Profit, Loss and Discount

 

Profit, Loss and Discount

M.Velrajan

If 4 bananas cost rupees 30 then cost of 6 = (30/4) × 6 = 45.

i.e. if 4 == 30 then 6 == (30/4) × 6

In general, if a == b then c == (b/a) × c = b × c/a = (b × c)/a.


1. Two – third of a consignment was sold at a profit of 5% and the remaining at a

loss of 2%. If the total profit was Rs. 400, then the value of the consignment was    

 (a)Rs. 10,000    (b)Rs. 12,000     (c)Rs. 15,000       (d)Rs.20,000

Since Two – third of a consignment was sold, 

we take the consignment value = 300 (Multiple of 100 and 3)  

Sold for profit = ⅔ × 300 = 200

Sold for loss = 300 - 200 = 100

Profit for 200 = 200 × 5/100 = 10

Loss for 100 = 2 

Total profit = 10 - 2 = 8

For profit 8, consignment = 300  (8 == 300)

For profit 400, consignment =  3008 × 400 = 15000 (400 == ?)

Ans. c.


2.  By selling a car for Rs. 1,40,000 a man suffered a loss of 20%. What was the

cost of  the car?  

(a)Rs. 1,50,000        (b)Rs. 1,25,000         (c)Rs. 2,00,000         (d)Rs. 1,75,000

We assume that the cost price = 100. Then the selling price = = 100 - 20 = 80

For selling price 80 cost = 100  (80 == 100)

For selling price 140000 cost = 10080 × 140000   (14000 == ?) 

                                                  = 100 × 1750 = 175000  


3. Raman buys a washing machine for Rs. 13,500 and sells it at a loss of 12%.

What is the selling price of the washing machine?  

(a)11,880        (b)11,800              (c)13,500        (d)11, 870

Loss = 12100 × 13500 = 1570

Selling price = 13500 - 1570 = 11880

Aliter : If he buys for 100, selling price = 100 - 12 = 88  (88 == 100)

Selling price = 88100 × 13500 (13500 == ?)

                                   = 1080 × 11 

                                   = 11880


4. A table is sold for Rs. 414 at a profit of 15%. How much did it cost? 

(a)Rs.400 (b)Rs.314 (c)Rs.326 (d)Rs. 360

If cost = 100 then selling price = 100 + 15 = 115  (115 == 100)

Cost = 100115 × 414 = 1005 × 18 = 360   (414 == ?) 

 

5. If the cost of 12 Articles is equal to the selling price of 10 Articles, the profit

percentage in the transaction is    

(a)18%              (b)16 23 %                 (c)20%                (d)25%

Take cost of one article = 100

Cost of 12 = 12 × 100 = selling of 10 article

So, selling of one article = 12 × 10010 = 120

profit percentage = 120 - 100 = 20%

(or) Taking Cost of one article = x

Cost of 12 = 12x = selling of 10 article

So, selling of one article = 12x10 = 6x5

profit = 6x5 - x = x5

profit percentage = x5x × 100 = ⅕ × 100 = 20%


6. The trader marks his goods at 20% above cost price and allows 10% discount.

Then the gain per cent is     (a)6%      (b)8%        (c)10%      (d)12%

Take cost price = 100

marked price = 100 + 20 = 120

discount = 120 × 10100 = 12

Selling = 120 - 12 = 108

Gain = 108 - 100 = 8      Ans. 8%


7. A shopkeeper marked up a shirt 50% above the cost price and allowed

successive discounts of 11 19 % and 10% on it. If the difference between profit

earned and discount given is Rs. 200 then find the marked price of the shirt?  

(a) Rs. 2100   (b) Rs. 3000   (c) Rs. 2400   (d) Rs. 3600  (e) Rs. 3300

If Cost = 100 then marked = 100 + 50 = 150

First discount for 100 = 11 1/9 = 100/9

First discount for 150 = (100/9) × (1/100) × 150 = 1/9 × 150 = 50/3

After I discount = 150 - 50/3 = (450 - 50) / 3 = 400/3

II discount for 400/3 = (400/3) × (10/100) = 40/3

After II discount = 400/3 - 40/3 = 360/3 = 120

Total discount = 150 - 120 = 30

profit = 120 - 100 = 20

Difference between profit and total discount = 30 - 20 = 10

If 10 is the difference then marked price = 150  (10 == 150)

If 200 is the difference then marked price = (150/10) × 200 = 3000  (200 == ?)

