BANK & INSURANCE (PROFIT LOSS AND DISCOUNT) PART 3

Total Questions: 70

1. A cruise operates between Mumbai and Dubai. Each ticket of the cruise costs Rs. 2,500. The cruise is operated by a private company that has to pay a fixed cost per journey and a variable cost that depends on the number of passengers on board, to the government. If 100 passengers aboard the cruise, then the company suffers a loss of Rs. 1,000 per ticket. However, when 400 passengers aboard the cruise, then the company earns Rs. 500 per ticket. Find the profit earned by the company, when 600 passengers aboard the cruise.

Correct Answer: (c) Rs. 4,00,000
Solution:

Let the fixed cost and variable cost paid by the company be Rs. ‘F’ and be Rs. ‘V’, respectively.
ATQ:
F + 100V = 2500 × 100 + 1000 × 100
Or, F + 100V = 250000 + 100000
Or, F + 100V = 350000 …… (I)

Also,
F + 400V = 2500 × 400 - 500 × 400
Or, F + 400V = 1000000 - 200000
Or, F + 400V = 8,00,000 …… (II)

On subtracting equation (I) from equation (II), we have;
300V = 4,50,000
Or, V = 1500

On, putting V = 1500 in equation (I), we have;
F + 100 × 1500 = 350000
Or, F = 2,00,000

So, profit earned when 600 passengers aboard the cruise = 2500 × 600 - (200000 + 600 × 1500)
= 1500000 - 1100000 = Rs. 4,00,000

2. A shopkeeper marked an article 80% above the cost price and sold it after two successive discount of Rs. 600 and 16%, respectively. Had he bought the article for Rs. 500 less and sold it for Rs. ___ more, then he would have a profit of ___%. If same article is sold for Rs. 1800, then the shopkeeper will end up having a certain profit. The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 180, 80%
II. 136, 90%
III. 57.4, 75%

Correct Answer: (b) Only II
Solution:

Let cost price of the article is Rs. ‘x’
Selling price of the article = Rs. (0.84 × (1.8x - 600))

Since, when article is sold at Rs. 1800, there will be profit.
So, cost price of article must be less than Rs. 1800

For ‘I’:
1.80 × (x - 500) = 0.84(1.8x - 600) + 180
Or, 1.8x - 900 = 1.512x - 504 + 180
Or, 0.288x = 576
Or, x = 2000

So, cost price of the article = Rs. 2000
Since, selling price of the article = Rs. 1800 < 2000
So, ‘I’ is not true.

For ‘II’:
1.90 × (x - 500) = 0.84(1.8x - 600) + 136
Or, 1.9x - 950 = 1.512x - 504 + 136
Or, 0.388x = 582
Or, x = 1500

So, cost price of the article = Rs. 1500
Since, selling price of the article = Rs. 1800 > 1500
So, ‘II’ is true.

For ‘III’:
1.75 × (x - 500) = 0.84(1.8x - 600) + 57.4
Or, 1.75x - 875 = 1.512x - 504 + 57.4
Or, 0.238x = 428.4
Or, x = 1800

So, cost price of the article = Rs. 1800
Since, selling price of the article = Rs. 1800
So, ‘III’ is not true.

3. A shopkeeper bought an article for Rs. 2000 and marked it 60% above its cost price and sold it after giving two successive discounts of Rs. ‘12a’ and (a − 20)%, respectively and earned an overall profit of (11a/50)%. If cost price and selling price of article ‘B’ is Rs. (12a + 80) and Rs. 992, respectively, then find the profit/loss earned/incurred on selling article ‘B’.

Correct Answer: (b) 77(1/7)%
Solution:

Marked price of the article = 1.60 × 2000 = Rs. 3200
ATQ:
{3200 - 12a} × (1 - 2a/100) = {1 + 0.22a/100} × 2000

Or, (3200 - 12a)(120 - a) = (100 + 0.22a) × 2000
Or, 384000 - 1440a - 3200a + 12a² = 200000 + 440a
Or, 12a² - 5080a + 184000 = 0
Or, 3a² - 1270a + 46000 = 0
Or, 3a² - 120a - 1150a + 46000 = 0
Or, 3a(a - 40) - 1150(a - 40) = 0
Or, (3a - 1150)(a - 40) = 0

Or, a = 40 or a = 1150/3 (not possible)
So, cost price of article ‘B’ = 12 × 40 + 80 = Rs. 560

Desired profit = [(992 - 560)/560] × 100
= 77(1/7)%

4. A shopkeeper marked an article 75% above the cost price and sold it after two successive discounts of __% and 20%. In this transaction, the shopkeeper had a profit of __%. The values given in which of the following options will fill the blanks in the same order in which is it given to make the above statement true:

A. 15, 19
B. 20, 12
C. 25, 

Correct Answer: (d) All A, B and C
Solution:

Let the cost price of the article = Rs. 100
So the marked price of the article = 1.75 × 100 = Rs. 175

For option A:
175 × 0.80 × 0.85 = 100 × 1.19
119 = 119
So option A can be the answer

For option B:
175 × 0.80 × 0.80 = 100 × 1.12
112 = 112
So option B can be the answer

