Exercise 6.5

1. A shopkeeper bought a suit case for ₹480 and sold it for ₹540. Find his gain percent?

Solution:

Given:

Cost Price = ₹

Selling Price = ₹

Let's find the gain:

Gain = Selling Price - Cost Price

= ₹540 - ₹480 = ₹

Let's find gain percentage:

Gain percent = (Gain / Cost Price) × 100

= × 100

= × 100

= %

Therefore, the gain percent is 12.5%

2. Ajay bought a TV for ₹15000 and sold it for ₹14100. Find the loss percent?

Solution:

Given:

Cost Price = ₹

Selling Price = ₹

Let's find the loss:

Loss = Cost Price - Selling Price

= ₹15000 - ₹14100 = ₹

Let's find loss percentage:

Loss percent = (Loss / Cost Price) × 100

= × 100

= × 100

= %

Therefore, the loss percent is 6%

3. Ramu sold a plot of land for ₹2,40,000 gaining 20%. For how much did he purchase the plot?

Solution:

Given:

Selling Price = ₹

Gain percent = %

Let's find the Cost Price:

When gain is 20%, SP = CP + 20% of CP

₹240000 = CP + (20/100 × CP)

₹240000 = CP × (1 + )

₹240000 = CP ×

CP = ₹

Therefore, Ramu purchased the plot for ₹2,00,000

4. On selling a mobile for ₹750, a shop keeper loses 10%. For what amount should he sell it to gain 5%?

Solution:

Given:

Selling Price with 10% loss = ₹

Loss percent = %

Let's find the Cost Price first:

When loss is 10%, SP = CP - 10% of CP

= CP × (1 - )

= CP ×

₹750 = CP ×

CP = ₹

Now, let's find SP for 5% gain:

Required SP = CP + 5% of CP

= ₹833.33 + ( × ₹833.33)

= ₹

Therefore, he should sell it for ₹875 to gain 5%

5. A farmer sold 2 bullocks for ₹24000 each. On one bullock he gained 25% and on the other he lost 20%. Find his total profit or loss percent?

Solution:

Given:

Cost Price of each bullock = ₹

For first bullock:

Gain = 25% of CP

= ( × ₹24000)

= ₹

SP of first bullock = ₹24000 + ₹6000

= ₹

For second bullock:

Loss = 20% of CP

= ( × ₹24000)

= ₹

SP of second bullock = ₹24000 - ₹4800

= ₹

Let's find total:

Total CP = ₹24000 + ₹24000 = ₹

Total SP = ₹30000 + ₹19200 = ₹

Total Gain = ₹49200 - ₹48000 = ₹

Let's find gain percentage:

Gain percent = (Gain/Total CP) × 100

= () × 100

= × 100

= %

Therefore, his total gain percent is 2.5%

6. Sravya bought a watch for ₹480. She sold it to Ridhi at a gain of 6¼%. Ridhi sold it to Divya at a gain of 10%. How much did Divya pay for it?

Solution:

Given:

Sravya's CP = ₹

First transaction:

Gain = 6¼% of CP

= ( × ₹480)

= ₹

Sravya's SP = Ridhi's CP = ₹480 + ₹30

= ₹

Second transaction:

Ridhi's gain = 10% of CP

= ( × ₹510)

= ₹

Divya's payment = ₹510 + ₹51

= ₹

Therefore, Divya paid ₹561 for the watch

7. The marked price of a book is ₹225. The publisher allows a discount of 10% on it. Find the selling price of it?

Solution:

Given:

Marked Price = ₹

Discount percent = %

Let's find the discount amount:

Discount = ( × ₹225)

= ₹

Selling Price = Marked Price - Discount

= ₹225 - ₹22.5

= ₹

Therefore, the selling price of the book is ₹202.5

8. A carpenter allows 15% discount on his goods. Find the marked price of a chair which is sold by him for ₹680?

Solution:

Given:

Selling Price = ₹

Discount percent = %

Let's find Marked Price:

After 15% discount, SP = 85% of MP

₹680 = ( × MP)

MP = (₹680 × 100)/85

= ₹

Therefore, the marked price of the chair is ₹800

9. A dealer allows a discount of 10% and still gains by 10%. What should be the marked price if the cost price is ₹900?

Solution:

Given:

Cost Price = ₹

Let's first find SP with 10% gain:

SP = CP + 10% of CP

= ₹900 + ( × ₹900)

= ₹

Now, this SP is 90% of MP (after 10% discount)

₹990 = ( × MP)

MP = (₹990 × 100)/90

= ₹

Therefore, the marked price should be ₹1100