss of $$10\%$$. Find his overall gain or loss.
(Hint: Find C.P. of each).

Video Solution
Comparing Quantities
Ex 8.2 | Question 7

## Text Solution

What is known?

S.P of each buffalo is $$\rm{Rs}\, 20,000$$

Buffalo $$1 =$$ On selling one gain $$\%$$ made is $$= 5\%$$

Buffalo $$2 =$$ On selling one loss$$\%$$ made is $$= 10\%$$

Number of buffaloes sold $$= 2$$

What is unknown?

Overall gain or loss

Reasoning:

(C.P of buffalo $$1$$ + C.P of buffalo $$2$$) is compared with S.P of $$\rm{Rs}\, 40,000$$ to know gain or loss

\begin{align}\rm{S.P}&= \frac{100 + \rm{Gain\%} }{100}{ \times \rm{C}{.P}}\\\rm{S.P}&= \frac{{{100} - {\rm{Loss\%} }}}{{{100}}}{ \times\rm{ C}{.P}}\end{align}

Steps:

C.P. of buffalo ($$5\%$$ gain)

\begin{align}20000& = \frac{105}{100} \times \rm C.P. \\ \rm C.P. &= \frac{100}{105} \times 20000 \\ \rm C.P. &= \frac{20}{21} \times 20000 \\ \rm C.P. &= {\rm{Rs}}\;19,047.62\end{align}

C.P. of buffalo ($$10\%$$ loss)

\begin{align}20000& = \frac{90}{100} \times \rm C.P.\\ \rm C.P. &= \frac{100}{90} \times 20000 \\ \rm C.P. &= \frac{10}{9} \times 20000 \\ \rm C.P. &={\rm{Rs}\,22,222.22}\end{align}

Total Cost Price of two buffaloes

\begin{align}&= 19,047.62 + 22,222.22\\&=\rm{ Rs}\; 41,269.84\end{align}

Loss $$=$$ Cost Price $$–$$ Selling Price

\begin{align} &=41,269.84 \,–40,000 \\&= \,1269.84\end{align}

$$\rm{Loss}= \rm{Rs}\; 1269.84$$

The milkman incurred a loss of $$\rm{Rs}\, 1269.84$$ on the whole transaction.

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