PROFIT, LOSS AND DISCOUNT - Q&A
Exercise 8 (A)
1. Megha bought 10 note-books for Rs. 40 and sold them at Rs. 4.75 per note-book. Find her gain percent.
Solution:
Cost Price (C.P.) of 10 note-books = Rs. 40
Selling Price (S.P.) of 1 note-book = Rs. 4.75
S.P. of 10 note-books = 10 × 4.75 = Rs. 47.50
Gain = S.P. - C.P. = 47.50 - 40 = Rs. 7.50
Gain % = (Gain / C.P.) × 100
= (7.50 / 40) × 100
= (750 / 40)
= 18.75% or 18 3/4 %
2. A fruit-seller buys oranges at 4 for Rs. 3 and sells them at 3 for Rs. 4. Find his profit percent.
Solution:
Let the number of oranges bought be the LCM of 4 and 3, which is 12.
C.P. of 4 oranges = Rs. 3
C.P. of 12 oranges = (3/4) × 12 = Rs. 9
S.P. of 3 oranges = Rs. 4
S.P. of 12 oranges = (4/3) × 12 = Rs. 16
Profit = S.P. - C.P. = 16 - 9 = Rs. 7
Profit % = (Profit / C.P.) × 100
= (7 / 9) × 100
= 700/9 % = 77 7/9 %
3. A man buys a certain number of articles at 15 for Rs. 112.50 and sells them at 12 for Rs. 108. Find:
(i) his gain as percent;
(ii) the number of articles sold to make a profit of Rs. 75.
Solution:
(i)
C.P. of 15 articles = Rs. 112.50
C.P. of 1 article = 112.50 / 15 = Rs. 7.50
S.P. of 12 articles = Rs. 108
S.P. of 1 article = 108 / 12 = Rs. 9
Gain per article = 9 - 7.50 = Rs. 1.50
Gain % = (1.50 / 7.50) × 100 = (1/5) × 100 = 20%
(ii)
Profit on 1 article = Rs. 1.50
Total Profit required = Rs. 75
Number of articles = Total Profit / Profit per article
= 75 / 1.50 = 7500 / 150 = 50 articles.
4. A boy buys an old bicycle for Rs. 162 and spends Rs. 18 on its repairs before selling the bicycle for Rs. 207. Find his gain or loss percent.
Solution:
Cost Price = Rs. 162
Repair charges (Overheads) = Rs. 18
Total C.P. = 162 + 18 = Rs. 180
Selling Price (S.P.) = Rs. 207
Since S.P. > C.P., there is a gain.
Gain = 207 - 180 = Rs. 27
Gain % = (27 / 180) × 100
= (3 / 20) × 100 = 3 × 5 = 15%
5. An article is bought from Jaipur for Rs. 4,800 and is sold in Delhi for Rs. 5,820. If Rs. 1,200 is spent on its transportation, etc., find the loss or the gain as percent.
Solution:
Cost Price = Rs. 4,800
Transportation charges = Rs. 1,200
Total C.P. = 4,800 + 1,200 = Rs. 6,000
Selling Price (S.P.) = Rs. 5,820
Since C.P. > S.P., there is a loss.
Loss = 6,000 - 5,820 = Rs. 180
Loss % = (180 / 6000) × 100
= 18 / 6 = 3%
6. Mohit sold a T.V. for Rs. 3,600; gaining one-sixth of its selling price. Find:
(i) the gain
(ii) the cost price of the T.V.
(iii) the gain percent.
Solution:
S.P. = Rs. 3,600
(i) Gain = 1/6 of S.P. = (1/6) × 3600 = Rs. 600
(ii) C.P. = S.P. - Gain = 3,600 - 600 = Rs. 3,000
(iii) Gain % = (Gain / C.P.) × 100 = (600 / 3000) × 100 = 20%
7. By selling a certain number of goods for Rs. 5,500, a shopkeeper loses equal to one-tenth of their selling price. Find:
(i) the loss incurred
(ii) the cost price of the goods
(iii) the loss as percent.
Solution:
S.P. = Rs. 5,500
(i) Loss = 1/10 of S.P. = (1/10) × 5,500 = Rs. 550
(ii) C.P. = S.P. + Loss = 5,500 + 550 = Rs. 6,050
(iii) Loss % = (Loss / C.P.) × 100
= (550 / 6050) × 100
= (1 / 11) × 100 = 9 1/11 %
8. The selling price of a sofa-set is 4/5 times of its cost price. Find the gain or the loss as percent.
Solution:
Given: S.P. = (4/5) × C.P.
