# PE 2 - Profit & Loss | Arithmetic - Profit & Loss

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

Girish bought 100 kg of Rice for Rs. 1100 and sold it at a loss of as much money as he received for 20 kg rice. At what price did he sell the rice?

- (a)
Rs. 9/kg

- (b)
Rs. 9.167/kg

- (c)
Rs. 9.5/kg

- (d)
Rs. 10.33/kg

Answer: Option B

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**Explanation** :

CP per kg = 1100/100 = Rs. 11.

Loss on 100 kg is equal to selling price of 20 kgs.

∴ 100 × (CP - SP) = 20 × SP

⇒ SP = 5/6 × CP = 5/6 × 11 = 9.167

**Alternately,**

The loss is covered by the sale of 20 extra kgs of rice i.e. CP of 100 kg = SP of 120 kg

∴ SP of 1 kg = CP of 100/120 kg = 100/120×11 = Rs. 9.1666

Hence, option (b).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

A merchant marks a profit of 20% by selling an article. What would be the percentage change in the profit% had he paid 10% less for it and the customer paid 10% more for it?

- (a)
120%

- (b)
125%

- (c)
133.33%

- (d)
150%

Answer: Option C

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**Explanation** :

Initially let the cost price = 100 and selling price = 120.

Later, CP = 100 × 0.9 = 90 and SP = 120 × 1.1 = 132.

∴ New Profit % = $\frac{132-90}{90}$ × 100 = 46.66%

% change in profit % = $\frac{46.66-20}{20}$ × 100 = 133.33%

Hence, option (c).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

Rajesh sells his laptop to Amiya at a loss of 20% who subsequently sells it to Chandra at a profit of 25%. Chandra, after finding some defect in the laptop, returns it to Amiya but could recover only Rs. 90 paise for every rupee he had paid. Find the amount of Chandra’s loss if Rajesh had paid Rs. 3.5 lakh for the laptop.

- (a)
Rs. 7,000

- (b)
Rs. 5,000

- (c)
Rs, 35,000

- (d)
None of these

Answer: Option C

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**Explanation** :

Assume Rajesh’s cost price as 100.

Then Amiya buys at 100 × 0.8 = 80, sells at 80 × 1.25 = 100 and buys back from Chandra at 0.9 × 10 = 90.

For every Rs. 100 spent by Rajesh, Chandra lost Rs. 10.

∴ If Rajesh spent Rs. 3.5 lakh Chandra loses Rs. 0.35 lakh i.e., Rs. 35,000.

Hence, option (c).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

A driver of a Autorickshaw makes a profit of 10% on every trip when he carries 3 passengers and his total cost per km is Rs. 100. Find the percentage profit for same journey if he goes for four passengers per trip and the his cost per km reduces to Rs. 90? (Assume that revenue per passenger is the same in both the cases)

- (a)
43.33%

- (b)
65.66%

- (c)
62.9%

- (d)
Cannot be determined

Answer: Option C

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**Explanation** :

Assuming 3 passengers travel for exactly 1 km.

Cost of the trip = Rs. 100 and income from a trip = Rs. 110

Since cost per km reduces by 10%, total cost will also reduce by 10%.

∴ New total cost = 100 × 0.9 = Rs. 90.

Now number of passengers increase from 3 to 4 i.e., 33.33% hence income also increases 33.33%.

∴ New total income = 110 × 1.3333 = 146.67.

% Profit = (146.67 - 90)/90 × 100 = 62.9%

Hence, option (c).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

A shopkeeper professes to sell the goods at cost price. He uses a false weight with the intention of selling an item at 33.33% profit. After selling the item, he realizes that the customer has paid 25% less than what he should have paid. Find the actual profit percentage made by the shopkeeper.

- (a)
6.25%

- (b)
No profit, no loss

- (c)
8.33%

- (d)
None of these

Answer: Option B

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**Explanation** :

Let the shopkeeper bought goods worth Rs. 300.

To earn 33.33% profit his total selling price should be 300 + 1/3 × 300 = Rs. 400

But the customer paid 25% less than this.

∴ Amount received by the shopkeeper = 75% of 400 = Rs. 300.

∴ For shopkeeper total cost price = total selling price.

∴ Shopkeeper earns no profit no loss.

Hence, option (b).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

A shopkeeper purchased 40 litres of milk at the rate of Rs. 2.00 per litre and 60 litres of milk at the rate of Rs. 2.5 from two sellers. He sold the whole milk at the rate of Rs. 2.3 per litre. Find his profit or loss percent.