Ans. b.


8. The population of a village decreased by 10% in the first year and then increased

by 20% in the second year. Find the population of the village at the end of the

second year if two years ago it was 15,000?   

(a) 16180   (b) 16200   (c) 16320   (d) 16360   (e) 16480

Taking population two years ago = 100, 

after I year  = 100 - 10 = 90 and 

after II yr = 90 + (20/100) × 90 = 90 + 18 = 108

If 100 is the population two years ago then population at present(at the end of

two years) = 108 (100 == 108)

If 15000 is the population two years ago then population at present(at the end of

two years) =  (108/100) × 15000 = 16200  (15000 == ?)


9. Tax on a commodity is increased by 20% and its consumption is decreased by

15%. Find the effect on revenue.    (1) +5%       (2) - 5%   (3) +2%      (4) - 2% 

Take the number of commodities = 100 and original tax = 100.

Since consumption is decreased by 15%,

number of commodity on tax revenue = 100 - 15 = 85

Tax after increase = 100 + 20 = 120

Original tax revenue = 100 × 100

Tax revenue after consumption decrease =  85 × 120

effect on revenue = 85 × 120 - 100 × 100 = 10200 - 10000 = 200 = + 200

For 100 × 100 original tax revenue the effect on revenue = 200

Percentage of effect on revenue = 200100 × 100 × 100 = 2 = +2%


10. The salary of an employee is first increased by 10% and then decreased by 10%.

What is the change in his salary? 

(1) 0%   (2) +1%   (3) -1%      (4) +5%

Taking the salary = 100

Salary after first increase = 100 + 10 = 110

Decrease in salary = (10/100) × 110 = 11

Salary after decrease = 110 - 11 = 99

Change in salary = 99 - 100 = -1  Ans. (3)


11. If A’s height is 25% less than that of B, then how much percent is B’ s height more

than that of A?        

(a)50%             (b)45%               (c) 2213%                  (d) 3313%

Taking height of B = 100, height of  A = 100 - 25 = 75

B’s height more than A = 100 - 75 = 25

If height of A is 75 then B is more by 25 

Percentage of B more than that of A = (25/75) × 100

                                                               = ⅓ × 100 = 3313%


12. A man purchased an article at 75 % of the listed price and sold at half more

than the listed price. What was his gain percentage?   

(1) 25%  (2) 50% (3) 75%      (4) 100%

Taking listed price = 100

purchased price = 75

sold price = 100 + 50 = 150

Gain = 150 - 75 = 75

For purchased price 75 gain = 75

Gain percentage = (75/75) × 100 = 100%


13. Two tables were bought at Rs.27,000. One of them was sold at a loss of 6% and the

other at a gain of 7.5%. On the whole neither loss nor gain was the result of the

transaction. What did each table cost?  

(1) 13500, 13500     (2) 14000, 13000   (3) 15000, 12000      (4) 16000, 11000

Since there is no loss or gain, 

Cost of First × 6/100 = Cost of second × 7.5/100

i.e. Cost of First × 6 = Cost of second × 7.5 = Cost of second × 15/2

Clearly from the answer choice only 15000, 12000 satisfies this condition

(since 12000 × 15/2 = 6000 × 15 = 15000 × 6)

Aliter : Let x be the cost of the table sold at loss.

Then cost of the other table = 27000 - x

Since there is no loss or gain, x × 6/100 = (27000 - x) × 7.5/100

Multiplying by 200, 12 x = 27000 × 15 - 15x

27x = 27000 × 15

x = 1000 × 15 = 15000 

Hence the cost of the tables are 15000, 27000 - 15000 = 12000  Ans. 3. 

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