Direction (1-5): Study the following data carefully and answer the questions:

There are five items A, B, C, D and E sold by a shopkeeper P. Below given information is about cost price, marked price and selling price of those five items.

Item A is marked 80% above its cost price and sold at Rs.806 after allowing two successive discounts of 20% and Rs.130 respectively. Ratio of marked price of item A to that of item B is 13: 15 and item B is sold after allowing two successive discounts of Rs.150 and 17.5% respectively. Cost price of item B is Rs.200 more than that of item C which is marked 40% above its cost price and when sold, profit percent earned is 5% only. The total profit amount earned after selling items B and C together is Rs.125. Cost price of item D is 75% of that of item E and profit amount earned after selling item D is 40%. If item D is sold for Rs.81 less, then profit percent would be 25% only. Profit amount earned after selling item E is Rs.9 when sold after allowing two successive discounts of 10% and 25% respectively.

1) If two successive discounts of ‘r’% and Rs.113.4respectively is equivalent to a single discount percent of ‘r + 12’% on item D, then what is the marked-up percent of item D?

a) 80%

b) 45%

c) 75%

d) 60%

e) None of these

2) Selling price of item B would be how much more than the selling price of item A when the shopkeeper sold both the items after interchanging the profit percent from the actual profit percent that is offered initially?

a) Rs.413

b) Rs.387

c) Rs.365

d) Rs.401

e) None of these

3) Which of the following pair of items will get second most profit percent when sold together?

a) A-C

b) C-D

c) B-E

d) A-D

e) C-E

4) If the shopkeeper interchanges the marked-up percent and discount percent of only item E, then what will be the approximate loss percent incurred to the shopkeeper after selling itemsC and E together?

a) 12.75%

b) 14.65%

c) 8.25%

d) 11.15%

e) 16.35%

5) If by mistake the shopkeeper applied marked-up percent and profit percent of item A when a customer purchase item B, then what will be the difference between amount of discount offered and marked-up amount on item B?

a) Rs.216

b) Rs.156

c) Rs.192

d) Rs.208

e) None of these

Answers :

1) Answer: c)

Let cost price of item A = 100a

Marked price = 180% of 100a = 180a

Selling price = (80% of 180a) – 130 = 806

144a = 936

a = 6.5

Cost price of item A = 100a = Rs.650

Marked price of item A = 180a = Rs.1170

Selling price of item A = Rs.806

Marked price of item B = 1170 * (15/13) = Rs.1350

Selling price of item B = 82.5% of (1350 – 150) = Rs.990

Let cost price of item B and C is ‘x’ and ‘x – 200’ respectively.

Marked price of item C = 140% of (x – 200) = (1.4x – 280)

Selling price of item C = 105% of (x – 200) = (1.05x – 210)

According to the question:

[990 + (1.05x – 210)] – [x + (x – 200)] = 125

780 + 1.05x – 2x + 200 = 125

0.95x = 855

x = 900

Cost price of item B = x = Rs.900

Cost price of item C = (x – 200) = Rs.700

Marked price of item C = (1.4x – 280) = Rs.980

Selling price of item C = (1.05x – 210) = Rs.735

Let cost price of item D and E is ‘75y’ and ‘100y’ respectively.

Selling price of item D = 140% of 75y = 105y

According to the question:

105y – 81 = 125% of 75y

105y – 81 = 93.75y

11.25y = 81

y = 7.2

Cost price of item D = 75y = Rs.540

Selling price of item D = 105y = Rs.756

Cost price of item E = 100y = Rs.720

Selling price of item E = 720 + 9 = Rs.729

Marked price of item E = 729 * (100/90) * (100/75) = Rs.1080

Let marked price of item D = 100d

Selling price of item D = [(100 – r)]% of 100d] – 113.4 = [100 – (r + 12)]% of 100d = 756

[(100 – r)]% of 100d] – 113.4 = 756

(100 – r)d = 869.4 ……… (1)

[100 – (r + 12)]% of 100d = 756

(88 – r)d = 756 …….. (2)

From (1) and (2):

(100 – r): (88 – r) = 23: 20

2000 – 20r = 2024 – 23r

3r = 24

r = 8 and d = 9.45

Marked price of item D = 100d = Rs.945

Required percent = [(945 – 540)/540] * 100 = 75%

2) Answer: d)

Actual profit percent earned on item A = [(806 – 650)/650] * 100 = 24%

Actual profit percent earned on item B = [(990 – 900)/900] * 100 = 10%

New selling price of item A = 110% of 650 = Rs.715

New selling price of item B = 124% of 900 = Rs.1116

Required difference = 1116 – 715 = Rs.401

3) Answer: b)

Total cost price of items A and C together = 650 + 700 = Rs.1350

Total selling price of items A and C together = 806 + 735 = Rs.1541

Profit percent = [(1541 – 1350)/1350] * 100 = 14.15% (Approx)

Total cost price of items C and D together = 700 + 540 = Rs.1240

Total sellingprice of items C and D together = 735 + 756 = Rs.1491

Profit percent = [(1491 – 1240)/1240] * 100 = 20.24% (Approx)

Total cost price of items B and E together = 900 + 720 = Rs.1620

Total sellingprice of items B and E together = 990 + 729 = Rs.1719

Profit percent = [(1719 – 1620)/1620] * 100 = 6.11% (Approx)

Total cost price of items A and D together = 650 + 540 = Rs.1190

Total sellingprice of items A and D together = 806 + 756 = Rs.1562

Profit percent = [(1562 – 1190)/1190] * 100 = 31.26% (Approx)

Total cost price of items C and E together = 700 + 720 = Rs.1420

Total sellingprice of items C and E together = 735 + 729 = Rs.1464

Profit percent = [(1464 – 1420)/1420] * 100 = 3.1% (Approx)

Hence, correct option (b) is correct.

4) Answer: b)

Marked-up percent on item E = [(1080 – 720)/720] * 100 = 50%

Discount percent offered on item E = [(1080 – 729)/1080] * 100 = 32.5%

New selling price of item E after interchanging marked-up percent and discount percent = 50% of 132.5% of 720 = Rs.477

Total cost price of items C and E together = 700 + 720 = Rs.1420

Total selling price of items C and E together = 735 + 477 = Rs.1212

Required loss percent = [(1420 – 1212)/1420] * 100 = 14.65% (Approx)

5) Answer: a)

Marked-up percent on item A = [(1170 – 650)/650] * 100 = 80%

Profit percent on item A = [(806 – 650)/650] * 100 = 24%

New marked price of item B = 180% of 900 = Rs.1620

New selling price of item B = 124% of 900 = Rs.1116

Changed amount of discount offered on item B = 1620 – 1116 = Rs.504

Changed marked-up amount on item B = 1620 – 900 = Rs.720

Required difference = 720 – 504 = Rs.216