07-09-2021 Answers

1. A dishonest seller uses 860 grams instead of 1kg weight scale. Find his actual profit or loss if the seller says he sells his items on 5% gain on cost price.

Answer: Gain of 22.09%

Solution: Let x be the proper weight and y be the actual weight used. Let p be the gain percentage mentioned.

The shortcut to calculate the actual gain percentage is = (100+p)(x/y) -100.

So gain % = (100+5) * (1000/860)  - 100 = 22.09%

2. A shopkeeper proposes to sell at cost price but has a faulty balance which shows 1000 grams for 800 grams. What is his profit percentage?

Answer: 25%

Solution: Difference = 1000 - 800 = 200 grams.

Profit percentage = (200/800) * 100 = 25%

3. A manufaturer supplies 50 tables at the marked price of 42 tables to the retailer. The retailer sells them at a 10% discount on the marked price. What is the approximate profit or loss percentage of the retailer?

Answer: Profit of 7.14%

Solution: Let marked price of a table be x.

C.P of 50 tables for the retailer = 42x.

S.P of 50 tables for the retailer = 50x * 0.9 = 45x.

Profit = 45x-42x = 3x.

Profit % = (3x/42x)*100 = 7.14% approx

4. A TV reseller wants to obtain a profit of 10% on his current label price after offering a 30% discount. What should be the increase in the current label price to arrive at the revised label price?

Answer: 57.14% increase.

Solution: Shortcut: The formula is (x+y) * 100/(100-y), where x is profit% and y is discount%.

Here x=10%, y=30%.

So required % increase = 40 * 100/(100-30) = 57.14% approx.

5. In a pet store, selling price of two puppies are same. But one is sold at a profit of 20% while the other is sold at a loss of 20%. What is the net overall profit or loss percentage?

Answer: 4% loss

Solution: When selling price is same but one is sold at a profit % of x and another at loss % of x, it will always be a loss.

The loss% is given using the formula x^2/100.

Hence loss% = 20*20/100 = 4%

6. If a seller got Rs.80 more by selling an article at 5% profit when compared to selling the same article at 5% loss, what was the cost price of the article?

Answer: Rs.800

Solution: Shortcut to find C.P = 100*Diff/(profit - Loss) = 100 * 80/(5 - (-5)

= 100 * 80/(10)  = 800

7. In a showroom, a TV priced at Rs.16000 had a, “15% off” tag on it. What was the selling price of the TV?

Answer: Rs.13600

Solution: Tagged price = Rs .16000

Discount = 15%

Selling price = 16000 * [(100-15)/100]

= 16000 * 85/100 = Rs.13600

8. If a pen is being sold at 4% profit instead of 4% loss, the net difference in profit is Rs 16. What is the actual cost price of the pen? 

Answer: Rs.200

Solution: Let x be the CP. (104/100)x - (96/100)x = 16

Solving we get x = 16*100/8 = Rs.200.

9. The cost price of a cow and a horse is 3 lakhs. The cow is sold at 20% profit and horse at 10% loss. Overall gain is Rs.4200. What is the cost price of the cow?

Answer: Rs. 114000

Solution: C.P of cow = c and horse =h.

c+h=300000 - Eq1

1.2c + 0.9h = 300000+4200,

Using Eq1, 1.2c + 0.9(300000-c) = 304200,

0.3c = 304200 - 270000,

c=34200/0.3 = 342000/3 = Rs. 114000.

10. A man says he sells corn at a profit of 20% and uses weights that are 30% less than actuals. The net gain earned by him is

Answer: 71.42%

Solution: Assume the cost price of 100 grams is Rs.x

Selling price is 1.2x

But actual cost price for 70 grams = 0.7x

Profit = 1.2x - 0.7x = 0.5x

Gain % =  100 * 0.5x/0.7x = 500/7 = 71.42%

11. If a seller got Rs.756 more by selling an article at 7% profit when compared to selling the same article at 7% loss, what was the cost price of the article?

Answer: Rs.5400

Solution: Shortcut to find C.P = 100*Diff/(profit - Loss) = 100 * 756/(7 - (-7)

= 100 * 756/(14)  = 5400

12. Two laptops(different models) are sold at same selling price. While the first one is sold at 10% profit, the second laptop is sold at 5% loss. What is the ratio of the cost price of first laptop to the cost price of second laptop?

Answer: 19/22

Solution: Shortcut formula:

Ratio = (100-5)/(100+10) = 95/110 = 19/22

13. On selling 16 balls at Rs.880, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:

Answer: 80

Solution: (C.P. of 16 balls) - (S.P. of 16 balls) = (C.P. of 5 balls)

C.P. of 11 balls = S.P. of 16 balls = Rs.880. C.P of 1 ball = 880/11 = Rs.80

14. A photographer offered to supply 12 copies and 20 copies for Rs.60 and Rs.80 respectively, and then his profits will be Rs.5 and Rs.7 respectively. What amount will he get to supply 30 copies in order to make a profit of Rs.10?

