Question

A shopekeeper sells one machine for 990 rupees at profit 10% and another machine for 1960 rupees at loss of 2% what is his gain or loss percentage​

Answer 1

C. P of first machine = (990 × 100) ÷ 100 = 900rupees

C. P. of second machine = (990 × 100) ÷ 90 = 1100 rupees

Total C.P. = 1100 + 900 = 2000

Total S. P. = 990 × 2 = 1980

Loss = 2000 - 1980 = 20 rupees is the answer

Answer 2

Step-by-step explanation:

$.\huge\bf{\underline{\underline{\gray{GIVEN:-}}}}GIVEN:−</p><p></p><p>A shopkeeper sells,</p><p></p><p>One machine for Rs.990 at profit of 10% .</p><p></p><p>Another machine for Rs.1960 at loss of 2% .</p><p></p><p>\begin{gathered}\\\end{gathered}</p><p></p><p>\huge\bf{\underline{\underline{\gray{TO\:FIND:-}}}}TOFIND:−</p><p></p><p>His gain or loss percentage .</p><p></p><p>\begin{gathered}\\\end{gathered}</p><p></p><p>\huge\bf{\underline{\underline{\gray{SOLUTION:-}}}}SOLUTION:−</p><p></p><p>ᴄᴀsᴇ - 1 ;-</p><p></p><p>☯︎ In the first transaction,</p><p></p><p>\begin{gathered}{\color{aqua}\bigstar}\:\bf{\pink{\overbrace{\underbrace{\blue{Profit\%\:=\:\dfrac{S.P\:-\:C.P}{C.P}\times{100}\:}}}}} \\\end{gathered}★Profit%=C.PS.P−C.P×100</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:10\:=\:\dfrac{990\:-\:C.P}{C.P}\times{100}\:} \\\end{gathered}:⟹10=C.P990−C.P×100</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:\dfrac{10}{100}\:=\:\dfrac{990\:-\:C.P}{C.P}\:} \\\end{gathered}:⟹10010=C.P990−C.P</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:0.1\times{C.P}\:=\:990\:-\:C.P\:} \\\end{gathered}:⟹0.1×C.P=990−C.P</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:0.1\times{C.P}\:+\:C.P\:=\:990\:} \\\end{gathered}:⟹0.1×C.P+C.P=990</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:1.1\times{C.P}\:=\:990\:} \\\end{gathered}:⟹1.1×C.P=990</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:C.P\:=\:\dfrac{990}{1.1}\:} \\\end{gathered}:⟹C.P=1.1990</p><p></p><p>\begin{gathered}\\ \bf\green{:\implies\:C.P\:=\:Rs.900\:} \\ \\\end{gathered}:⟹C.P=Rs.900</p><p></p><p>ᴄᴀsᴇ - 2 ;-</p><p></p><p>☯︎ In the second transaction,</p><p></p><p>\begin{gathered}\purple\bigstar\:\bf{\red{\overbrace{\underbrace{\green{Loss\%\:=\:\dfrac{C.P\:-\:S.P}{S.P}\times{100}\:}}}}} \\\end{gathered}★Loss%=S.PC.P−S.P×100</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:2\:=\:\dfrac{C.P\:-\:1960}{1960}\times{100}\:} \\\end{gathered}:⟹2=1960C.P−1960×100</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:\dfrac{2}{100}\:=\:\dfrac{C.P\:-\:1960}{1960}\:} \\\end{gathered}:⟹1002=1960C.P−1960</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:0.02\times{1960}\:=\:C.P\:-\:990\:} \\\end{gathered}:⟹0.02×1960=C.P−990</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:39.2\:=\:C.P\:-\:1960\:} \\\end{gathered}:⟹39.2=C.P−1960</p><p></p><p>\begin{gathered}\\ \bf\green{:\implies\:C.P\:=\:Rs.1999.2\:} \\ \\\end{gathered}:⟹C.P=Rs.1999.2</p><p></p><p>So,</p><p></p><p>\begin{gathered}\bf{:\implies\:Total\:C.P\:=\:Rs.\:(900\:+\:1999.2)\:} \\\end{gathered}:⟹TotalC.P=Rs.(900+1999.2)</p><p></p><p>\begin{gathered}\\ \bf\gray{:\implies\:Total\:C.P\:=\:Rs.2899.2\:} \\ \\\end{gathered}:⟹TotalC.P=Rs.2899.2</p><p></p><p>And</p><p></p><p>\begin{gathered}\bf{:\implies\:Total\:S.P\:=\:Rs.\:(990\:+\:1960)\:} \\\end{gathered}:⟹TotalS.P=Rs.(990+1960)</p><p></p><p>\begin{gathered}\\ \bf\gray{:\implies\:Total\:S.P\:=\:Rs.2950\:} \\ \\ \\\end{gathered}:⟹TotalS.P=Rs.2950</p><p></p><p>Since,</p><p></p><p>S.P > C.P</p><p></p><p>✈︎ Hence here gain or profit is occured .</p><p></p><p>\begin{gathered}\\\end{gathered}</p><p></p><p>✯ Pʀᴏғɪᴛ = S.ᴘ - C.ᴘ</p><p></p><p>➤ Pʀᴏғɪᴛ = 2950 - 2899.2</p><p></p><p>➤ Pʀᴏғɪᴛ = Rs.50.8</p><p></p><p>\begin{gathered}\\\end{gathered}</p><p></p><p>\huge\red\checkmark✓ \begin{gathered}\bf\orange{Gain\%\:=\:\dfrac{Profit}{C.P}\times{100}\:} \\\end{gathered}Gain%=C.PProfit×100</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:Gain\%\:=\:\dfrac{50.8}{2899.2}\times{100}\:} \\\end{gathered}:⟹Gain%=2899.250.8×100</p><p></p><p>\begin{gathered}\\ \bf{:\implies\:Gain\%\:=\:\dfrac{5080}{2899.2}\:} \\\end{gathered}:⟹Gain%=2899.25080</p><p></p><p>\begin{gathered}\\ \bf\blue{:\implies\:Gain\%\:=\:1.75\%\:} \\ \\\end{gathered}:⟹Gain%=1.75%</p><p></p><p>\huge{\color{orange}\therefore}∴ The gain% is '1.75%' .</p><p></p><p>$