Discount

1. A single discount of 50 % on an article costing ₹10000 is better than two successive discounts of 40% and 10 % by

(a)₹ 400                    (b)₹ 1000

(c)₹ 500                    (d)₹ 600

Solution: (a) Single Discount = 50%

Two successive Discount = $=40+10-\frac{(40\times 10)}{100}=50-4$

Difference =  50-50+4=4\%

Difference amount=4\% of 10000   $=\frac{4}{100}\times 10000=400$  Ans.

2. A dealer buys a table listed at ₹1,500 and gets discounts of 20% and 10%. He spends ₹20 on transportation and sells at a profit of 20 %. Find the selling price of the table (in rupee).

(a)1320                     (b)1080

(c)1200                     (d)1230

Solution: (a) L.P (Listed Price) of table = ₹ 1500

After discount , C.P. = =1500\times \frac{80}{100}\times \frac{90}{100}= Rs1080

After transportation charges

= 1080+20 = C.P. = ₹ 1100

S.P. of table= 120\% of 1100=\frac{120}{100}\times 1100 = Rs 1320

3. Which of the following successive discounts is better to a customer?

(1)20%, 15%, 10%

(2) 25%, 12%, 8%

(a) (1) is better

(b) (2) is better

(c) (1) or (2) (both are same)

(d) None of these

Solution: (b)

(i) 20%,  15%,  10%

Successive discount of 20% and 15%  $=20+15-\frac{20\times 15}{100}$   =35-3=32\%

Successive discount of 32% and 10%  $=32+10-\frac{32\times 10}{100}$  =42-3.2=38.8\%

(ii) 25%, 12% and 8%

$=25+12-\frac{25\times 12}{100}=37-3=34\%$

Successive discount of 34% and 8% $=34+8-\frac{34\times 8}{100}$

=42-2.72=39.28\%

Second  case is better for the customer.

4. The marked price of an article is ₹100. A discount series of 5%,10% successively reduces the price of an article by

(a) ₹4.5                     (b)₹14.5

(c) 24.5                      (d) none of these

Solution: (b) two successive discount of 5% and 10%  $=5+10-\frac{5\times 10}{100}=15-0.5=14.5\%$

After discount M.P. decreases = 14.5\% of 100 =Rs 14.5

5. Two successive discounts of 10% and 5%, in the order , are given on a bill of ₹110. Find the net amount of money payable to clear the bill (answer to the nearest rupee)

(a)₹ 94                      (b) ₹ 95

(c) ₹ 96                     (d) ₹ 97

Solution: (a) Bill amount = ₹ 110

After discount net amount of bill 90% of 95% of 110  =\frac{90}{100}\times \frac{95}{100}\times 110= Rs 94 (approx)

6. A profit of 10% is a made after giving discount of 5% on a T.V. If the marked price of the TV is ₹2640.00, the cost price of the TV was :

(a) 2280                    (b) ₹2296

(c) 2380                    (d) ₹ 2396

Solution (a) M.P. of T.V. = ₹ 2640

S.P. of T.V$=\frac{95}{100}\times 2640= 2508$  Rs

C.P. of TV = 2508\times \frac{100}{110}=2280

7. Discount on a pair of shoes marked at ₹ 475 and discounted at 15% is

(a) ₹ 70                     (b) ₹72

(c) ₹ 71.25                (D) ₹ 75.25

Solution: (c) M.P. of shoes = ₹ 475

Discount=\frac{15}{100}\times 475=\frac{285}{4}= 71.25 Rs

8.  A shopkeeper marks his goods 20% above the cost price and gives 15% discount on the marked price. His gain percent is

(a) 5%                       (b) 4%

(c) 2%                       (d) 1%

Solution: (c) Let the C.P. = ₹ 100

M.P.= 120% of 100=₹ 120

S.P. = 85% of 120 =\frac{85}{100}\times 120=102

Gain \%=\frac{102-100}{100}\times 100=2\%

9. With 5% discount on the cost of sugar, a buyer could purchase 2 kg more sugar for ₹ 608 original selling price of sugar is.

