Question 10 - Figure it out - Page 19, 20 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 10 A milkman sold two buffaloes for ₹80,000 each. On one of them, he made a profit of 5% and on the other a loss of 10%. Find his overall profit or loss.Given, Selling Price of buffalos = ₹ 80,000 each Total Selling price (SP) = 2 × Selling price of 1 buffalo = 2 × 80,000 = ₹ 1,60,000 And, Total Cost Price (CP) = Cost Price of first buffalo + Cost price of Second buffalo Cost Price of first Buffalo Selling Price = ₹ 80,000 Gain Percentage = 5% Let the Cost Price = 𝑥 We know that, Gain = Selling Price − Cost Price Gain = 80,000 − 𝑥 Also, Gain Percentage = 𝐺𝑎𝑖𝑛/(𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒) × 100 5 = (𝟖𝟎,𝟎𝟎𝟎 − 𝒙)/𝒙 × 100 Cost Price of second Buffalo Selling Price = ₹ 80,000 Loss Percentage = 10% Let the Cost Price = y We know that, Loss = Cost Price − Selling Price Loss = y − 80,000 Also, Loss Percentage = 𝐿𝑜𝑠𝑠/(𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒) × 100 10 = (𝒚 −𝟖𝟎,𝟎𝟎𝟎)/𝒚 × 100 5𝑥 = (80,000 − x) × 100 5𝑥 = 80,00,000 − 100x 5x + 100𝑥 = 80,00,000 105𝑥 = 80,00,000 x = (𝟖𝟎,𝟎𝟎,𝟎𝟎𝟎)/𝟏𝟎𝟓 10y = (y − 80,000) × 100 10y = 100y − 80,00,000 10y – 100y = −80,00,000 − 90y = −80,00,000 90y = 80,00,000 y = (𝟖𝟎,𝟎𝟎,𝟎𝟎𝟎)/𝟗𝟎 ∴ Cost Price of first buffalo = ₹ 80,00,000/105 & Cost Price of Second buffalo = ₹ 80,00,000/90 Putting values in equation (1) Total Cost Price (CP) = Cost Price of first buffalo + Cost Price of Second Buffalo = (𝟖𝟎,𝟎𝟎,𝟎𝟎𝟎)/𝟗𝟎 + (𝟖𝟎,𝟎𝟎,𝟎𝟎𝟎)/𝟏𝟎𝟓 = 80,00,000 (1/90 " + " 1/105) = 80,00,000 ((105 + 90)/(105 × 9)) = 80,00,000 (195/(105 × 90)) = 8,00,000 (𝟏𝟗𝟓/(𝟏𝟎𝟓 × 𝟗)) = 8,00,000 (65/(105 × 3)) = 8,00,000 (13/(21 × 3)) = (𝟏,𝟎𝟒,𝟎𝟎,𝟎𝟎𝟎)/𝟔𝟑 = 165079.365 Thus, Total Cost price = 1,65,079.365 Total Selling price = 1,60,000 Since Cost Price > Selling Price, He Made a loss And, Loss = CP − SP = 1,65,079.365 - 1,60,000 = ₹ 5,079.365 Thus, milkman made an overall loss of approx ₹5,079