BANK & INSURANCE (PROFIT LOSS AND DISCOUNT) PART 2

Total Questions: 70

1. An article is sold at 9.09% profit after giving two successive discounts of 14.28% and 12.5%. Find how much the above article price was marked up on cost price?

Correct Answer: (b) 45.45%
Solution:

Given: Profit = 9.09%
Successive discounts are 14.28% and 12.5%

Concept:
Fractional value of 9.09% = 1/11
Fractional value of 14.28% = 1/7
Fractional value of 12.5% = 1/8

Formula used:
Cost price × (100 + profit) = Marked price × (100 – Discount)

Calculation:
Let the cost price be 100x and marked price be 100y
SP = CP + Profit
⇒ SP = 100x + (1/11) × 100x = 1200x/11

SP = MP – discount
⇒ SP after allowing first discount = 100y – (1/7) × 100y
⇒ 100y = 600y/7

⇒ SP after allowing second discount = 600y/7 – (1/8)(600y/7) = 75y

Now,
⇒ 1200x/11 = 75y
⇒ x/y = 825/1200 = 11/16

∴ Mark up percentage = 5 × 100/11 = 500/11 = 45.45%

2. A shopkeeper sets the marked price of an article at 25% above the cost price of the article. He gives 5% discount on the marked price and sells the article at Rs. 3990. Find the profit percentage he has in this transaction.

Correct Answer: (e) 18.75%
Solution:

The selling price of the article = 3990
Discount percentage = 5%

Let the marked price of the article be Rs. M.
Marked price of the article =
⇒ 3990 = M – M × 5/100
⇒ 3990 = 19M/20
⇒ M = 4200

Marked price of the article = Rs. 4200
Let the cost price of the article be Rs. N.

⇒ 4200 = N × 25/100 + N
⇒ N = 3360

Cost price of the article = Rs. 3360

Profit percentage =
= [(3990 – 3360)/3360] × 100 = 18.75%

3. Piyush sold a bag to Rohit at ¼ of profit, Rohit spends Rs. 840 on its maintenance, and marked his cost 2/3 rd more than cost price (price at which he bought + maintenance charges) and sold it to Junaid after two successive discounts of 15% and 25%, and making profit of Rs. 427.5. Maintenance charges is ____ % of cost price of bag for Piyush?

Correct Answer: (d) 17.5%
Solution:

Let cost price of bag for Piyush be Rs. m
Cost price of bag for Rohit = (1.25m + 840)

Price at which Rohit sold the bag = 5/3 × 85% × 75% × (1.25m + 840)
= 106.25% of (1.25m + 840)

× (1.25m + 840) – 100% of (1.25m + 840) = Rs. 427.50

So, (1.25m + 840) = 427.50/6.25 × 100 = 6840
So, value of m = 6000/1.25 = Rs. 4800

Required % = 840/4800 × 100 = 17.5%

4. A dishonest shopkeeper sells an article, 20% less than its original weight. Even after that, he marks up the price 14.29% and then he offers a discount of 10% on the marked price. Find his profit percentage.

Correct Answer: (c) 28.57%
Solution:

Given:
The shopkeeper sells 20% less amount of an article
The markup% = 14.29%
Discount% = 10%

Formula used:
M.P = (C.P × (100 + markup%))/100%
S.P = (M.P × (100 - discount%))/100%
Discount% = [(M.P - S.P)/M.P] × 100%
Profit% = [(S.P - C.P)/C.P] × 100%

Where M.P = Marked price, S.P = Selling price, C.P = Cost price

Calculation:
Let the C.P be 700x
So, M.P will be = 700x × (1 + 1/7) = 800x (Here, we use the fractional value of 14.29% = 1/7)
⇒ 800x

Now, he gave a 10% discount
So, after the discount S.P will be = (800x × (100 - 10))/100 = 720x

According to the question, he sells 20% less than the original weight of the article
So, if he bought 100 units he sold only 80 units

So, the C.P of 80 units = (700x/100) × 80 = 560x
But, he sold it at Rs. 720x

So, profit% = [(720x - 560x)/560x] × 100%
= 28.57%

5. The cost price of a chair and a table together is 12000 Rs. A shopkeeper marked the chair 60% above the cost price and the table 80% above the cost price. He sold both chair and table after two consecutive discounts of 20% and 25% each. Find the difference between the cost prices of the table and the chair if the shopkeeper earned an overall profit of Rs. 360 on selling the chair and the table.

Correct Answer: (a) Rs. 2000
Solution:

Let the cost price of the chair = 100x Rs.
Therefore the marked price of the chair = 160x Rs.

Let the cost price of the table = 100y Rs.
Therefore, the marked price of the table = 180y Rs.

The cost price of a chair and a table together is 12000 Rs.
Therefore, 100x + 100y = 12000
⇒ x + y = 120 ...(a)

the shopkeeper earned an overall profit of Rs. 360 on selling the chair and the table and he sold both chair and table after two consecutive discounts of 20% and 25% each.

