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A shopkeeper earns a profit of Rs 1 by selling one pen and earns a loss of 30 paise on sale of one pencil. In a particular month, he incurs a loss of Rs 5. In that month, he sold 40 pens. How many pencils did he sell in that period?
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Step-by-step explanation:
Given :-
To find :-
Solution :-
Given that :
Number of pens sold by the shopkeeper in a particular month = 40
Profit by selling a pen = Rs. 1
Profit on 40 pens = 40×1 = Rs. 40
Profit may be represented by a positive number
Profit on 40 pens = Rs. (+40)
Let the number of pencils sold by the shopkeeper be X
Loss by selling a pencil = 30 Paisa
Loss on all X pencils = X×30 Paisa
= 30X Paisa
Since it is loss it is represented by a negative number.
Loss on X pencils = (-30) Paisa
Total Loss in the month = Rs. 5 = Rs.(-5)
Therefore,
Total Loss = Profit on pens + Loss on pencils
=> Rs. -5 = (Rs. +40)+(-30X Paisa )
We know that
1 Rupee = 100 Paisa
=> -500 = 4000+(-30X)
=> -500 -4000 = -30X
=> -4500 = -30X
=> 4500 = 30X
=> 30X = 4500
=> X = 4500/30
=> X = 150
Therefore, pencils = 150
Answer :-
The number of pencils sold by the shopkeeper in the particular month is 150
Used Formulae:-
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Profit by +
Loss by -
Profit earned by selling 1 pen = ₹1
Profit earned by 40 pens = ₹40 , which we denote by + ₹40
Total loss given = Rs. 5, which we denote by -₹5.
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We know that,
Profit earned + Loss incurred = Total Loss
Therefore, Loss incurred = Total Loss - Profit earned
=> (-5) - (+40)
=> (-5) - 40
=> - 45 = - 4500 paise
Loss incurred by selling one pencil = 30 paise, which we write as -30 paise.
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Hence total loss incurred = -4500 paise
Loss on each pencil = -30 paise
So, number of pencils sold -->
[tex] = \frac{Total \: \: loss \: \: incurred}{Loss \: \: on \: \: each \: \: pencil } \\ [/tex]
[tex] = > \frac{ - 4500}{ - 30} \\ [/tex]
[tex] = > 150[/tex]
Therefore, she sold 150 pencils.
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