For option C:
175 × 0.80 × 0.75 = 100 × 1.05
105 = 105
So option C can be the answer

5. Which of the following options can be used to fill the blank in order to make the given statement true?

A shopkeeper sold some candies such that cost price of a candy is Rs. (x + 30) and it is sold at 20% profit. Discount of 25% was given when the marked price was set as Rs. 528. If the shopkeeper wants to earn ___ profit after giving a discount of Rs. 81, then the marked price of the candies will be ___.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:
I. 30%, Rs. (x + 210)
II. 25%, Rs. (x + 190)
III. 40%, Rs. (x + 243)
IV. 10%, Rs. (x + 144)

Correct Answer: (d) Only I, III and IV
Solution:

Cost price of the candy = Rs. (x + 30)
Selling price of the candy = (x + 30) × 120%

Marked price of the candy = [(x + 30) × 120%]/75%

528 = [(x + 30) × 120%]/75%
396 = (x + 30) × 120%
330 = x + 30
x = 300

For I:
30%, Rs. (x + 210)
Selling price of the candy = 330 × 130% = Rs. 429
Marked price of the candy = 429 + 81 = Rs. 510
(x + 210) = (300 + 210) = 510
This is satisfying the condition.

For II:
25%, Rs. (x + 190)
Selling price of the candy = 330 × 125% = Rs. 412.5
Marked price of the candy = 412.5 + 81 = Rs. 493.5
(x + 190) = (300 + 190) = 490
This is not satisfying the condition.

For III:
40%, Rs. (x + 243)
Selling price of the candy = 330 × 140% = Rs. 462
Marked price of the candy = 462 + 81 = Rs. 543
(x + 243) = (300 + 243) = 543
This is satisfying the condition.

For IV:
10%, Rs. (x + 144)
Selling price of the candy = 330 × 110% = Rs. 363
Marked price of the candy = 363 + 81 = Rs. 444
(x + 144) = (300 + 144) = 444
This is satisfying the condition.

6. Article ‘A’ is marked Rs. 250 above its cost price and then sold after giving two successive discounts of x% and (x − 5)%, respectively. The discount equivalent to given two successive discounts is 95%. If the article had been sold at x% discount then there would have been a loss of Rs. 950. Find the ratio of cost price and marked price of the article.

Correct Answer: (a) 5:6
Solution:

Let the cost price of the article be Rs. ‘p’
Therefore, marked price of the article = Rs. (p + 250)

Also, x + (x - 5) - {x(x - 5)/100} = 95
Or, 200x - 500 - x² + 5x = 9500
Or, x² - 205x + 10000 = 0
Or, x² - 80x - 125x + 10000 = 0
Or, x(x - 80) - 125(x - 80) = 0
Or, (x - 125)(x - 80) = 0
Or, x = 80 (Since discount cannot be more than 100%)

Therefore, p - 950 = 0.2 × (p + 250)
Or, p - 0.2p = 1000
Or, 0.8p = 1000
Or, p = 1250

Therefore, cost price of the article = Rs. 1250
Marked price of the article = 1250 + 250
= Rs. 1500

Required ratio = 1250 : 1500 = 5 : 6

7. There are two articles A and B and the sum of the cost prices of the articles A and B is Rs. 3136. Article A is sold at 20% profit and article B is sold at 25% profit and the ratio of the marked price of article A to article B is 4:5. The discount given on article A and article B is b% and (d + 16)% respectively and the selling prices of both the articles A and B are same. Which of the following can be determined by using the above given data?

(i) Discount percentage given on article B.
(ii) Total profit earned on article A and article B together.
(iii) Marked price of article A is ___% more than the cost price of article A.
(iv) Difference between the cost prices of articles A and B.

Correct Answer: (e) All (i), (ii), (iii) and (iv)
Solution:

Let the marked price of article A = Rs. 4x
Marked price of article B = Rs. 5x

According to the question,
4x (100 - d)% = 5x (100 - d - 16)%

(100 - d)/25 = (84 - d)/20
2000 - 20d = 2100 - 25d
5d = 100
d = 20%

Discount on article A = 20%
Discount on article B = 36%

Let the cost price of article A = Rs. x
Cost price of article B = Rs. (3136 - x)

According to the question,
(x × 120% × 100/80) : [(3136 - x) × 125% × 100/64] = 4 : 5

5 × 3x/2 = 4 × (3136 - x) × 125/64
15x/2 = 125/16 × (3136 - x)
120x = 125(3136 - x)
120x = 392000 - 125x
245x = 392000
x = 1600

Cost price of article A = Rs. 1600
Cost price of article B = Rs. 1536

Marked price of Article A = 1600 × 120% × 100/80 = Rs. 2400
Marked price of article B = 1536 × 125% × 100/64 = Rs. 3000

(i) Discount percentage given on article B.
Required discount percentage = 36%
So it can be answer.

(ii) Total profit earned on article A and article B together.
Required profit = 1600 × 20% + 1536 × 25%
= Rs. 704

So it can be answer.

