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ICSE-VIII-Mathematics

08: Profit, Loss and Discount Class 8 Maths

with Solutions - page 3

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  • #1-i
    C.P. = Rs. 950 and profit = 8%
    Ans : C.P. = Rs. 950 Profit = 8%
    ∴ S.P. = {950 × (100 + 8)}/100
    = (950 × 108)/100
    = 19 × 54
    = Rs. 1026
  • #1-ii
    C.P. = Rs. 1,300 and loss = 13%
    Ans : C.P. = Rs. 1,300
    Loss = 13%
    ∴ S.P. = {1300 × (100 - 13)}/100
    = 13 × 87
    = Rs. 1131
  • #2-i
    S.P. = Rs. 1,680 and profit = 12%
    Ans : S.P. = Rs. 1, 128, Profit = 12%
    C.P. = 100/(100 + profit) × S.P.
    ∴ C.P. = 100/(100 + 12) × 1680
    = (100 × 1680)/112
    = (25 × 1680)/28
    = 25 × 60
    = Rs. 1500
  • #2-ii
    S.P. = Rs. 1,128 and loss = 6%
    Ans : S.P. = Rs. 1,128, Loss = 6%
    C.P. = 100/(100 - Loss) × S.P.
    ∴ C.P. = (100 × 1128)/(100 - 6)
    = (100 × 1128)/94
    = 100 × 12
    = Rs. 1200
  • Qstn #3
    By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.
    Ans : S.P. of an article = Rs. 900
    Gain = 20%
    C.P. = 100/(100 + Gain%) × S.P.
    ∴ C.P. = 100/(100 + 20) × Rs. 900
    = Rs. 100/120 × 900
    = Rs. 9000/12
    = Rs. 750
    Gain = S.P. - C.P.
    = Rs. 900 - Rs. 750
    = Rs. 150
  • Qstn #4
    By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss
    Ans : S.P. of an article = Rs. 704
    Loss = 12%
    C.P. = 100/(100 - Loss%) × S.P.
    = 100/(100 - 12) × Rs. 704
    = Rs. 100/88 × 704
    = Rs. 100 × 8
    = Rs. 800
    Loss = C.P. - S.P.
    = Rs. 800 - Rs. 704
    = Rs. 96
  • #5-i
    C.P. = Rs.352; overheads = Rs.28 and profit = 20
    Ans : C.P. = Rs 352
    Overheads = Rs. 28
    Net C.P. = Rs. 352 + Rs. 28
    = Rs. 380
    Profit = 20%
    We know = S.P. = (100 + Gain%)/100 × C.P.
    = (100 + 20)/100 × 380 =
    = Rs. 120/100 × 380
    = 12 × 38
    = Rs. 456
  • #5-ii
    C.P. = Rs.576; overheads = Rs.44 and loss = 16%
    Ans : C.P. = Rs. 576
    Overheads = Rs. 44
    Net C.P. = Rs. 576 + Rs. 44
    = Rs. 620
    Loss = 16%
    We know :
    S.P. = (100 - Loss%)/100 × C.P.
    = (100 - 16)/100 × Rs. 620
    = Rs. 84/100 × 620
    = Rs. 5208/10
    = Rs. 520.80
  • Qstn #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 %?
    Ans : S.P. = Rs. 637, Loss = 9%
    ∴ C.P. = (100 × S.P.)/(100 - 9)
    = 100/91 × 637
    = 100 × 7
    = Rs. 700
    Profit = 5%
    S.P. = (100 + Profit)/100 × C.P.
    S.P. = (100 + 5)/100 × 700
    = 105 × 7
    = 735
  • Qstn #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 %?
    Ans : In the first condition,
    S.P. of a radio-set = Rs. 605
    C.P. = 100/(100 + gain%) × S.P.
    = 100/(100 + 10) × Rs. 605
    = Rs. 100/110 × 605
    = Rs. (100 × 605)/110
    = 10 × 55
    = Rs. 550
    In the second condition:
    C.P. = Rs. 550
    Gain = 16%
    S.P. = (100 + gain%)/100 × C.P.
    = (100 + 16)/100 × Rs. 550
    = Rs. 116/100 × 550
    = Rs. (116 × 550)/100
    = 58 × 111
    = Rs. 638
    ∴ Radio should be sold at Rs. 638
  • Qstn #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.3150.
    Ans : In the first condition:
    S.P. of a Sofa-set = Rs. 2500
    Loss = 20%
    ∴ C.P. = 100/(100 - Loss%) × S.P.
    = 100/(100 - 20) × Rs. 2500
    = Rs. 100/80 × 2500
    = Rs. (100 × 2500)/80
    = (5 × 2500)/4
    = 5 × 625
    = Rs. 3125
    In the second condition:
    S.P. of the sofa-set = Rs. 3150
    C.P. of the sofa-set = Rs. 3125
    Gain = S.P. - C.P.
    = Rs. 3150 - Rs. 3125
    = Rs. 25
    Gain% = Gain/C.P. × 100
    = 25/3125 × 100
    = (25 × 100)/3125
    = 100/125
    = 4/5%
    = 0.8%
  • Qstn #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.
    Ans : In the case of first tape - recorder :
    S.P. = Rs. 990
    Gain = 10%
    C.P. = 100/(100 + Gain%) × S.P.
    = 100/(100 + 10) × Rs. 990
    = Rs. 100/110 × 990
    = Rs. 100 × 9
    = Rs. 900
    In the case of second tape-recorder :
    S.P. = Rs. 990
    Loss = 10%
    C.P. = 100/(100 - Loss%) × S.P.
    = 100(100 - 10) × Rs. 990
    = 100/90 × 990
    = 100 × 11
    = Rs. 1100
    Total C.P. of both the tape-recorders,
    = Rs. 900 + Rs. 1100
    = Rs. 2000
    Total S.P. of both the tape-recorders = Rs 990 + Rs. 990
    = Rs. 1980
    Loss on the whole transaction = C.P. - S.P.
    = Rs. 2000 - Rs. 1980
    = Rs. 20
    Loss% = Loss/C.P. × 100
    = Rs. 20/Rs. 2000 × 100 - 2/2%
    = 1%
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