Question

A shopkeeper bought 800pens for $3200 . he sold 600 of them at $5each. he sold the rest at $3 each . find the gain or loss percent.​

Answer 1

$\underline{ \Large \sf \orange {Clarification}}$

Here, we are given that the total number of pens bought by the shopkeeper is 800 pens. The total cost price of 800 pens is $ 3200. Then, he sold 600 of these pens at $ 5 each. And sold remain pens at $ 3 each. We have to find the gain or loss %.

In order to find whether here is gain or loss, we'll find the gain or loss here, first. So, to find gain or loss, we'll find total selling price.If selling price will be greater than the cost price , then there'll be profit and if cost price will be greater than the cost price, then there'll be loss. After that by using the formula to calculate gain/loss % ,we'll find gain or loss %.

$\underline{ \Large \sf \orange {Explication \: of \: steps :}}$

As per the given question,

$\bigstar \: \boxed{\sf {Cost \: Price_{(800 \: Pens)} = \ \: 3200 }}$

Now, calculating total selling price,

• 600 pens were sold at the rate of $ 5 each.

→ SP of 1 pen = $ 5

→ SP of 600 pens = $ ( 5 × 600 )

→ SP of 600 pens = $ 3,000

• Rest pens were sold at the rate of $ 3 each.

→ Rest pens = ( 800 - 600 ) pens

→ Rest pens = 200 pens

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

This means that 200 pens were sold at the rate of $ 3 each.

→ SP of 1 pen = $ 3

→ SP of 200 pens = $ ( 3 × 200 )

→ SP of 200 pens = $ 600

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

→ Total SP = SP of 600 pens + SP of 200 pens

→ Total SP = $ ( 3,000 + 600 )

→ Total SP = $ 3600

$\bigstar \: \boxed{\sf {Selling \: Price_{(800 \: Pens)} = \ \: 3600 }}$

Here,

• Selling price > Cost price

So, he got gain. Now, let's find out how much gain he got.

→ Gain = Selling Price - Cost Price

→ Gain = $ ( 3600 - 3200 )

$\longrightarrow \underline{\boxed{\sf{ Gain = \ \: 400}}} \: \red{\bigstar}$

Now, as we know that,

• $\boxed{ \bf { Gain \: \% = \Bigg \lgroup \dfrac{Gain}{C.P} \times 100 \Bigg \rgroup\%}}$

$\longrightarrow \sf { Gain \: \% = \Bigg \lgroup \dfrac{400}{3200} \times 100 \Bigg \rgroup\%}$

$\longrightarrow \sf { Gain \: \% = \Bigg \lgroup \dfrac{400}{32} \Bigg \rgroup\%}$

$\longrightarrow \sf { Gain \: \% = \Bigg \lgroup \dfrac{100}{8} \Bigg \rgroup\%}$

$\longrightarrow \sf { Gain \: \% = \Bigg \lgroup \dfrac{50}{4} \Bigg \rgroup\%}$

$\longrightarrow \sf { Gain \: \% = \Bigg \lgroup \dfrac{25}{2} \Bigg \rgroup\%}$

$\underline{\boxed{\sf{ Gain \: \% = 12.5 \: \% }}} \: \red{\bigstar}$

Therefore, gain % is 12.5 %.