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Question
A lady buys some pencils for Rs 3 and an equal number for Rs 6. She sells them for Rs 7. Find her gain or loss%.
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Solution
Let the lady buys x number of pencils for ₹ 3.
Cost price for one pencil, CP1 = `₹ 3/x`
Also, she buys same number of pencils for ₹ 6.
∴ Cost price for one pencil, CP2 = `₹ 6/x`
Now, total pencils = x + x = 2x
∵ She sells, 2x pencils = ₹ 7
∴ Selling price of 1 pencil = `₹ 7/(2x)`
Case I: We know that,
Gain = SP – CP
∴ Gain = `₹(7/(2x) - 3/x)`
= `₹((7 - 6)/(2x))`
= `₹ 1/(2x)`
∴ Gain % = `"Gain"/"CP" xx 100`
= `(1/(2x))/(3/x) xx 100`
= `100/(2 xx 3)`
= `50/3%`
Case II: Also, we know that,
Loss = CP – SP
Loss = `6/x - 7/(2x)`
= `(6 xx 2 - 7)/(2x)`
= `₹ 5/(2x)`
∴ Loss % = `"Loss"/"CP" xx 100`
= `(5/(2x))/(6/x) xx 100`
= `250/6`
= `125/3%`
∴ Net gain % = `125/3 - 50/3`
= `75/3`
= 25%
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