S.P./C.P. = 4/5
Let C.P. = 5x and S.P. = 4x
Since C.P. > S.P., it is a loss.
Loss = 5x - 4x = x
Loss % = (Loss / C.P.) × 100
= (x / 5x) × 100 = 20%
9. The cost price of an article is 4/5 times of its selling price. Find the loss or the gain as percent.
Solution:
Given: C.P. = (4/5) × S.P.
C.P./S.P. = 4/5
Let S.P. = 5x and C.P. = 4x
Since S.P. > C.P., it is a gain.
Gain = 5x - 4x = x
Gain % = (Gain / C.P.) × 100
= (x / 4x) × 100 = 25%
10. A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loss.
Solution:
Let C.P. = Rs. 100
S.P. = 80% of C.P. = Rs. 80
Loss = 100 - 80 = Rs. 20
Loss % = (20 / 100) × 100 = 20%
11. The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Solution:
Let S.P. = Rs. 100
C.P. = 90% of 100 = Rs. 90
Profit = 100 - 90 = Rs. 10
Profit % = (10 / 90) × 100 = 100/9 % = 11 1/9 %
Exercise 8 (B)
1. Find the selling price, if:
(i) C.P. = Rs. 950 and profit = 8%
(ii) C.P. = Rs. 1,300 and loss = 13%
Solution:
(i) Profit = 8% of 950 = (8/100) × 950 = Rs. 76
S.P. = C.P. + Profit = 950 + 76 = Rs. 1,026
(ii) Loss = 13% of 1300 = (13/100) × 1300 = Rs. 169
S.P. = C.P. - Loss = 1300 - 169 = Rs. 1,131
2. Find the cost price, if:
(i) S.P. = Rs. 1,680 and profit = 12%
(ii) S.P. = Rs. 1,128 and loss = 6%
Solution:
(i) S.P. = C.P. × (1 + Profit%/100)
1680 = C.P. × (1 + 12/100) = C.P. × (112/100)
C.P. = (1680 × 100) / 112 = 168000 / 112 = Rs. 1,500
(ii) S.P. = C.P. × (1 - Loss%/100)
1128 = C.P. × (1 - 6/100) = C.P. × (94/100)
C.P. = (1128 × 100) / 94 = Rs. 1,200
3. By selling an article for Rs. 900, a man gains 20%. Find his cost price and the gain.
Solution:
S.P. = Rs. 900, Gain% = 20%
C.P. = (S.P. × 100) / (100 + Gain%)
C.P. = (900 × 100) / 120 = 90000 / 120 = Rs. 750
Gain = S.P. - C.P. = 900 - 750 = Rs. 150
4. By selling an article for Rs. 704, a person loses 12%. Find his cost price and the loss.
Solution:
S.P. = Rs. 704, Loss% = 12%
C.P. = (S.P. × 100) / (100 - Loss%)
C.P. = (704 × 100) / 88 = 70400 / 88 = Rs. 800
Loss = C.P. - S.P. = 800 - 704 = Rs. 96
5. Find the selling price, if:
(i) C.P. = Rs. 352; overheads = Rs. 28 and profit = 20%
(ii) C.P. = Rs. 576; overheads = Rs. 44 and loss = 16%
Solution:
(i) Total C.P. = 352 + 28 = Rs. 380
S.P. = Total C.P. × (1 + 20/100) = 380 × 1.2 = Rs. 456
(ii) Total C.P. = 576 + 44 = Rs. 620
S.P. = Total C.P. × (1 - 16/100) = 620 × 0.84 = Rs. 520.80
6. If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5%?
Solution:
Case 1: S.P. = 637, Loss = 9%
C.P. = (637 × 100) / (100 - 9) = 63700 / 91 = Rs. 700
Case 2: C.P. = 700, Desired Profit = 5%
New S.P. = 700 × (1 + 5/100) = 700 × 1.05 = Rs. 735
7. A man sells a radio-set for Rs. 605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16%?
Solution:
S.P. = 605, Gain = 10%
C.P. = (605 × 100) / 110 = Rs. 550
For 16% gain:
New S.P. = 550 × (1 + 16/100) = 550 × 1.16 = Rs. 638
8. By selling a sofa-set for Rs. 2,500, the shopkeeper loses 20%. Find his loss percent or profit percent, if he sells the same sofa-set for Rs. 3,150.
