Question

A milkman sold two of his buffaloes for Rs. 18,000 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
CP of each)​

Answer 1

buffalo = Rs 20000 The milkman made a gain of 5% while selling one buffalo. This means if C.P. is Rs 100, then S.P. is Rs 105. C.P. of one buffalo =2000×100/105= Rs 19,047.62 Also, the second buffalo was sold at a loss of 10%. This means if C.P. is Rs 100, then S.P. is Rs 90. ∴C.P. of other buffalo =2000×100/90= Rs 22222.22 Total C.P. = Rs 19047.62 + Rs 22222.22 = Rs 41269.84 Total S.P. = Rs 20000 + Rs 20000 = Rs 40000 Loss = Rs 41269.84 − Rs 40000 = Rs1269.84 Ans,- ,the loss of milkman is, Rs 1,269.84.

Answer 2

Solution :

$\underline{\bf{Given\::}}}$

A milkman sold two of his buffaloes for Rs.18000 each. On one he made a gain of 5% & on the other a loss of 10% .

$\underline{\bf{Explanation\::}}}$

$\underbrace{\bf{1^{st}\:Case\::}}}$

Using formula of the cost price as given gain % :

$\boxed{\bf{Cost\:price\:(C.P.) = \dfrac{100}{100+gain(\%) } \times S.P. }}}$

• A milkman sold one buffalo = Rs.18000
• On his buffalo gain = 5%
• Cost price on first buffalo = ?

A/q

$\longrightarrow\sf{C.P.=\dfrac{100}{100 + 5} \times 18000}\\\\\\\longrightarrow\sf{C.P.= \dfrac{100}{105} \times 18000}\\\\\\\longrightarrow\sf{C.P. =\cancel{\dfrac{1800000}{105}} }\\\\\\\longrightarrow\bf{C.P. = Rs.17142.85}$

$\underbrace{\bf{2^{nd}\:Case\::}}}$

Using formula of the cost price as given loss % :

$\boxed{\bf{Cost\:price\:(C.P.) = \dfrac{100}{100-loss(\%) } \times S.P. }}}$

• A milkman sold other buffalo = Rs.18000
• On his buffalo loss = 10%
• Cost price of other buffalo= ?

$\longrightarrow\sf{C.P.=\dfrac{100}{100 -10} \times 18000}\\\\\\\longrightarrow\sf{C.P.= \dfrac{100}{90} \times 18000}\\\\\\\longrightarrow\sf{C.P. =\cancel{\dfrac{1800000}{90}} }\\\\\\\longrightarrow\bf{C.P. = Rs.20000}$

Total cost price of both buffalo = Rs.17142.85 + Rs.20000 = Rs.37142.85

Total selling price of both buffalo = Rs.18000 + Rs.18000 = Rs.36000

C.P > S.P

⇒ Loss = Cost price - Selling price

⇒ Loss = Rs.37142.85 - 36000

⇒ Loss = Rs.1142.85

Now;

$\mapsto\sf{Loss\:(\%) =\bigg( \dfrac{Loss}{C.P.} \times 100\bigg)\%}\\\\\\\mapsto\sf{Loss\:(\%) =\bigg( \dfrac{1142.85}{37142.85} \times 100\bigg)\%}\\\\\\\mapsto\sf{Loss\:(\%) =\bigg( \dfrac{1142.85\times 100}{37142.85\times 100} \times 100\bigg)\%}\\\\\\\mapsto\sf{Loss\:(\%) =\bigg( \dfrac{114285}{3714285} \times 100\bigg)\%}\\\\\\\mapsto\sf{Loss\:(\%) =\cancel{ \bigg( \dfrac{11428500}{3714285}\bigg)} \%}\\\\\\\mapsto\bf{Loss\:(\%) = 3.07\:\%}$

Thus;

The overall his loss% will be 3.07 % .