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A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method?
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A man by some orange at rate of five for Rs.1 and same number of orang...
**Given Information:**
- The man buys oranges at two different rates: 5 oranges for Rs.1 and 4 oranges for Rs.1.
- He sells all the oranges at a rate of 9 oranges for Rs.2.
- The total loss incurred during the transaction is Rs.30.
**Let's assume the number of oranges bought at the rate of 5 for Rs.1 as 'x' and the number of oranges bought at the rate of 4 for Rs.1 as 'y'.**
**Calculating the Cost Price:**
The cost price of 'x' oranges bought at the rate of 5 for Rs.1 = Rs.(x/5)
The cost price of 'y' oranges bought at the rate of 4 for Rs.1 = Rs.(y/4)
**Calculating the Selling Price:**
The selling price of 'x' oranges at the rate of 9 oranges for Rs.2 = Rs.(2x/9)
The selling price of 'y' oranges at the rate of 9 oranges for Rs.2 = Rs.(2y/9)
**Calculating the Loss:**
According to the question, the total loss incurred during the transaction is Rs.30. Therefore:
Loss = Cost Price - Selling Price
Loss = [(x/5) + (y/4)] - [(2x/9) + (2y/9)]
Loss = (4x + 5y - 10x - 10y) / 45
Given that the loss is Rs.30, we can write the equation:
(4x + 5y - 10x - 10y) / 45 = -30
Simplifying this equation, we get:
-6x - 5y = -135
6x + 5y = 135
**Shortcut Method:**
To find the number of oranges purchased, we can use the shortcut method.
Step 1: Multiply the selling price of 1 orange by the total number of oranges sold.
Rs.(2/9) * (x + y) = Rs.(2x/9 + 2y/9)
Step 2: Subtract the cost price of 1 orange from the selling price of 1 orange.
Rs.(2x/9 + 2y/9) - Rs.(x/5 + y/4) = Rs.[(8x + 18y - 9x - 9y) / 45]
Step 3: Set up the equation for the loss.
[(8x + 18y - 9x - 9y) / 45] = Rs.30
Simplifying this equation, we get:
- x + 9y = 150
**Solving the Equations:**
By solving the equations obtained from the shortcut method:
6x + 5y = 135
-x + 9y = 150
We can solve these equations to find the values of 'x' and 'y', which represent the number of oranges purchased at different rates.
Upon solving, we find that x = 45 and y = 15.
Therefore, the man purchased 45 oranges at the rate of 5 for Rs.1 and 15 oranges at the rate of 4 for Rs.1.
- The man buys oranges at two different rates: 5 oranges for Rs.1 and 4 oranges for Rs.1.
- He sells all the oranges at a rate of 9 oranges for Rs.2.
- The total loss incurred during the transaction is Rs.30.
**Let's assume the number of oranges bought at the rate of 5 for Rs.1 as 'x' and the number of oranges bought at the rate of 4 for Rs.1 as 'y'.**
**Calculating the Cost Price:**
The cost price of 'x' oranges bought at the rate of 5 for Rs.1 = Rs.(x/5)
The cost price of 'y' oranges bought at the rate of 4 for Rs.1 = Rs.(y/4)
**Calculating the Selling Price:**
The selling price of 'x' oranges at the rate of 9 oranges for Rs.2 = Rs.(2x/9)
The selling price of 'y' oranges at the rate of 9 oranges for Rs.2 = Rs.(2y/9)
**Calculating the Loss:**
According to the question, the total loss incurred during the transaction is Rs.30. Therefore:
Loss = Cost Price - Selling Price
Loss = [(x/5) + (y/4)] - [(2x/9) + (2y/9)]
Loss = (4x + 5y - 10x - 10y) / 45
Given that the loss is Rs.30, we can write the equation:
(4x + 5y - 10x - 10y) / 45 = -30
Simplifying this equation, we get:
-6x - 5y = -135
6x + 5y = 135
**Shortcut Method:**
To find the number of oranges purchased, we can use the shortcut method.
Step 1: Multiply the selling price of 1 orange by the total number of oranges sold.
Rs.(2/9) * (x + y) = Rs.(2x/9 + 2y/9)
Step 2: Subtract the cost price of 1 orange from the selling price of 1 orange.
Rs.(2x/9 + 2y/9) - Rs.(x/5 + y/4) = Rs.[(8x + 18y - 9x - 9y) / 45]
Step 3: Set up the equation for the loss.
[(8x + 18y - 9x - 9y) / 45] = Rs.30
Simplifying this equation, we get:
- x + 9y = 150
**Solving the Equations:**
By solving the equations obtained from the shortcut method:
6x + 5y = 135
-x + 9y = 150
We can solve these equations to find the values of 'x' and 'y', which represent the number of oranges purchased at different rates.
Upon solving, we find that x = 45 and y = 15.
Therefore, the man purchased 45 oranges at the rate of 5 for Rs.1 and 15 oranges at the rate of 4 for Rs.1.
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A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method?
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A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method?.
A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method?.
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A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method?, a detailed solution for A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method? has been provided alongside types of A man by some orange at rate of five for Rs.1 and same number of orange at rate of four for Rs.1, he sold all of them at the rate of nine for Rs.2 during the whole transaction he incurs loss of Rs.30. Find the number of oranges he purchased. shortcut method? theory, EduRev gives you an
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