Question

A milkman sold two of his buffaloes for 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. ​

Answer 1

$\underline{ \underline{\rm \large{Given :}}}$

• S.P of buffaloes = ₹20,000
• Gain = 5%
• Loss = 10%

$\underline{ \underline{\rm \large{To Find :}}}$

His overall gain or loss.

$\underline{ \underline{\rm \large{Solution :}}}$

$\textbf{\textrm{Selling Price = 2 × Selling Price}}$

$= 2 \times 20000$

$= 40000$

Cost Price :

C.P of first buffalo + C.P of second buffalo

CP of 1st Buffalo :-

• S.P = 20000
• Gain = 5%
• C.P (Unknown value) = x

$\: \: \: \: \: \: \: \: \: \: \: \: \rule{140pt}{1pt}$

As We know,

$\textbf{\textrm{Gain = S.P - C.P}}$

$= \rm 20000 - x$

Gain :

$\dashrightarrow \rm \: Gain = \dfrac{Gain}{C.P} \times 100$

$\dashrightarrow \rm{5 = \dfrac{20000 - x}{ x} \times 100}$

$\dashrightarrow \rm{5x= ({20000 - x})\times100}$

$\dashrightarrow \rm{5x= {2000000 } - 100x}$

$\dashrightarrow \rm{2000000 =100x + 5x}$

$\rm{x = \dfrac{2000000}{105}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \rule{140pt}{1pt}$

C.P of 2nd Buffalo :-

• Selling Price = 20000
• Loss = 10%
• C.P (Unknown value) = z

$\: \: \: \: \: \: \: \: \: \: \: \: \rule{140pt}{1pt}$

As we Know,

$\textbf{\textrm{Loss = C.P - S.P}}$

$\rm = z - 20000$

Loss :

$\dashrightarrow \rm{Loss = \dfrac{ Loss }{C.P} } \times 100$

$\dashrightarrow \rm{10= \dfrac{ z - 20000}{z} } \times 100$

$\dashrightarrow\rm{10z= (z - 20000) } \times 100$

$\dashrightarrow \rm{10z= 100z - 2000000}$

$\dashrightarrow \rm{10z - 100z= - 2000000}$

$\dashrightarrow \rm{ - 90z= - 2000000}$

$\dashrightarrow \rm{z = \dfrac{ \cancel- 2000000}{ \cancel- 90}}$

$\rm{z = \dfrac{ 2000000}{ 90}}$

$\rule{190pt}{3pt}$

$\rm C.P \begin{cases} \rm Of \: 1st \: Buffalo = \rm{ \dfrac{2000000}{105}} \\ \\ \rm Of \: 2nd \: Buffalo = \dfrac{2000000}{90}\end{cases}$

$\rule{230pt}{3pt}$

C.P of first buffalo + C.P of second buffalo

$\dashrightarrow\rm{ \dfrac{2000000}{105}} + \rm{ \dfrac{2000000}{90}}$

$\dashrightarrow\rm{ 2000000 \bigg (\dfrac{1}{105}} + \rm{ \dfrac{1}{90} \bigg)}$

$\dashrightarrow\rm{ 2000000 \bigg (\dfrac{ 105 + 90}{105 \times 90} \bigg)}$

$\dashrightarrow\rm{ 2000000 \bigg (\dfrac{ 195}{105 \times 90} \bigg)}$

$\dashrightarrow\rm{ 2000000 \bigg (\dfrac{ \cancel{195}}{105 \times \cancel{90} } \bigg)}$

$\dashrightarrow\rm{ 2000000 \bigg (\dfrac{ 65}{105 \times 30 } \bigg)}$

$\dashrightarrow\rm{ 200000 \cancel0 \bigg (\dfrac{ 65}{105 \times 3 \cancel0 } \bigg)}$

$\dashrightarrow\rm{ 200000 \bigg (\dfrac{ \cancel {65}}{ \cancel{105} \times 3 } \bigg)}$

$\dashrightarrow\rm{ 200000 \bigg (\dfrac{ {13}}{{21} \times 3 } \bigg)}$

$\dashrightarrow\rm{ \dfrac{ {2600000}}{{63} } }$

$\dashrightarrow\rm{ \cancel\dfrac{ {2600000}}{{63} } }$

$\dashrightarrow\rm{ 41269.83}$

$\rule{230pt}{3pt}$

∴S.P = ₹40000

C.P = ₹41269.83

C.P > SP

Loss !!

Loss = C.P - S.P

= 41269.83 - 40000

= 1269.83

His Over all Loss is = 1269.83

Additional information:-

$\qquad \overset{\textsf{ \textbf{ ★Profit and Loss★}}}{\boxed{ \begin{align}&\sf {{\footnotesize\sf{ \bigstar}}}\:S.P. =\sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times 100\\\\\\ &\sf {{\footnotesize\sf{ \bigstar}}} \:\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%}\\\\\\&\sf{{\footnotesize\sf{ \bigstar}}} \:\:Profit = \sf \dfrac{Profit \% \times C.P.}{100}\\\\\\ &\sf{{\footnotesize\sf{ \bigstar}}} \: \:Profit (gain) = S.P. - C.P. \\\\\\&\sf{{\footnotesize \sf{ \bigstar}}} \: \:\sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{align}}}$