Ex 8.2, 7 A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. (Hint: Find CP of each)
Given,
Selling Price of buffalos = 20000 each
Total Selling price (SP) = 2 × Selling price of 1 buffalo
= 2 × 20000
= 40000
Total Cost Price (CP)
= Cost Price of first buffalo + Cost price of Second buffalo
Cost Price of first Buffalo
Selling Price = 20000
Gain Percentage = 5%
Let the cost Price = 𝑥
We know that,
Gain = Selling Price − Cost Price
Gain = 20000 − 𝑥
Also,
Gain Percentage = 𝐺𝑎𝑖𝑛/(𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒) × 100
5 = (20000 − 𝑥)/𝑥 × 100
5𝑥 = (20000 − x) × 100
5𝑥 = 200000 − 100x
5x + 100𝑥 = 2000000
105𝑥 = 2000000
x = 2000000/105
Cost Price of first Buffalo
Selling Price = 20000
Gain Percentage = 5%
Let the cost Price = 𝑥
We know that,
Gain = Selling Price − Cost Price
Gain = 20000 − 𝑥
Also,
Gain Percentage = 𝐺𝑎𝑖𝑛/(𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒) × 100
5 = (20000 −𝑥)/𝑥 × 100
Cost Price of second Buffalo
Selling Price = 20000
Loss Percentage = 10%
Let the cost Price = y
We know that,
Loss = Cost Price − Selling Price
Loss = y − 20000
Also,
Loss Percentage = 𝐿𝑜𝑠𝑠/(𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒) × 100
10 = (𝑦 − 20000)/𝑦 × 100
5𝑥 = (20000 − x) × 100
5𝑥 = 200000 − 100x
5x + 100𝑥 = 2000000
105𝑥 = 2000000
x = 2000000/105
10y = (y − 20000) × 100
10y = 100y − 2000000
10y – 100y = −2000000
− 90y = −2000000
90y = 2000000
y = 2000000/90
∴ Cost Price of first buffalo = Rs 2000000/105
& Cost Price of Second buffalo = Rs 2000000/90
Putting values in equation (1)
Total Cost Price (CP)
= Cost Price of first buffalo + Cost Price of Second Buffalo
= 2000000/90 + 2000000/105
= 2000000 (1/90 " + " 1/105)
= 2000000 ((105 + 90)/(105 × 9))
= 2000000 (195/(105 × 90))
= 200000 (195/(105 × 9))
= 200000 (65/(105 × 3))
= 200000 (13/(21 × 3))
= 2600000/63
= 41269.83
∴ SP = Rs 40,000
& CP = Rs 41,269.83
Since CP > SP,
He Made a loss Loss = CP − SP
= 41269.83 − 40000
= 1269.83
∴ His overall loss is of Rs 1,269.83

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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