Question

A shopkeeper brought 200 eggs out of which 20 were broken. he sold fhe remaining eggs at the rate of Rs15 per dozen and thus gained 25÷2%. find his total investment.
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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A shopkeeper brought 200 eggs out of which 20 were broken. He sold fhe remaining eggs at the rate of Rs15 per dozen and thus gained 25/2 %.

So, it means

Total egg purchased = 200

Number of broken eggs = 20

Total number of eggs left = 200 - 20 = 180

We know, 12 eggs = 1 dozen

So, 180 eggs = 15 dozen

Further given that Selling Price of 1 dozen eggs = Rs 15

So, Selling Price of 15 dozen of eggs = 15 × 15 = 225

Profit % = 25/2 % = 12.5 %

We know,

$\boxed{ \rm{ \:Cost \: Price \: = \: \frac{100 \times Selling \: Price}{100 + Profit\%} \: }}$

So, on substituting the values, we get

$\rm \: Cost \: Price \: = \: \dfrac{100 \times 225}{100 + 12.5}$

$\rm \: Cost \: Price \: = \: \dfrac{22500}{112.5}$

$\rm \: Cost \: Price \: = \: \dfrac{22500 \times 10}{1125}$

$\rm \: Cost \: Price \: = \: \dfrac{ 22500 \times 10}{1125}$

$\rm\implies \:Cost \: Price \: = \: Rs \: 200$

So, it means his total investment is Rs 200

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Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$