Get profit & loss concept right

1. A person sold 3/4th of his articles at a profit of 25% and the rest of his articles at a profit of 17 %.

The overall percentage of his profit is: A. 24% B. 23% C. 22% D. 21%

Ans: B

Explanation:

Let the price of each article be 100 units and number of articles 4.
Total CP = 4 × 100 = 400 units
CP of 3/4th articles = 400 × ¾ = 300 units
Profit1 = CP × (Profit %)/100
⇒ 300 × 25/100 = 75 units

CP of 1/4th articles = 400 × ¼ = 100 units

Profit2 = CP × (Profit %)/100

⇒ 100 × 17/100 = 17 units
Total Profit = 75 17 = 92 units
Profit = Total CP × (Total Profit %)/100
⇒ 92 = 400 × (Total Profit %)/100

⇒ Total Profit % = 92/4 = 23%
The overall percentage of profit is 23%.

Alternative method:

Compare profit on individual article with overall profit of 4 articles.

3 × 25% = 75%

1 × 17% = 17%
4 × P% = 92%

P% = 23%
The overall percentage of profit is 23%

2. The profit earned by selling an article for Rs 1,000 is double the loss incurred when the same article is sold for Rs 850. At what price should the article be sold to make 30% profit?
A. 1100 B. 1150 C. 1170 D. 1270
Ans: C
Explanation:
Let ‘x’ be the CP of the article.

i.e. Rs 1000-x = 2(x-850)

1000-x = 2x-1700

1000 1700 = 3x, therefore, x = 2700/3 = Rs 900

SP = 900 30% of 900 = 900 270 = 1170

3. By selling two articles each at Rs 480, a merchant gets 20% profit on one and loses 20% on the other. In the total transaction the merchant gets:

A. 4% loss B. no loss no gain
C. 5% loss D. 5% gain
Ans:A
Explanation:

Whenever two selling prices are equal, percentage of profit equal to percentage of loss we always get loss only.
% Loss = (x/100)^2= 400/100 = 4% loss
4. The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill is Rs 22. Then the amount of the bill (in rupees) is
A. 1,100 B. 2,000 C. 2,200 D. 2,640
Ans: C
Explanation:
Let the amount of the bill be Rs x, then

(65% of x) – (80% of 80% of x) = 22

⇒ (65/100×x) – (80/100×80/100×x) = 22

⇒ (65/100)x – (64/100)x = 22

X/100 = 22, x = 2200.

5. A sells a house to B at a profit of 12%. B sells it to C at a loss of 10% and C sells it to D for Rs 21,44,520 making a profit of 15%. The cost of the house for A (in rupees) is

A. 20,00,000 B. 18,50,000 C. 25,00,000 D. 22,50,000

Ans: B

Explanation:

Let x be the cost price of house for A.
Then, The cost of house for B = x 12% of x

= x 0.12x = 1.12 x

The cost of house for C = 1.12x-10% of 1.12x

= 1.12x – 0.112x = 1.008x
The cost of house for D = 1.008x 15% of 1.008x

1.008x 0.1512x = 1.1592x
Since the cost of house for D = Rs 21,44,520

Therefore,

1.1592x = 21,44,520

=>; x = 21,44,520/1.1592 = 1850000