Question

A shopkeeper sells a bike at 40% profit after allowing 16% discount. If the profit earned is Rs.8,000 more
than the discount allowed on the bike, then find the cost price of the bike?
1. Rs. 80,000 2. Rs. 50,000
5. Rs. 40,000
3. Rs. 60,000
4. Rs. 90,000​

Answer 1

Answer:

• The cost price of the bike is Rs 60,000.
• Hence, 3. Rs 60,000 is required answer.

Step-by-step explanation:

Given that:

• A shopkeeper sells a bike at 40% profit after allowing 16% discount.
• If the profit earned is Rs.8,000 more than the discount allowed on the bike.

To Find:

• The cost price of the bike.

Let us assume:

• The cost price of the bike be x.

Formula used:

1. SP = {(100 + profit%) × CP}/100
2. Profit = SP - CP
3. MP = (SP × 100)/(100 + Discount%)
4. Discount = MP - SP

Where,

• SP = Selling price
• CP = Cost price
• MP = Marked price

Finding the selling price:

⇒ SP = {(100 + 40) × x}/100

⇒ SP = {(140) × x}/100

⇒ SP = 140x/100

⇒ SP = 1.4x

∴ Selling price = 1.4x

Finding the profit:

⇒ Profit = 1.4x - x

⇒ Profit = 0.4x

∴ Profit = 0.4x

Finding the marked price:

⇒ MP = (1.4x × 100)/(100 - 16)

⇒ MP = 140x/84

⇒ MP = 5x/3

∴ Marked price = 5x/3

Finding the discount:

⇒ Discount = 5x/3 - 1.4x

⇒ Discount = (5x - 4.2x)/3

⇒ Discount = 0.8x/3

∴ Discount = 0.8x/3

Finding the cost price the bike:

According to the question.

Profit earned = Discount allowed + Rs 8000

⟶ 0.4x = 0.8x/3 + 8000

⟶ 0.4x - 0.8x/3 = 8000

⟶ (1.2x - 0.8x)/3 = 8000

⟶ 0.4x/3 = 8000

⟶ 0.4x = 8000 × 3

⟶ 0.4x = 24000

⟶ x = 24000/0.4

⟶ x = 60000

∴ Cost price of the bike = Rs 60,000

Answer 2

Question:-

• A shopkeeper sells a bike at 40% profit after allowing 16% discount. If the profit earned is Rs.8,000 more than the discount allowed on the bike, then find the cost price of the bike?

To Find:-

• Find the cost price of the bike.

Solution:-

Here ,

• Let the cost price of the bike be ' x '

First ,

We have to find the selling price:-

$\longrightarrow\sf \: SP = \dfrac { ( 100 + 40 ) x } { 100 }$

$\longrightarrow\sf \: SP = \cancel\dfrac { 140x } { 100 }$

$\longrightarrow\sf \: SP = \dfrac { 7x } { 5 }$

$\longrightarrow\sf \: SP = 1.4x$

Now ,

We have to find the profit:-

$\longrightarrow\sf \: Profit = 1.4x - x$

$\longrightarrow\sf \: Profit = 0.4x$

Now ,

We have to find the Marked Price:-

$\longrightarrow\sf \: MP = \dfrac { 1.4x \times 100 } { 100 - 16 }$

$\longrightarrow\sf \: MP = \cancel\dfrac{ 140x } { 84 }$

$\longrightarrow\sf \: MP = \dfrac { 5x } { 3 }$

And ,

We have to find the discount:-

$\longrightarrow\sf \: Discount = \dfrac { 5x } { 3 } - 1.4x$

$\longrightarrow\sf \: Discount = \dfrac { 0.8x } { 3 }$

Now ,

We have to find the cost of the bike:-

• $\sf \: Profit = Discount + Rs \: 8000$

$\longrightarrow\sf \: 0.4x = \dfrac { 0.8x } { 3 } + 8000$

$\longrightarrow\sf \: \dfrac { 1.2x - 0.8x } { 3 } = 8000$

$\longrightarrow\sf \: 0.4x = 8000 \times 3$

$\longrightarrow\sf \: x = \cancel\dfrac { 8000 \times 3 } { 0.4 }$

$\longrightarrow\sf \: x = 60,000$

Hence ,

• The cost of bike is Rs 60,000