Question

Chandan bought 1600 bananas at Rs 3.75 a dozen.He sold 800 of them at 2 for Rs 5 and the reamaining at 6 for Rs 2.Find gain or loss percent​

Answer 1

Step-by-step explanation:

Given :-

Chandan bought 1600 bananas at Rs 3.75 a dozen.

He sold 800 of them at 2 for Rs 5 and the reamaining at 6 for Rs 2.

To find :-

Gain or Loss percentage

Solution :-

Given that

The cost of a dozen bananas = Rs. 3.75

Total number of bananas were bought

= 1600

We know that

12 objects = 1 dozen

1600 objects = 1600/12 dozen

=> 1600 objects = 400/3 dozen

The cost of 1600 bananas

=The cost of 400/3 dozen bananas

= (400×3.75)/3

= (4×375)/3

= 1500/3

= Rs. 500

The cost of 1600 bananas = Rs. 500

And

The selling price of 2 bananas = Rs. 5

The selling Price of 1 banana = Rs. 5/2

The selling price of 800 bananas

= (800×5)/2

= 400×5

= Rs. 2000

The selling price of 800 bananas

= Rs. 2000

Remaining bananas = 1600-800 = 800

The selling price of 6 bananas = Rs. 2

The selling price of 1 banana = Rs. 2/6

= Rs. 1/3

The selling price of 800 bananas

= 800 ×( 1/3)

= Rs. 800/3

Total Selling price of all 1600 bananas

= 2000+(800/3)

= (6000+800)/3

= Rs. 6800/3

We have ,

Total Selling Price of 1600 bananas

= Rs. 6800/3

Total cost price of 1600 bananas

= Rs. 500

Selling Price > Cost Price

=> Gain occurs

Chandan got gain .

We know that

Gain = Selling Price - Cost Price

=> Gain = (6800/3)-500

=> Gain = (6800-1500)/3

=> Gain = Rs. 5300/3

We know that

Gain % = (Gain/Cost Price)×100

=> G% = [(5300/3)/500]×100

=> G% = [5300/(3×500)]×100

=> G% = (5300/1500)×100

=> G% = (53/15)×100

=> G% = 5300/15

=> G% = 1060/3

=> G% = 353 1/3%

Answer :-

Chandan got 353 1/3% of gain percentage in the whole transaction

Used formulae:-

→ 1 dozen = 12 articles

→ Gain = Selling Price-Cost Price

→ Gain % = (Gain / Cost Price)×100

Answer 2

$\large{\underline{\underline{\maltese{\orange{\pmb{\sf{ \; Solution \; :- }}}}}}}$

~ How to Solve :

$\longrightarrow$ First ,we will calculate the Cost price of the Bananas .Than, we will calculate the Selling price of first 800 bananas and after that the cost of Rest Bananas . On adding the selling price of these bananas we will get that he got profit or loss .On this basis ,by applying the formula for loss or gain % we will get the answer .Let's Solve :

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~ Formula Used :

• ${\underline{\boxed{\purple{\sf{ Gain \; \% = \dfrac{Gain}{Cost \; Price} \times 100 }}}}}$

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~ Calcuting the Cost Price :

${\longmapsto{\sf{ Cost \; Price = \dfrac{Total \; Bananas}{No. \; of \; Bananas \; in \; 1 \; Dozen} \times Cost \; of \; Bananas{\small_{(1 \; Dozen)}} }}}$

Here :

• ➬ Total Bananas = 1600
• ➬ Bananas in 1 Dozen = 12
• ➬ Cost of 1 Dozen Banana = Rs. 3.75

Calculation Starts :

${\longmapsto{\sf{ Cost \; Price = \dfrac{Total \; Bananas}{No. \; of \; Bananas \; in \; 1 \; Dozen} \times Cost \; of \; Bananas{\small_{(1 \; Dozen)}} }}}$