Answer: Rs.105.50

Solution: Let f be fixed cost and v be variable cost

f + 12v = 60 - 5 = 55

f + 20v = 80 - 7 = 73

Solving the above equation we get v= 9/4

Substituting v in any of the equations we get f = 28

Cost Price for 30 copies = f + 30v = 28 + 30*9/4 =  95.50 Rs.

Selling price with Rs.10 as profit =  95.50 + 10 = Rs.105.50

15. A man says he sells sugar at a profit of 10% and uses weights that are 20% less than actuals. The net gain earned by him is

Answer: 37.5%

Solution: Assume the cost price of 100 grams is Rs.x

Selling price is 1.1x

But actual cost price for 80 grams = 0.8x

Profit = 1.1x - 0.8x = 0.3x

Gain % =  100 * 0.3x/0.8x = 75/2 = 37.5%

16. A grocery shop owner proposes to sell at cost price but still manages to get 25% profit as he has manipulated the measuring balance. How many grams is he selling actually instead of 1 kg?

Answer: 800 grams

Solution: Let the grams sold instead of 1kg (1000 grams) be x.

100 * (1000-x)/x = 25.

Solving x= 800 grams

17. A person sells an item at 12.5% loss. If he sells for Rs. 112 more, he will have a profit of 5%. What is the cost price?

Answer: Rs.640

Solution: Proposed S.P = 1.05*CP

Difference = CP (1.05-0.875) = 112

Hence cost price = Rs.640

18. A Samsung duo and a Galaxy are bought for Rs.40000. The Duo is sold at a profit of 33.33% and the Galaxy is sold at a loss of 20%. There was no loss or gain. Find the cost price of the Samsung duo ?

Answer: Rs.15000

Solution: Let the cost price (buying price) of Duo and Galaxy be d and g.

d+g=40000, g=40000-d

d*4/3 + g*4/5 = 40000 (As no loss or gain)

d*4/3 + (40000-d)*4/5 = 40000

4d/3 - 4d/5 = 40000*1/5

8d/15 = 8000,

d=15000

19. A person sells 36 peanuts per rupee and suffers a loss of 4%. How many peanuts should he sell per rupee to obtain a gain of 8%?

Answer: 32

Solution: 36 peanuts sold for Rs.1. Selling price of 1 peanut = 1/36 rs.

As 4% loss is incurred, cost price of 1 peanut = 1/36 * 1/0.96

To obtain a profit of 8%, selling price of 1 peanut = Rs. 1.08 * 1/36 * 1/0.96 = 0.03 * 1/0.96 = Rs. 1/32.

Hence 32 peanuts must be sold per rupee to obtain a gain of 8%.

20. A shirt was sold at a 50% discount but the seller made a profit of 20%. What percent of cost price was the marked price?

Answer: 240%

Solution: Let C.P be x.

Selling price = 1.2x = M.P * 50/100

Hence M.P = 2.4x

Hence required % = (2.4x/x) * 100 = 240%.

21. When a chair is sold at Rs. 450, the owner loses 10%. At what price must that chair is be sold in order to gain 20%?

Answer: 600 Rs

Solution: Let the C.P be x.

0.9x=450, Hence x=500.

To obtain 20% profit, the amount = 500 * 1.2 = 600

22. A LCD television was sold at a 34% discount but the seller made a profit of 10%. What percentage is the markup over cost price?

Answer: 66.66%

Solution: Let C.P be x.

Selling price = 1.1x = M.P * 66/100

M.P = 5x/3

Markup over cost price = 5x/3 - x = 2x/3

Required % = 100 * (2x/3)/x = 66.66%

23. A person sells 24 candies per rupee and suffers a loss of 5%. How many candies should he sell per rupee to obtain a gain of 20%?

Answer: 19

Solution: 24 candies sold for Rs.1. Selling price of 1 candy = 1/24 rs.

As 5% loss is incurred, cost price of 1 candy = 1/24 * 1/0.95

To obtain a profit of 20%, selling price of 1 candy = Rs. 1.2 * 1/24 * 1/0.95 = 0.05 * 1/0.95 = Rs. 1/19.

Hence 19 candies must be sold per rupee to obtain a gain of 20%.

24. If 5% more is gained by selling an article for Rs.350 than by selling it for Rs. 340, the cost of the article is:

Answer: Rs. 200

Solution: Let x be the C.P

(350-340)/x = 5/100

x = 200

25. A man sold 12 candies at Rs.10 had loss of a%. When he again sold 12 candies at Rs.12 he had a profit of a%. Find the value of a.

Answer: 9.09%