BANK & INSURANCE (PROFIT LOSS AND DISCOUNT) PART 3

Total Questions: 70

11. A shopkeeper is selling chairs and tables. He sells a chair at a profit of 40% and a table at the profit of 25%. If the cost price of a chair and a table are in the ratio 3:5, respectively, then find his approximate percentage profit earned on selling both chair and table.

Correct Answer: (b) 30%
Solution:

Let the cost price of a chair and a table be Rs. 3x and Rs. 5x, respectively.
Total cost price of a chair and a table = 3x + 5x
= Rs. 8x

Total selling price of a chair and a table = 3x × 1.4 + 5x × 1.25
= 4.2x + 6.25x = Rs. 10.45x

Therefore, profit % = [(10.45x - 8x)/8x] × 100
= 30%

12. The cost price of article ‘A’ is 12.5% less than that of article ‘B’. Article ‘A’ is when marked ‘p%’ above its cost price and sold after two successive discounts of 20% and Rs. 76, respectively, then it is sold for a profit of Rs. 50. Article ‘B’ when marked ‘p%’ above its cost price and sold after two successive discounts of 12.5% and Rs. 70, respectively, then it is sold for a profit of Rs. 200. Find the difference between the cost price of articles ‘A’ and ‘B’.

Correct Answer: (c) Rs. 150
Solution:

Let the cost price of article ‘B’ = Rs. ‘200x’
Then, cost price of article ‘A’ = 200x × 0.875 = Rs. ‘175x’

Marked price of article ‘A’ = 175x × ((100 + p)/100)
= Rs. (175x + 1.75xp)

Final selling price of article ‘A’ = Rs. {(175x + 1.75xp) × 0.8 - 76}

So, (140x + 1.4xp - 76) = 175x + 50
Or, 35x + 126 = 1.4xp …… [equation I]

Marked price of article ‘B’ = 200x × ((100 + p)/100)
= Rs. (200x + 2xp)

Final selling price of article ‘B’ = Rs. {(200x + 2xp) × 0.875 - 70}

So, (175x + 1.75xp - 70) = (200x + 200)
Or, 25x + 270 = 1.75xp …… [equation II]

Multiplying [equation II] by 0.8, we get
1.4xp = 20x + 216 = 35x + 126

Or, 15x = 90
So, x = (90/15) = 6

So, difference between cost price of the articles ‘A’ and ‘B’ = 200x - 175x = 25x = Rs. 150

13. The average cost price of articles ‘A’ and ‘B’ together is Rs. 100 more than the average cost price of articles ‘A’, ‘B’ and ‘C’ together. If article ‘A’ was marked 25% above its cost price and sold after a discount of Rs. 50 while article ‘C’ was marked 20% above its cost price and sold after a discount of Rs. 360, then the ratio of their selling prices will be 11:12, respectively. Find the selling price of article ‘B’ if it is sold at a profit of 15%, given that cost price of article ‘B’ is Rs. 1,600 more than that of ‘A’.

Correct Answer: (e) Rs. 3,910
Solution:

Let the average cost price of articles ‘A’, ‘B’ and ‘C’ together = Rs. ‘100x’

Then, sum of cost price of all 3 articles = 100x × 3
= Rs. ‘300x’

Average cost price of articles ‘A’ and ‘B’ = Rs. (100x + 100)

Sum of cost price of articles ‘A’ and ‘B’ = (100x + 100) × 2 = Rs. (200x + 200)

So, cost price of article ‘C’ = 300x - 200x - 200
= Rs. (100x - 200)

Let the cost price of article ‘A’ = Rs. ‘Y’
Then, cost price of article ‘B’ = Rs. (Y + 1600)

We have, Y + Y + 1600 = 200x + 200
Or, 2Y + 1600 = 200x + 200
Or, Y = (200x - 1400) ÷ 2 = Rs. (100x - 700)

So, cost price of articles ‘A’ and ‘B’ are Rs. (100x - 700) and Rs. (100x + 900), respectively

Selling price of article ‘A’ = (100x - 700) × 1.25 - 50
= 125x - 875 - 50 = Rs. (125x - 925)

Selling price of article ‘C’ = (100x - 200) × 1.2 - 360
= 120x - 240 - 360 = Rs. (120x - 600)

According to the question,
(125x - 925) : (120x - 600) = 11 : 12

Or, 1500x - 11100 = 1320x - 6600
Or, 180x = 4500
So, x = 25

And, cost price of article ‘B’ = 100x + 900
= Rs. 3,400

So, required selling price of article ‘B’ = 3400 × 1.15
= Rs. 3,910

14. The cost price of a book is Rs. 720 and it is sold at the profit of P%. If the cost price and the selling price are interchanged, the loss incurred is L%. L is 20% less than that by P.

