Question

If the cost price of 18 articles
is equal to the selling price of
16 articles, the gain or loss is
18 वस्तुओं का क्रय मूल्य 16 वस्तुओं के
विक्रय मूल्य के बराबर है,तो प्रतिशत लाभ या
हानि ज्ञान करें।
(a) 25% gain (b) 25% loss
(c) 12.5 % loss (d) 12.5% gain​

Answer 1

✰Answer✰

♦️GiveN

• CP of 18 articles= SP of 16 articles

♦️To FinD

• Gain or loss percentage.

✰We must know✰

☛Some basic formulae

$\large{ \underline{ \underline{ \red{ \sf{profit}}}}} \\ \\ \large{ \tt{ \star{ \: profit = sp - cp}}} \\ \\ \large{ \tt{ \star{ \: profit\% = \frac{profit}{cp} \times 100}}} \\ \\ \large{ \sf{ \underline{ \underline{ \red{loss}}}}} \\ \\ \large{ \tt{ \star{ \: loss =cp - sp}}} \\ \\ \large{ \tt{ \star{ \: loss\% = \frac{loss}{cp} \times 100}}}$

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☛By using this concept, Let's solve this question

$\large{ \tt{let \: the \: cost \: of \: 18 \: articles = x}} \\ \\ \large{ \tt{ \therefore{ then \: cp \: of \: 1 \: article = \frac{x}{18}}}} \\ \\ \large{ \tt{ \underline{ \underline{ \red{ According \: to \: question }}}}} \\ \\\large{ \tt{Also \: selling \: price \: of \: 16 \: articles = x}} \\ \\ \large{ \tt{ \therefore{then \: sp \: of \: one \: article = \frac{x}{16} }}} \\ \\ \large{ \tt{ \star{ \: comparing \: cp \: and \: sp \: of \: one \: article}}} \\ \\ \large{ \tt{(we \: know \: if \: numerator \: is \: same }} \\ \large{ \tt{then \: smaller \: denomiantor \: fraction \: is \: greater)}} \\ \\ \large{ \tt{so \: \: \: \frac{x}{16} > \frac{x}{18} }} \\ \\ \large{ \tt{ \circ{ \: sp \: of \: 1 \: article > cp \: of \: 1 \: article}}} \\ \\ \large{ \tt{ \green{when \: sp > cp \implies \: \underline{profit}}}}$

☛Now using profit formula

$\large{ \tt{profit = \frac{x}{16} - \frac{x}{18} }} \\ \\ \large{ \tt{ \rightarrow{ profit \: = \frac{9 x- 8x}{144} }}} \\ \\ \large{ \tt{ \rightarrow \: profit = \frac{x}{144} }}$

☛Now using profit% formula

$\large{ \tt{profit \: \% = \cancel{ \frac{\frac{x}{144} }{ \frac{x}{18} }} \times 100}} \\ \\ \large{ \tt{ \rightarrow \: profit\% = \frac{1}{8} \times 100}} \\ \\ \large{ \rightarrow{ \boxed{ \tt{ \purple{profit\% = 12.5\%}}}}}$

✰So Final Answer✰

♦️ Option D - 12.5% gain