(a)₹15.50                  (b) ₹ 15

(c) ₹ 16.50                (d) ₹ 16

Solution: (d)  5\%\to 2 kg

 100\%\to 2\times20 =40 kg

Original Quantity= 40-2 = 38 kg

Original price = \frac{608}{38}= Rs 16 per kg

10.  A man saves ₹ 25 on the purchase of an article on which a discount of 20% is allowed. How much did the man pay?

(a) ₹ 75                     (b) ₹ 150

(c) ₹ 100                   (d) ₹ 125

Solution: (c) 20\% \to 25

100\%\to 25\times 5= 125  Rs

He pay  80\%\to 25\times 4= 100 Rs

11. A shopkeeper marks the price of an article at ₹80. What will be the selling price, if he allows two successive discounts at 5% each?

(a)₹72.2                     (b)₹72

(c)₹85                       (d₹7.2

Solution: (a) M.P. of article  = ₹ 80

Two successive discount= $=5+5-\frac{5\times 5}{100}=10-0.25=9.75\%$

Discount of article   =9.75\%of 80   $=\frac{9.75}{100}\times 80= 7.80$

S.P. of article = 80-7.80 = ₹ 72.20

12. A  purchased a dining table marked at ₹ 3000 at a successive discounts of 10% and 15% respectively .He gave ₹105 as transportation charge and sold it at₹3200 .What is his again percentage?

(a) 22\frac{1}{3}%                   (b)25%

(c)  33\frac{1}{3}%                 (d) 37\frac{17}{24}%

Solution: (c) M.P. of Dining table = ₹ 3000 after discount ,

C.P. = 3000\times \frac{90}{100}\times \frac{85}{100}= 2295

After transport charges

= 2295+105

C.P. = ₹ 2400

S.P. = ₹ 3,200

profit$=\frac{3200-2400}{2400}\times 100   $=\frac{800\times 100}{2400}=33\frac{1}{3}\%$

13.  An article is marked as ₹5,000.The shopkeeper allows successive discounts of x%, y%, z% on it. The net selling price is

(a) Rs.    \frac{(100-x)(100+y)(100+z)}{200}

(b) Rs.  \frac{(100+x)(100+y)(100-z)}{200}

(c) Rs.  \frac{(100-x)(100-y)(100-z)}{200}

(d) Rs.  \frac{(100-x)(100+y)(100-z)}{200}

Solution: (c) After three successive Discount S.P.of an article

=5000\times \frac{100-x}{100}\times \frac{100-y}{100}\times \frac{100-z}{100}

=\frac{(100-x)(100-y)(100-z)}{200}\\

14.  A merchant allows a discounts of 10% on marked price for the cash payment . To make a profit of 17%, he must mark his goods higher than their cost price by

(a) 33%                     (b) 40%

(c) 27%                     (d) 30%

Solution: (d) Let the C.P. = ₹ 100

S.P. = 117 % of 100 = ₹ 117

M.P. =  M.P. = $117\times \frac{100}{90}= 130

M.P. above %

 $=\frac{130-100}{100}\times 100\%=30\%$

15. A shopkeeper purchased a chair marked at ₹ 600 at two successive discounts of 15% and 20 % respectively. He spent ₹258 on transportation and sold the chair for ₹ 545. His again percentage was

(a)25%                      (b) 30%

(c)35%                      (d) 20%

Solution: (c) M.P. of chair = ₹ 600

After Discount C.P. = $=600\times \frac{85}{100}\times \frac{80}{100}= 408 $

After Transportation charges

C.P. = 408+28=₹ 436

Gain \% =\frac{545-436}{436}\times 100\%

$=\frac{109}{436}\times 100\%=25\%$

16. If the discount is equal to one fifth of the marked price and the loss is half the discounts, Then the percentage of loss is

(a) 10\frac{1}{9}%                  (b) 11\frac{1}{9}%

(c) 12\frac{1}{9}%                 (d) 13\frac{1}{9}%

Solution: (b) let the M.P. = ₹ 100

Discount  =\frac{1}{5}\times 100= 20

Loss =\frac{1}{2}\times 20= 10

C.P.= 100-20+10= ₹ 90

Loss\% =\frac{10}{90}\times 100=\frac{100}{9}\ %

17. A machine is marked at ₹ 6,800 and available at a discount of 10%. The shopkeeper gives another off season discount to the buyer and sells the machine for ₹ 5,202 .Find the off season discount.