Therefore, (160x + 180y) × 0.80 × 0.75 = 12000 + 360
⇒ 160x + 180y = 20600
⇒ 8x + 9y = 1030 ...(b)

From (a) and (b)
9y - 8y = 1030 - 120 × 8
⇒ y = 70

and, x = 120 - 70
⇒ x = 50

Difference between the cost prices of the table and the chair = 100y - 100x = 100 × (70 - 50) = 2000 Rs.

6. A shopkeeper purchased 150 calculator at Rs.220 each, he spends the Rs.7,000 on transportation, He fixed the label price of each calculator as Rs.400 and also decides to give a discount of 5% on printed price. Find his gain percentage.

Correct Answer: (c) 42.5%
Solution:

Cost for purchase 150 calculator = 150 × 220
⇒ Rs.33,000

Total amount spent including transportation = 33000 + 7000
= Rs.40,000

Labelled price for 150 calculators = 150 × 400
= Rs.60,000

Selling price after discount of 5% = 60000 × (1 - 5/100)

⇒ 60000 × (95/100)
⇒ Rs.57,000

Gain = 57000 - 40000
⇒ 17,000

Gain% = (17000/40000) × 100
⇒ 42.5%

7. Maler sells keyboards, each of Rs. 390, after giving a discount of 22% on the marked price. Had she not given any discount, she would have earned a profit of 25%. If the cost price of the keyboards is decreased by 30%, and she still wants to earn 25% profit, she should sell it for?

Correct Answer: (a) 350
Solution:

Selling Price = Rs. 390
Selling Price = Marked Price (100% - Discount%)

390 = Marked Price (100% - 22%)
390 = Marked price × 78/100

390 × 100/78 = Marked price
Marked Price = Rs. 500

Had she not given any discount, she would have earned a profit of 25%,
then, Marked price = Selling price
Selling Price = Cost Price (100% + Profit%)

500 = Cost Price (100% + 25%)
500 = Cost Price × 125/100

500 × 100/125 = Cost Price
Cost Price = Rs. 400

If the cost price of the keyboard is decreased by 30%,
Decreased cost price = 400 (100% - 30%)
= 400 × 70/100
= Rs. 280

Now she still wants to earn a profit of 25% from the decreased cost price,
Selling Price = 280 (100% + 25%)
= 280 × 125/100 = Rs. 350

She should sell it for Rs. 350.

8. A shopkeeper has two items X and Y. Marked price of item Y is 40% more than the marked price of item X. The shopkeeper sold item X at 30% discount and item Y at 15% discount. On this transaction he made 20% loss on item X and 12% profit on item Y. If the total loss of the shopkeeper was Rs. 228, then find the marked price of the item Y?

Correct Answer: (c) Rs. 6720
Solution:

Let the marked of item X is = Rs. 100x
So, marked price of item Y is = 100x × 140/100 = Rs. 140x

Now, selling price of item X is
= 100x × 70/100 = 70x

Selling price of item Y is = 140x × 85/100 = 119x

Cost price of item X is = 70x × 100/80 = 87.5x
Cost price of item Y is = 119x × 100/112 = 106.25x

Then, according to the question,
(106.25x + 87.5x) - (70x + 119x) = 228
= 193.75x - 189x = 228
= 4.75x = 228
⇒ x = 48

Thus, the marked price of item Y is = 48 × 140
= Rs. 6720.

9. A shopkeeper purchases Aeron chair listed at Rs. 3000. He gets discounts successively as of 40% and 20% respectively. He incurs a spending of money Rs. 40 on transportation and sold that chair at a profit of 40%. Calculate the selling price of Aeron chair?

Correct Answer: (a) 2072
Solution:

⇒ Single equivalent discount of 40% and 20% = (40 + 20 – (40 × 20)/100)% = 52%
⇒ MP of chair in company = Rs.3000 also Discount = 52%

⇒ 3000 × (100 - 52)/100 = SP
⇒ 3000 × 48/100 = SP
⇒ Rs. 1440

⇒ CP of dealers = Rs. 1440
⇒ Total CP of dealers = Rs.(1440 + 40) = Rs. 1480

⇒ CP of dealers = Rs. 1480 and Profit = 40% then
⇒ 1480 × (100 + 40)/100 = SP
⇒ 1480 × 140/100 = SP
⇒ Rs. 2072 = SP

10. An article is bought by two shopkeepers A and B at the same price. A and B marked 50% and 25% more than the cost price respectively. B did not give any discount, while the discount given by A is 20 percent. Find by how much percent the selling price of A is more or less than the selling price of B.

Correct Answer: (c) 4% less
Solution:Cost price of the article be x
Marked price by A = 1.5x and by B = 1.25x
Selling price of A = 1.5x - discount = 1.5x - 1.5x × 20/100
= 1.5x - 0.3x = 1.2x
Selling price of B = 1.25x
Percentage (1.25x - 1.2x / 1.25x) × 100 = 4% less