${\longmapsto{\sf{ \dfrac{1600}{12} \times 3.75 }}}$

${\longmapsto{\sf{ \dfrac{1600}{12} \times \dfrac{375}{100} }}}$

${\longmapsto{\sf{ \dfrac{16\cancel{00}}{12} \times \dfrac{375}{\cancel{100}} }}}$

${\longmapsto{\sf{ \dfrac{16}{12} \times 375}}}$

${\longmapsto{\sf{ \dfrac{6000}{12} }}}$

${\longmapsto{\sf{ \cancel\dfrac{6000}{12} }}}$

${\longmapsto{\qquad{\orange{\sf{ Cost \; Price = ₹ \; 500 }}}}}$

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~ Calculating the Selling price of 800 Bananas :

${\dashrightarrow{\sf{ Selling \; Price = \dfrac{Total \; No. \; of \; Bananas}{No. \; of \; Bananas} \times Cost }}}$

Here :

• ➬ Total no. of Bananas = 800
• ➬ No. of Bananas = 2
• ➬ Cost = 5

Calculation Starts :

${\dashrightarrow{\sf{ \dfrac{Total \; No. \; of \; Bananas}{No. \; of \; Bannas} \times Cost }}}$

${\dashrightarrow{\sf{ \dfrac{800}{2} \times 5 }}}$

${\dashrightarrow{\sf{ \dfrac{4000}{2} }}}$

${\dashrightarrow{\sf{ \cancel\dfrac{4000}{2} }}}$

${\dashrightarrow{\qquad{\red{\sf{ Selling \; Price = ₹ \; 2000 }}}}}$

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~ Calculating the Cost price of Rest Bananas :

${\dashrightarrow{\sf{ Selling \; Price = \dfrac{Rest \; Bananas}{No. \; of \; Bananas} \times Cost }}}$

Here :

• ➬ Rest Bananas = 1600 - 800 = 800
• ➬ No. of Bananas = 6
• ➬ Cost = 2

Calculation Starts :

${\dashrightarrow{\sf{ Selling \; Price = \dfrac{Rest \; Bananas}{No. \; of \; Bannas} \times Cost }}}$

${\dashrightarrow{\sf{ \dfrac{800}{6} \times 2 }}}$

${\dashrightarrow{\sf{ \dfrac{800}{\cancel6} \times \cancel2 }}}$

${\dashrightarrow{\qquad{\red{\sf{ Selling \; Price = ₹ \; \dfrac{800}{3} }}}}}$

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~ Calculating the Total S.P :

$\begin{gathered} \implies{\sf{ Total \; Selling \; Price = Selling \; Price{\small_{(800 \; Bananas)}} + Selling \; Price{\small_{(Rest \; Bananas)}} }} \\ \end{gathered}$

$\begin{gathered} \implies{\sf{ \dfrac{2000}{1} + \dfrac{800}{3} }} \\ \end{gathered}$

$\begin{gathered} \implies{\sf{ \dfrac{2000}{3} + \dfrac{800}{3} }} \\ \end{gathered}$

$\begin{gathered} \implies{\sf{ \dfrac{6000 + 800}{3} }} \\ \end{gathered}$

$\begin{gathered} \implies{\qquad{\green{\sf{ Total \; Selling \; Price = ₹ \; \dfrac{6800}{3} }}}} \\ \end{gathered}$

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~ Calcuting the Profit % :

$\begin{gathered} \dashrightarrow \; \; \sf { Profit \; \% = \dfrac{Profit}{Cost \; Price} \times 100 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{\dfrac{5300}{3}}{500} \times 100 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{5300}{500 \times 3} \times 100 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{5300}{1500} \times 100 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{53\cancel{00}}{15\cancel{00}} \times 100 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{53}{15} \times 100 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{5300}{15} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; {\qquad{\pink{\sf { Profit \; \% = 353\dfrac{1}{3} \; \% }}}} \\ \end{gathered}$

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❛❛ Chandan had a profit of ${\sf{ 353\dfrac{1}{3} \; \% }}$ on the whole transaction . ❜❜

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