Question

Profit and loss
pls help urgently:)
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Answer 1

Question 1
₹
`42000`

Question 2
First table: ₹
`1920`

Second table ₹
`1200`

Explanation:

Question 1

I will use R and V to denote Ravish and Vineet respectively

• Let the original cost of the motorcycle for R be X

• R sold the bike to V for a loss of 28%

• Therefore the sales price for the bike to V is
  
  `X(1-0.28) = 0.72X`

• V bought the bike for
  `0.72X` and added repairs worth
  `1680`

• So total cost incurred by V = buying price + repairs
  `= 0.72X + 1680`

• He then sold it at a profit of
  `12.5\%(0.125)` which would be at a price of
  
  `(0.72X + 1680)(1+0.125) = (0.72X + 1680)(1.125) = 0.81X + 1890`

• Thus V sold back the bike at a price of
  `0.81X + 1890`

• We are given that this price is
  `35910`

• Equating the two we get
  
  `0.81X + 1890 = 35910\\`
  
  
  `0.81X = 35910 - 1890\\`
  
  `0.81X = 34020\\`
  
  
  `X = (34020)/(0.81)`
  
  
  `X = 42,000`

• So the cost price of the bike for R is ₹
  `\mathrm{42,000}\\`

Question 2

• Let the cost of the first table be X and that of the second table be Y

• We are given the total cost is 3120

• 
  `X + Y = 3120 \cdots [1]`

• We are given that the first table was sold for a loss of 15%. A loss of 15% implies that the table was sold for 85% of its original value

• 85% = 0.85

• So the first table was sold for 0.85X

• The second table was sold at a profit of 36%. Profit of 36% implies the table was sold at 136% of its original price

• 136% = 1.36

• So the second table was sold for 1.36Y

• We are given both tables were sold for the same price

• Therefore
  0.85X = 1.36Y
  
  
  `085X - 1.36Y = 0 \cdots [2]`

• We now have a set of two equations which we can use to solve for X and Y
  
  
  `X + Y = 3120 \cdots [1]`
  
  `0.85X - 1.36Y = 0 \cdots [2]`

• Eliminate one of variables by making their coefficients the same by multiplication by an appropriate value and adding/subtracting the resulting equations
  

• Choose Equation [1]

• Multiply by 1.36 throughout
  
  `1.36X + 1.36Y = 1.36 * 3120`
  
  
  `1.36X + 1.36Y = 4,243.20\cdots [3]`

• Add equations [2] and [3] to eliminate the Y term
  0.85X - 1.36Y = 0
  +
  1.36X + 1.36Y = 4243.20
  ------------------------------------------
  2.21X + 0 = 4243.20
  -------------------------------------------

• 
  `X = (4243.20)/(2.21)`
  
  X = 1920

• From equation [1], substituting for X we get
  1920 + Y = 3120
  
  Y = 3120 - 1920
  
  Y = 1200

So one table cost ₹1920 and the second table cost ₹1200 ANSWER