Solution:
S.P. = 2500, Loss = 20%
C.P. = (2500 × 100) / (100 - 20) = 250000 / 80 = Rs. 3,125
If New S.P. = Rs. 3,150
Since New S.P. > C.P., it is a profit.
Profit = 3150 - 3125 = Rs. 25
Profit % = (25 / 3125) × 100 = 0.8%
9. Mr. Sinha sold two tape-recorders for Rs. 990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.
Solution:
Tape 1: S.P. = 990, Gain = 10%
C.P.1 = (990 × 100) / 110 = Rs. 900
Tape 2: S.P. = 990, Loss = 10%
C.P.2 = (990 × 100) / 90 = Rs. 1,100
Total S.P. = 990 + 990 = Rs. 1,980
Total C.P. = 900 + 1100 = Rs. 2,000
Since C.P. > S.P., there is a loss.
Total Loss = 2000 - 1980 = Rs. 20
Loss % = (20 / 2000) × 100 = 1%
10. A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10%. Find:
(i) the C.P. of the tape-recorder
(ii) the C.P. of the C.D. player
(iii) the total C.P. of both
(iv) the total S.P. of both
(v) the gain % or the loss % on the whole.
Solution:
(i) Tape-recorder: S.P. = 2760, Gain = 15%
C.P. = (2760 × 100) / 115 = Rs. 2,400
(ii) C.D. Player: S.P. = 3240, Loss = 10%
C.P. = (3240 × 100) / 90 = Rs. 3,600
(iii) Total C.P. = 2400 + 3600 = Rs. 6,000
(iv) Total S.P. = 2760 + 3240 = Rs. 6,000
(v) Since Total C.P. = Total S.P., there is No Profit, No Loss (0%).
11. Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter, find:
(i) the S.P. and the C.P. of the scooter for Rahim
(ii) the S.P. and the C.P. of the scooter for Rajesh.
Solution:
(i) For Rahim:
S.P. (price Prem paid) = Rs. 14,490
Gain = 5%
C.P. = (14490 × 100) / 105 = Rs. 13,800
(ii) For Rajesh:
S.P. (price Rahim paid) = Rs. 13,800
Loss = 8%
C.P. = (13800 × 100) / 92 = Rs. 15,000
So, Rajesh's S.P. = Rs. 13,800 and Rajesh's C.P. = Rs. 15,000.
Exercise 8 (C)
1. An article is marked for Rs. 1,300 and is sold for Rs. 1,144; find the discount percent.
Solution:
Marked Price (M.P.) = Rs. 1,300
Selling Price (S.P.) = Rs. 1,144
Discount = M.P. - S.P. = 1300 - 1144 = Rs. 156
Discount % = (Discount / M.P.) × 100
= (156 / 1300) × 100 = 12%
2. The marked price of a dining table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.
Solution:
M.P. = Rs. 23,600
Discount = 8%
S.P. = M.P. × (1 - Discount/100)
= 23600 × (1 - 8/100) = 23600 × 0.92 = Rs. 21,712
3. A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400; find the discount given and the selling price of the watch.
Solution:
List Price (M.P.) = Rs. 1,400
Discount % = 9%
Discount Amount = 9% of 1400 = 126
S.P. = M.P. - Discount Amount = 1400 - 126 = Rs. 1,274
4. A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.
Solution:
S.P. = Rs. 248.50
Discount = 10%
Let List Price be x.
x - 10% of x = 248.50
0.9x = 248.50
x = 248.50 / 0.9 = Rs. 276.11
5. A shopkeeper buys an article for Rs. 450. He marks it at 20% above the cost price. Find:
(i) the marked price of the article.
(ii) the selling price, if he sells the article at 10% discount.
(iii) the percentage discount given by him, if he sells the article for Rs. 496.80.
Solution:
C.P. = Rs. 450
(i) M.P. = C.P. + 20% of C.P. = 450 + 90 = Rs. 540
(ii) Discount = 10%
S.P. = 540 - 10% of 540 = 540 - 54 = Rs. 486
(iii) New S.P. = Rs. 496.80
Discount = M.P. - S.P. = 540 - 496.80 = Rs. 43.20
Discount % = (43.20 / 540) × 100 = 8%
6. The list price of an article is Rs. 800 and is available at a discount of 15%. Find:
(i) selling price of the article;
(ii) cost price of the article, if a profit of 13 1/3 % is made on selling it.
