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

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).

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.