I: The selling price of the book if the shopkeeper wants to earn the profit of (L + P)%, is Rs. 1044.

II: If the marked price of the book is 2P% more than that of cost price and L% of discount is given on its marked price, then the selling price of the book will be Rs. 864.

III: If the ratio of the cost price to selling price of the book is 10:7, then the loss on the book will be (P + 10)%.

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

Cost price of the book = Rs. 720

Selling price of the book = Rs. 720 × (100 + P)%
= Rs. (720 + 7.2P)

Profit on the book = 720 + 7.2P - 720 = Rs. 7.2P

Profit percentage (P%) = (7.2P/720) × 100

After interchanging the cost price and selling price,
Cost price of the book = Rs. (720 + 7.2P)
Selling price of the book = Rs. 720

Loss on the book = Rs. (720 + 7.2P) - 720
= Rs. 7.2P

Loss percentage (L%) = [7.2P/(720 + 7.2P)] × 100

Ratio of L to P = 80 : 100 = 4 : 5

{[(7.2P/(720 + 7.2P)) × 100] : [(7.2P/720) × 100]} = 4 : 5

720 × 5 = 4 × (720 + 7.2P)
3600 = 2880 + 28.8P
720 = 28.8P
P = 25

∴ L = [7.2 × 25/(720 + 7.2 × 25)] × 100
= (180/900) × 100 = 20

For I:
The selling price of the book if the shopkeeper wants to earn the profit of (L + P)%, is Rs. 1044

(L + P)% = (20 + 25)% = 45%
Selling price of the book = Rs. 720 × 145%
= Rs. 1044
Therefore, this statement is true.

For II:
If the marked price of the book is 2P% more than that of cost price and L% of discount is given, the selling price of the book will be Rs. 864.
Marked price of the book = 720 × (100 + 50)%
= Rs. 1080
Selling price of the book = 1080 × 80% = Rs. 864.
Therefore, this statement is true.

For III:
If the ratio of the cost price to selling price of the book is 10:7, the loss on the book will be (P + 10)%.
Cost price of the book = Rs. 720
Selling price of the book = (720/10) × 7 = Rs. 504
Loss on the book = 720 - 504 = Rs. 216
Loss percentage = (216/720) × 100 = 30%
So, (P + 10)% = 25 + 10 = 35%
Therefore, this statement is not true.

15. Directions (15-16): Answer the questions based on the information given below.

Four milk sellers namely ‘A’, ‘B’, ‘C’ and ‘D’ purchased milk from the same supplier at the same rate while ‘A’ and ‘C’ sold milk at the price they bought it from the supplier. But it is seen that ‘A’ used a container of 725 ml instead of 1000 ml while selling his milk and ‘C’ uses a containers of volumes 15% less and 20% more while selling and purchasing milk. ‘B’ sold milk at a profit of 12.5% and gave the customer only 800 ml of milk instead of 1 litre. ‘D’ sold milk at a profit of 10% and used 900 ml container while selling and 1250 ml container while purchasing milk.

Ques. If ‘A’ uses a container of 1200 ml in place of 1000 ml while purchasing milk and makes a profit of Rs. 950 while ‘C’ makes a profit of Rs. 350 on selling the same quantity of milk as by ‘A’, then find the difference between selling price paid by ‘A’ and ‘C’ while buying desired quantity of milk.

Correct Answer: (a) Rs. 1200
Solution:

Let ‘A’ purchased 1000 ml of milk for Rs. 1000
According to question;
‘A’ purchased 1200 ml of milk for Rs. 1000
And, sold 725 ml of milk for Rs. 1000

‘A’ will purchase 34800 ml or (1200 × 29) ml of milk for Rs. 29000
And, sell 34800 ml or (725 × 48) ml of milk for Rs. 48000

So, ratio of selling price to cost price of the milk = 48000 : 29000 = 48 : 29

Selling price of milk purchased by ‘A’ = 48 × (950/(48 - 29)) = Rs. 2400

Let ‘C’ also purchased 1000 ml of milk for Rs. 1000.
According to question;
‘C’ purchased 1200 ml of milk for Rs. 1000
And, ‘C’ sold 850 ml of milk for Rs. 1000

So, ‘C’ sell purchase 20400 (850 × 24) ml of milk for Rs. 24000
And, ‘C’ will purchase 20400 (1200 × 17) ml of milk for Rs. 17000

So, ratio of selling price to cost price of the milk for ‘C’ = 24000 : 17000 = 24 : 17