Solution:
(i) M.P. = Rs. 800, Discount = 15%
S.P. = 800 - (15/100 × 800) = 800 - 120 = Rs. 680
(ii) Profit = 13 1/3 % = 40/3 %
S.P. = C.P. × (1 + Profit/100)
680 = C.P. × (1 + 40/300) = C.P. × (340/300)
C.P. = (680 × 300) / 340 = 2 × 300 = Rs. 600
7. An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find:
(i) the selling price of the article.
(ii) the cost price of the article for the dealer.
Solution:
(i) M.P. = 2250, Discount = 12%
S.P. = 2250 - 12% of 2250 = 2250 - 270 = Rs. 1,980
(ii) Profit = 10%
C.P. = (S.P. × 100) / 110 = (1980 × 100) / 110 = Rs. 1,800
8. By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440; find:
(i) the marked price of the article.
(ii) the cost price of the article.
Solution:
S.P. = Rs. 1,440
(i) Discount = 20%
S.P. = M.P. × (1 - 20/100) => 1440 = 0.8 × M.P.
M.P. = 1440 / 0.8 = Rs. 1,800
(ii) Gain = 25%
C.P. = (S.P. × 100) / 125 = (1440 × 100) / 125 = Rs. 1,152
9. A shopkeeper marks his goods at 30% above the cost price and then gives a discount of 10%. Find his gain percent.
Solution:
Let C.P. = 100
M.P. = 100 + 30 = 130
Discount = 10% of 130 = 13
S.P. = 130 - 13 = 117
Gain = S.P. - C.P. = 117 - 100 = 17
Gain % = 17%
10. A ready-made garments shop in Delhi allows 20% discount on its garments and still makes a profit of 20%. Find the marked price of a dress which is bought by the shopkeeper for Rs. 400.
Solution:
C.P. = Rs. 400
Profit = 20%
S.P. = 400 + 20% of 400 = 480
Discount = 20% on M.P.
S.P. = M.P. × (1 - 20/100) => 480 = 0.8 × M.P.
M.P. = 480 / 0.8 = Rs. 600
11. At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.
Solution:
S.P. = 13.20, Discount = 12%
M.P. = S.P. / (1 - 0.12) = 13.20 / 0.88 = Rs. 15
New Discount = 5%
New S.P. = 15 - (5% of 15) = 15 - 0.75 = Rs. 14.25
12. The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400, find: (i) its marked price (ii) its selling price (iii) the profit percent.
Solution:
(i) C.P. = 2400. C.P. is 25% below M.P.
C.P. = M.P. × (1 - 25/100) = 0.75 M.P.
2400 = 0.75 M.P. => M.P. = 2400 / 0.75 = Rs. 3,200
(ii) Discount = 15%
S.P. = M.P. × (1 - 0.15) = 3200 × 0.85 = Rs. 2,720
(iii) Profit = S.P. - C.P. = 2720 - 2400 = Rs. 320
Profit % = (320 / 2400) × 100 = 13.33% or 13 1/3%
13. Find a single discount (as percent) equivalent to following successive discounts: (i) 20% and 12% (ii) 10%, 20% and 20% (iii) 20%, 10% and 5%.
Solution:
(i) Let M.P. = 100.
After 20%: 80. After 12%: 80 - 9.6 = 70.4.
Discount = 100 - 70.4 = 29.6%
(ii) Let M.P. = 100.
After 10%: 90. After 20%: 90 - 18 = 72. After 20%: 72 - 14.4 = 57.6.
Discount = 100 - 57.6 = 42.4%
(iii) Let M.P. = 100.
After 20%: 80. After 10%: 80 - 8 = 72. After 5%: 72 - 3.6 = 68.4.
Discount = 100 - 68.4 = 31.6%
14. When the rate of Tax is decreased from 9% to 6% for a coloured T.V.; Mrs Geeta will save Rs. 780 in buying this T.V. Find the list price of the T.V.
Solution:
Let List Price = x.
Original Tax = 9% of x. New Tax = 6% of x.
Difference = (9 - 6)% of x = 3% of x.
Given Difference = 780.
3x/100 = 780 => x = (780 × 100) / 3 = Rs. 26,000.
15. A shopkeeper sells an article for Rs. 21,384 including 10% tax. Find the price before tax.
Solution:
S.P. (inclusive of tax) = Rs. 21,384.
Tax rate = 10%.
Let List Price (before tax) be x.
x + 10% of x = 21,384
1.1x = 21,384
x = 21,384 / 1.1 = Rs. 19,440.