- (a)
No profit no loss

- (b)
10.3%

- (c)
11%

- (d)
12%

Answer: Option A

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**Explanation** :

CP = 40 × 2 + 60 × 2.5 = Rs. 230

SP = (40 + 60) × 2.3 = Rs. 230

∴ Profit % = 0%

Hence, option (a).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

A shopkeeper sells his goods at the same price as what he pays his supplier. But when he buys from his supplier he takes 10% more than the indicated weight and when he sells, he gives a quantity, such that if 10% of that is added to it, the indicated weight is obtained. Find his profit percentage

- (a)
18.25%

- (b)
22.22%

- (c)
20%

- (d)
21%

Answer: Option D

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**Explanation** :

Let CP = SP = 1/kg,

Shopkeeper buys 100 kgs from the supplier but he actually gets 10% more i.e., 110 kgs.

Now the shopkeeper will sell this 110 kgs but the indicated weight will be 110 + 10% of 110 = 121 kgs.

Total cost price = 1 × 100 = Rs. 100

Total selling price = 1 × 121 = Rs. 121

∴ Profit percentage = 21%.

Hence, option (d).

Workspace:

**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

The cost of running a printing machine is Rs. 450 per 1000 copies. The cost of setting is Rs. 5,000 for the first 10,000 copies and after this, the cost of setting is 50 paise per copy. The other cost is 40 paise per copy. About 20,000 copies of a magazine are printed, but only 16,520 copies are sold at the rate of Rs. 1.8 each. What is the amount earned from advertisement, if a profit of 20% on the cost price is made?

- (a)
Rs. 1455

- (b)
Rs. 2095

- (c)
Rs. 2055

- (d)
Rs. 2664

Answer: Option D

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**Explanation** :

Cost of running a printing machine for 20,000 copies = Rs. 450/1000 × 20,000 = Rs. 9,000

Cost of setting of 10,000 copies = Rs. 5000

Cost of setting of other 10,000 copies = 0.5 × 10,000 = Rs. 5,000

Other cost of 20,000 copies = 0.4 × 20,000 = Rs. 8,000

Total cost price of 20,000 copies = 9000 + (5000 + 5000) + 8000 = Rs. 27,000

Selling price of 16520 copies = 16520 × 1.8 = Rs. 29,736

Total income to earn 20% profit = 27000 × 1.2 = Rs. 32,400

Net amount earned from advertisement = Total income – Income from sale of 16520 copies

= 32,400 – 29,736 = 2,664.

Hence, option (d).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

Arnav sells his goods 10% cheaper than Bishnoi and 10% dearer than Chetan. A customer purchases goods worth Rs. 11,200 from Arnav. What will be the profit or loss for him to buy half of the goods from Bishnoi and half of the goods from Chetan?

- (a)
Rs. 113.11 loss

- (b)
Rs. 131.11 loss

- (c)
Rs. 113.13 loss

- (d)
None of these

Answer: Option C

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**Explanation** :

SP of Arnav = Rs. 11,200

SP of Arnav = 90% of SP of Bishnoi

∴ SP of Bishnoi = $\frac{11200}{90}$ × 100 = $\frac{112000}{9}$

⇒ SP of Bishnoi for half the goods = $\frac{112000}{9\times 2}$ = Rs. $\frac{56000}{9}$

Similarly, SP of Chetan = $\frac{11200}{110}$ × 100 = Rs. $\frac{112000}{11}$

⇒ SP of Chetan for half the goods = $\frac{112000}{11\times 2}$ = Rs. $\frac{56000}{11}$

Total SP of Chetan and Bishnoi = $56000\left(\frac{1}{9}+\frac{1}{11}\right)$ = $\frac{1120000}{99}$

∴ Cost for the customer will be more when he purchases from Chetan and Bishnoi by

Rs.$\left(\frac{1120000}{99}-11200\right)$ = Rs. 11200$\left(\frac{100}{99}-1\right)$

Rs. $\frac{11200}{99}$ = Rs. 113.13 loss.

Hence, option (c).

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**PE 2 - Profit & Loss | Arithmetic - Profit & Loss**

A trader sells two horses, each for Rs. 3.75. On the sale of one horse he gets a profit of 15% and on the sale of second horse he has a loss of 15%. Find the profit % on the whole.

- (a)
3.25%

- (b)
2.25%

- (c)
5.25%

- (d)
None of these

Answer: Option D

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**Explanation** :

When two articles are sold at same selling price earning p% loss on one and p% profit on the other, overall loss = p^{2}/100

∴ % Loss =(15)^{2}/100 = 2.25%

∴ % profit = - 2.25%

Hence, option (d).

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