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ICSE-VIII-Mathematics

08: Profit, Loss and Discount Class 8 Maths

with Solutions - page 5

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  • #2-i
    C.P. of 4 oranges,
    Ans : C.P. of 4 oranges = 4 ×1/2 = Rs. 2
  • #2-ii
    C.P. of one orange.
    Ans : C.P. of 1 oranges = Rs. ½ = Rs. (0.50)
  • #2-iii
    S.P. of one orange.
    Ans : S.P. of 1 orange = Rs. ¾ = Rs. 0.75
  • #2-iv
    profit made by selling one orange.
    Ans : Profit made by selling one orange = Rs. ¾ - Rs. ½
    = Rs. ¼
    = Rs. 0.25
  • #2-v
    number of oranges brought and sold in order to gain Rs. 24.
    Ans : If gain is Rs. ¼; number of oranges = 1
    If gain is Rs. 24, number of oranges = (1/1)/4 × 24
    = 1 × 4/1 × 24
    = 96
  • Qstn #3
    A man sells 12 articles for Rs. 80 gaining 33%. Find the number of articles bought by the man for Rs. 90.
    Ans : S.P. of 12 articles = Rs. 80,
    Gain = 33 1/3% = 100/3%
    C.P. = 100/(100 + Gain) × S.P.
    = 100/(100 + 100/3) × 80
    = 100/{(300 + 100)/3} × 80
    = 100/(400/3) × 80
    = 100 × 3/400 × 80
    = Rs. 60
    Rs. 60 is the cost of 12 articles
    Re. 1 is the cost of = 12/60 article
    Rs. 90 is the cost of = 12/60 × 90
    = 1/5 × 90 = 18
    Man can buy article for Rs. 90 = 18
  • Qstn #4
    The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.
    Ans : C.P. of 20 articles = S.P. of 16 articles.
    Let C.P. of 1 article = Re. 1
    C.P. of 20 articles = Rs.20
    and C.P. of 16 articles = Rs.16
    S.P. of 16 articles = Rs.20
    [S.P. of 16 articles = C.P. of 20 articles]
    Gain = Rs.20 - Rs.16 = Rs.4
    Gain% = 4/16 × 100
    = (4/16 × 100)
    = 25%
  • Qstn #5
    The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.
    Ans : S.P. of 15 articles = C.P. of 12 articles
    Let C.P. of 1 article = Re.1
    C.P. of 12 article = Rs.12
    and C.P. of 15 articles = Rs.15
    S.P. of 15 articles = Rs.12
    [S.P. of 15 articles = C.P. of 12 articles]
    Loss = Rs.15 - Rs.12 = Rs.3
    Loss% = 3/15 × 100 = 20%
  • Qstn #6
    By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.
    Ans : Let C.P. of 1 pen = Re.1
    C.P. of 2 pens = Rs.2
    and C.P. of 8 pens = Rs.8
    Loss = Rs.2 ...[Loss = C.P. of 2 Pens]
    Loss% = 2/8 × 100 = 25%
  • Qstn #7
    A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.
    If he desires a profit of 12% on the whole; find :
    Ans : C.P. of the rice = Rs. 4500
    Profit desired on the whole = 12%
    ∴ S.P. of the whole rice = (100 + gain%)/100 × C.P.
    = (100 + 12)/100 × Rs. 4500
    = Rs. 112/100 × 4500
    = 112 × 45
    = Rs. 5040
    C.P. of 1/3 of rice = 1/3 × Rs. 4500
    = Rs. 1500
    Since, gain on 1/3 of rice = 10%
    ∴ S.P. on it = (100 + gain%)/100 × C.P.
    = (100 + 10)/100 × Rs. 1500
    = Rs. 110/100 × 1500
    = 11 × 150
    = Rs. 1650
    Remaining C.P. of the Rice = Rs. 4500 - Rs. 1500
    = Rs. 3000
    Remaining S.P. of the rice = Rs. 5040 - Rs. 1650
    = Rs. 3390
    Profit on the remaining rice = Rs. 3390 - Rs. 3000
    = Rs. 390
    Gain% on the remaining rice = 390/3000 × 100
    = (390 × 100)/3000
    = 13%
  • #7-i
    the selling price of the rest of the rice ;
    Ans : ∴ S.P. of the rest of the Price = Rs. 3390
  • #7-ii
    the percentage profit on the rest of the rice.
    Ans : % Profit on the rest of the rice = 13%
  • Qstn #8
    Mohan bought a certain number of note-books for Rs.600. He sold of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole?
    Ans : C.P. of note books = Rs. 600
    Gain desired on the whole = 10%
    ∴ Total S.P. of all the note-books = (100 + gain%)/100 × C.P.
    = (100 + 10)/100 × Rs. 600
    = Rs. 110/100 × 600
    = Rs. 660
    C.P. of ¼ of the note-books = ¼ × Rs. 600
    = Rs. 150
    Loss on these note-books = 5%
    ∴ S.P. of these note-books = (100 - Loss%)/100 × C.P.
    = (100 - 5)/100 × Rs. 150
    = Rs. 95/100 × 150
    = Rs. 14250/100
    = Rs. 142.50
    Now, C.P. of the remaining note-books = Rs. 600 - Rs. 150
    = Rs. 450
    Required S.P. of the remaining note-books = Rs. 660 - Rs. 142.50
    = Rs. 517. 50
  • Qstn #9
    Raju sells a watch at 5% profit. Had he sold it for Rs.24 more; he would have gained 11%. Find the cost price of the watch.
    Ans : Let C.P. of the watch = Rs.100
    When profit = 5%;
    S.P. = Rs.(100 + 5) = Rs.105
    When profit = 11%;
    S.P. = Rs.(100 + 11) = Rs .111
    Difference of two selling prices = Rs. 111 - Rs. 105 = Rs.6
    When watch sold for Rs.6 more; then C.P. of the watch = Rs.100
    When watch sold for Re. 1 more; then C.P. of the watch = Rs. 100/6
    When watch sold for Rs.24 more; then C.P. of the watch = Rs. 100/6 × 24 = Rs.400
  • Qstn #10
    A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?
    Ans : Let C.P. of the bicycle = Rs.100
    In the I case :
    When Profit = 5% ;
    S.P. = Rs. (100 + 5) = Rs. 105
    In the II case:
    C.P. = (100 - 30/100 × 100)
    = Rs. (100 - 30)
    = Rs. 70
    Profit = 30%
    S.P. = (100 + Profit)/100 × C.P.
    = (100 + 30)/100 × Rs. 70
    = 130/100 × Rs. 70
    dlt2242997330673006213">= Rs. (130 × 70)/100
    = Rs. 91
    Difference of two selling prices = Rs. 105 - Rs. 91
    = Rs. 14
    If difference is Rs. 14 then C.P. of the bicycle = Rs. 100
    If difference is Re. 1 then C.P. of the bicycle = Rs. 100/14
    If difference is Rs. 63 then C.P. of the bicycle = Rs. 100/14 × 63
    = Rs. (100 × 63)/14
    = Rs. 50 × 9
    = Rs. 450
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