Selling price of milk purchased by ‘C’ = {24/(24 - 17)} × 350 = Rs. 1200

Desired difference = 2400 - 1200 = Rs. 1200

16. Find the difference between percentage profit earned by ‘B’ and ‘D’ if they sold same quantity of milk.

Correct Answer: (b) 12.15%
Solution:

Profit earned by ‘B’ = [(1125 - 800)/800] × 100
= 40.625%

Let ‘D’ bought 1250 ml milk for Rs. 1000
And, ‘D’ sold 900 ml of milk for Rs. 1.10 × 1000 = Rs. 1100

So, ‘D’ bought 22500 (1250 × 18) ml of milk for Rs. 18000
And, ‘D’ sold 22500 (25 × 900) ml of milk for Rs. 27500

So, profit earned by ‘D’ = [(27500 - 18000)/18000] × 100 = 52.77%

Desired difference = (52.77 - 40.625)% = 12.15%

17. Directions (17-18): Answer the questions based on the information given below.

A shopkeeper is selling three different articles: A, B and C. He marked each article somewhat above the cost price and sold it after certain discount. Cost prices of articles A, B and C are in the ratio 9:7:6, respectively. The shopkeeper marked articles A, B and C, 60%, 50% and 75%, respectively above their respective cost prices. The shopkeeper sold articles A, B and C after offering a discount of 25%, 20% and 40%, respectively.

Ques. What is the ratio of the selling price of article B to the selling price of article C?

Correct Answer: (b) 4:3
Solution:

Let the cost prices of articles A, B and C be Rs. 9x, Rs. 7x and Rs. 6x, respectively.
Marked price of article A = 1.60 × 9x = Rs. 14.4x
Selling price of article A = 0.75 × 14.4x = Rs. 10.8x

Marked price of article B = 1.50 × 7x = Rs. 10.5x
Selling price of article B = 0.80 × 10.5x = 8.4x

Marked price of article C = 1.75 × 6x = Rs. 10.5x
Selling price of article C = 0.60 × 10.5x = 6.3x

Desired ratio = 8.4x : 6.3x = 4 : 3

18. Find the sum of the cost price of articles A, B and C, if in the whole transaction the shopkeeper had a profit of Rs. 175.

Correct Answer: (c) Rs. 1,100
Solution:

Let the cost prices of articles A, B and C be Rs. 9x, Rs. 7x and Rs. 6x, respectively.

Marked price of article A = 1.60 × 9x = Rs. 14.4x
Selling price of article A = 0.75 × 14.4x = Rs. 10.8x

Marked price of article B = 1.50 × 7x = Rs. 10.5x
Selling price of article B = 0.80 × 10.5x = 8.4x

Marked price of article C = 1.75 × 6x = Rs. 10.5x
Selling price of article C = 0.60 × 10.5x = 6.3x

According to question: 10.8x + 8.4x + 6.3x - 9x - 7x - 6x = 175
3.5x = 175
x = 50

So, the sum of the cost prices of articles A, B and C
= 50 × (9 + 7 + 6) = Rs. 1,100

19. After receiving 40% discount on a product, Karan needs to pay 15% GST on the discounted price. If Karan would have got only 30% discount and paying the same GST on discounted price, he will need to pay Rs. 276 extra. Find the selling price of the product to earn a profit of 25%, if the marked price is equal to the cost price of the product.

Correct Answer: (d) Rs. 3000
Solution:

Let, the marked price of the product be Rs. P.
According to question,
P × (7/10) × (100 + 15)% - P × (6/10) × (100 + 15)% = 276

P × 1.15 (0.7 - 0.6) = 276
P × 0.115 = 276
P = 276/0.115
P = Rs. 2400

Therefore, required selling price = 2400 × 1.25
= Rs. 3000

20. Production cost of a shirt manufacturer on Diwali depends on the number of shirts manufactured. And total production cost of all the shirts = (200 × number of shirts manufactured + 25000).

If the manufacturer can sell the shirts within the Diwali season, he can sell each of them on their marked price of Rs. 300 but if he fails to do so, he has to sell the remaining at a discount of 30%. If he manufactured a total of 1600 shirts, find the minimum number of shirts he needs to sell during Diwali to breakeven (i.e. there is no profit no loss).
Note: Assume, the manufacturer was able to sell all the shirts manufactured by him

Correct Answer: (c) 100
Solution:

Total production cost = 200 × 1600 + 25000
= Rs. 345000

Let the number of shirts sold by him during Diwali season = x

Number of shirts sold by him after Diwali season = (1600 - x)

Selling price of each shirt after Diwali season = 300 × 0.7 = Rs. 210

According to the question,
300x + 210 × (1600 - x) = 345000

300x + 336000 - 210x = 345000
90x = 9000
x = 100

Minimum number of shirts to be sold during Diwali season = 100.