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%.

Answer 1

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%