Question

the Marked price of a cycle is 20% more than its cost price the shopkeeper allows 10% discount on the cycle then finds its gain percent ​

Answer 1

Given :

• Marked Price is 20% more than the Cost Price

• Discount allowed = 10%

To Find :

• Gain Percent

Solution :

Let the Cost Price of Bicycle be Rs 100 then

$\bigstar \sf \: Marked \: Price =Cost \: Price + 20 \% \: of \: Cost \: Price$

$\longrightarrow\sf \: Marked \: Price = 100 + (\dfrac{20}{100} \times 100)$

$\longrightarrow\sf \: Marked \: Price = 100 + ( \cancel\dfrac{2000}{100})$

$\longrightarrow\sf \: Marked \: Price = Rs( \: 100 + 20)$

$\longrightarrow\sf \: Marked \: Price = Rs \: 120$

Let's find the Discount Amount

$\bigstar \boxed{\sf \: Discount \: allowed = Discount\% \: of \: Marked \: Price }$

$\longrightarrow\sf \: Discount = 10\% \: of \: 120$

$\longrightarrow\sf \: Discount = \dfrac{10}{100} \: of \: 120$

$\longrightarrow\sf \: Discount = \cancel\dfrac{1200}{100}$

$\longrightarrow\sf \: Discount = Rs\: 12$

Let's Find Selling Price from the Given Discount

$\bigstar\boxed{\sf \: Selling \: Price = Marked \: Price - Discount}$

$\longrightarrow\sf \: S.P. = Rs\: 120 - Rs\: 12$

$\longrightarrow\sf \: S.P. = Rs\: 108$

When Selling Price is Greater than Cost Price It's Case of Gain.

$\bigstar\boxed{\sf \: Gain = Selling\: Price - Cost\: Price}$

$\longrightarrow\sf \: Gain = Rs\: 108 - Rs\: 100$

$\longrightarrow\sf \: Gain = Rs\: 8$

Let's Find Gain % now.

$\bigstar\boxed{\sf \: Gain \: \% = \dfrac{Gain}{Cost\:Price} \: \times 100}$

$\longrightarrow\sf \: Gain\: \% = \dfrac{8}{100}\: \times 100$

$\longrightarrow\sf \: Gain\: \% = \cancel\dfrac{800}{100}$

$\longrightarrow\sf \: Gain\: \% = 8\: \%$

Hence,Gain% is 8%

Answer 2

||✪✪ QUESTION ✪✪||

The Marked price of a cycle is 20% more than its cost price the shopkeeper allows 10% discount on the cycle then finds its gain percent ?

|| ✰✰ ANSWER ✰✰ ||

Lets assume That, Cost Price of The cycle is Rs.100.

As , Given That, Marked price is 20% more Than its Cost price.

So,

➪ MP = [100 * (100+20)]/100 = (100*120)/100 = Rs.120 .

________

Now, the shopkeeper allows 10% discount on the cycle,

So,

➼ SP = MP * (100 - Discount%)/100

➼ SP = [120 * (100-10)]/100

➼ SP = (120*90)/100

➼ SP = Rs.108 .

________

So,

➺ Gain = SP - CP

➺ Gain = 108 - 100 = Rs.8

➳ Gain % = (Gain in Rs.) * 100 / CP

➳ Gain % = (8 * 100) /100

➳ Gain % = 8 % .

Hence , The shopkeeper has a gain of 8% in this case.

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☙❦ Shortcut Trick ☙❦ :-

Relation Between MP and CP is :-

☛⟪(MP/CP) = (100 + Gain%) / (100 - Discount%) ⟫

Lets Assume That, our CP is Rs.100 . So, our MP will be Rs.120 ( 20% More Than CP).

Putting values In our Formula now, we get ::--

☞ (120/100) = (100 + Gain%) / (100 - 10%)

☞ (6/5) = (100 + Gain%) / 90

Cross - Multiply,

☞ 5(100 + Gain%) = 90 * 6

☞ 500 + 5Gain% = 540

☞ 5Gain% = 540 - 500

☞ 5Gain% = 40

Dividing both sides by 5,

☞ Gain% = 8 % .

∴ Gain % is 8% .

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