(a) 10%                     (b) 12%

(c) 15%                     (d) 8%

Solution: (c) M.P. of machine = ₹ 6800

After 1st discount  $=\frac{90}{100}\times 6800=6120$ Rs.

S.P. of machine = ₹ 5,202

 Discount\%=\frac{6120-5202}{6120}\times 100

$=\frac{918}{6120}\times 100= 15\%$

18. After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. The marked price is above the cost price by

(a) 25%                     (b) 30%

(c) 37.5%                  (d) 42.5%

Solution: (c) let the C.P. = ₹ 100

S.P. = 121% of 100 = ₹ 121

M.P. $=121\times \frac{100}{88}= 137.5  Rs.

M.P. above % =\frac{137.5-100}{100}\times 100  =37.5%

19. A double bed is marked at ₹ 7,5000. The shopkeeper allows successive discounts of 8% , 5% and 2 % on it what is the net selling price?

(a) ₹ 6,500                (b) ₹ 6,000

(c) ₹ 6,4239              (d) ₹ 6,500.00

Solution: (c) Net selling price  $=\frac{92}{100}\times \frac{95}{100}\times \frac{98}{100}\times 75000= 64239$  Rs.

20.  A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8 % on the discounted price. If the customer pays ₹ 3,402 as the price including the sales tax then the marked price is

(a) ₹ 3,400                (b) ₹3,500

(c) ₹ 3,600                (d) ₹ 3,800

Solution: (b) MP of the item  =3402\times \frac{100}{108}\times \frac{100}{90}= 3500 Rs.

21. The cost price of a table is ₹ 3,200. A merchant wants to make 25% profit by selling it. At the time of sale he declares a discount of 20 % on the marked price. The marked price (in ₹)  is

(a) 5,000                   (b) 6,000

(c) 4,000                   (d) 4,500

Solution: (a) MP of the table =3200\times \frac{125}{100}\times \frac{100}{80}= 5000 Rs.

22. A shopkeeper offers 15% discount on all plastic toys. He offers a further discount of 4% on the reduced price to those customers who pay cash. What does a customers have to pay (₹ in) in case for a toys of ₹ 200?

(a) 133.7                (b) 129.8

(c) 163.2                (d) 153.2

Solution: (c) According  to question

23. Successive discounts of 20% and 40% equal a single discount of

(a) 60%                     (b)20%

(c) 52%                     (d) 48%

Solution: (c) Single Discount =20+40-\frac{20\times 40}{100}=52\%

24. A shopkeeper allows a discount of 12.5% on the marked price of a certain article and makes a profit of 20 %. If the article cost the shopkeeper ₹ 210, then the marked price of the article will be

(a) ₹ 387                   (b) ₹ 350

(c) ₹ 386                   (d) ₹ 288

Solution:(d) MP of the article  =210\times \frac{120}{100}\times \frac{100}{87.5}= 288 RS.

25. How much percentage more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?

(a) 70%                     (b) 50%

(c) 60%                     (d) 55%

Solution: (c) Let of C.P =- ₹ 100

S.P. = 120% of 100=₹ 120

M.P.= 120 \times\frac{100}{75}= Rs. 160

Above % = \frac{160-100}{100}\times100 = 60 %

26.  A shopkeeper sold an item for ₹ 1,510 after giving a discount of 24\frac{1}{2} % and there by incurred a loss of 10%. Had he sold the item without discount his net profit would have been

(a) ₹ 641                    (B() ₹  322\frac{1}{2}

(C) ₹ 422\frac{2}{9}                  (D) ₹ 322\frac{2}{9}

Solution: (d) Let the M.P. of an item = ₹ x

S.P. of an item $=(100-24\frac{1}{2})\% of x$

$1510\times \frac{100}{90}=\frac{15100}{9}$

Without discount, gain

$=2000-\frac{15100}{9}=\frac{18000-15100}{9}$

$=\frac{2900}{9}= 322\frac{2}{9}$

 

 

 

 

 

 

 

 

 

 

 

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