Question

By selling 28 articles a man losses the cost price of 4 articles, then what is the loss %

Answer 1

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

Given that,

By selling 28 articles, a man losses the cost price of 4 articles.

So, it means

Loss = Cost Price of 4 articles. -----[ 1 ]

Also, we know that

Loss = Cost Price of 28 articles - Selling Price of 28 articles. -------[ 2 ]

So, from equation (1) and (2), we concluded that

Cost Price of 4 articles = Cost Price of 28 articles - Selling Price of 28 articles.

It means,

Cost Price of 4 articles - Cost Price of 28 articles = - Selling Price of 28 articles.

- Cost Price of 24 articles = - Selling Price of 28 articles

Cost Price of 24 articles = Selling Price of 28 articles.

Let assume that

Cost Price of 1 article = Rs x

Cost Price of 24 articles = Rs 24x

Cost Price of 28 articles = Rs 28x

So, we have

Selling Price of 28 articles = 24x

Cost Price of 28 articles = 28x

Loss = 28x - 24x = 4x

We know,

$\boxed{\sf{ \: \: Loss \: \% \: = \: \frac{Loss}{Cost \: Price} \times 100 \: \% \: \: }}$

So, on substituting the values, we get

$\rm \: Loss \: \% \: = \: \dfrac{4x}{28x} \times 100 \: \%$

$\rm \: Loss \: \% \: = \: \dfrac{1}{7} \times 100 \: \%$

$\rm\implies \: \: \: \boxed{\sf{ \: Loss \: \% \: = \: 14 \: \frac{2}{7} \: \% \: \: }}$

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