(iii) Marked price of article A is ____ % more than the cost price of article A.
Marked price of article A = Rs. 2400
Cost price of article A = Rs. 1600
Difference = Rs. 800
Required percentage = 800/1600 × 100 = 50%
So it can be answer.

(iv) Difference between the cost prices of articles A and B.
Required difference = 1600 - 1536 = Rs. 64
So it can be answer.

8. The marked price of the two articles ‘A’ and ‘B’ is Rs. 1500 and Rs. 1800, respectively. After giving discounts of 20% and 25% on articles ‘A’ and ‘B’, respectively, the shopkeeper earns the profit of __ and __ on selling article ‘A’ and ‘B’, respectively. The cost prices of both the articles are same. The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 20%, 35%
II. 10%, 16%
III. 50%, 68.75%
IV. 25%, 40%

Correct Answer: (d) Only I and III
Solution:

Marked price of article ‘A’ = Rs. 1500
Selling price of article ‘A’ = 1500 × 80% = Rs. 1200

Marked price of article ‘B’ = Rs. 1800
Selling price of article ‘B’ = 1800 × 75%
= Rs. 1350

For I:
According to the question,
Cost price of article ‘A’ = (1200/120) × 100
= Rs. 1000

Cost price of article ‘B’ = (1350/135) × 100
= Rs. 1000

This statement satisfies the condition.
So, ‘I’ is true.

For II:
According to the question,
Cost price of article ‘A’ = (1200/110) × 100
= Rs. 12000/11

Cost price of article ‘B’ = (1350/116) × 100
= Rs. 33750/29

This statement does not satisfy the condition.
So, ‘II’ is false.

For III:
According to the question,
Cost price of article ‘A’ = (1200/150) × 100
= Rs. 800

Cost price of article ‘B’ = (1350/168.75) × 100
= Rs. 800

This statement satisfies the condition.
So, ‘III’ is true.

For IV:
According to the question,
Cost price of article ‘A’ = (1200/125) × 100
= Rs. 960

Cost price of article ‘B’ = (1350/140) × 100
= Rs. 6750/7

This statement does not satisfy the condition.
So, ‘IV’ is false.

9. The average cost price of articles ‘B’ and ‘C’ together is 15% more than the average cost price of articles ‘A’, ‘B’ and ‘C’ together where the cost price of article ‘C’ is Rs. 600 more than that of ‘B’. If articles ‘A’, ‘B’ and ‘C’ are sold at profit of 40%, loss of 15% and loss of 30%, respectively, then the net profit on selling articles ‘A’ and ‘B’ together would be Rs. 480 more than that on selling articles ‘A’ and ‘C’ together. Find the cost price of article ‘C’.

Correct Answer: (e) Rs. 2,600
Solution:

Let the sum of cost price of articles ‘A’, ‘B’ and ‘C’ = Rs. ‘60x’

Then, average cost price of articles ‘A’, ‘B’ and ‘C’
= 60x ÷ 3 = Rs. ‘20x’

Average cost price of articles ‘B’ and ‘C’ = 20x × 1.15 = Rs. ‘23x’

And, sum of cost price of articles ‘B’ and ‘C’ = 23x × 2 = Rs. ‘46x’

So, cost price of article ‘A’ = 60x - 46x = Rs. ‘14x’

Let the cost price of article ‘B’ = Rs. ‘y’
Then, cost price of article ‘C’ = Rs. (y + 600)

So, y + y + 600 = 46x
Or, 2y + 600 = 46x
So, y = (46x - 600) ÷ 2 = (23x - 300)

So, cost price of articles ‘B’ and ‘C’ are Rs. (23x - 300) and Rs. (23x + 300), respectively

According to the question,
14x × 1.4 + (23x - 300) × 0.85 - (14x + 23x - 300)
= 14x × 1.4 + (23x + 300) × 0.7 - (14x + 23x + 300) + 480

Or, 19.6x + 19.55x - 255 - 37x + 300 = 19.6x + 16.1x + 210 - 37x - 300 + 480

Or, 2.15x + 45 = 390 - 1.3x
Or, 3.45x = 390 - 45 = 345
So, x = 345 ÷ 3.45 = 100

So, cost price of articles ‘A’, ‘B’ and ‘C’ are Rs. 1,400, Rs. 2,000 and Rs. 2,600, respectively.
So, cost price of article ‘C’ = Rs. 2,600

10. Mrityunjay bought an article for Rs. (x + 1500), and marked it up by 20%. If he sold it at a discount of (x − 35)% for Rs. 1581, then at what price it should be sold to get a profit of 40%? [Note: ‘x’ is a multiple of 10]

Correct Answer: (b) Rs. 2170
Solution:

According to question,
(x + 1500) × 1.2 × (100 - x + 35)% = 1581
(x + 1500)(135 - x) = 131750
135x - x² + 202500 - 1500x = 131750
x² + 1365x - 70750 = 0
x² + 1415x - 50x - 70750 = 0
x(x - 50) + 1415(x - 50) = 0
(x - 50)(x + 1415) = 0
x = 50 or x = -1415

So, cost price of an article = (50 + 1500)
= Rs. 1550

Therefore, required selling price = 1550 × 1.4
= Rs. 2170