a man purchased some oranges at the rate of 3 for rs 40 and the same quantity at 5 for rs 60.if he sells all the oranges at the rate of 3 for rs 50.find his gain or loss percent
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let x oranges purchased at rate 3 for 40
and same x oranges purchased at rate 5 for 60
oranges 3 for 40 costs 40/3 rs for one orange
so x oranges costs 40x/3 rs
oranges 5 for 60 costs 12 rs for one orange
so x oranges costs 12x rs
now total cost = 40x/3 + 12x
= 76x/3
total oranges purchased = 2x rs
now selling price is 3 for 50
so one orange price is 50/3
price of 2x oranges = 50/3 × 2x
= 100x/3
so gain is 100x/3 - 76x/3
= 24x/3
= 8x
now 76x/3 ---------- 8x
then 100 ----------- ???
solving , gain percentage = 100 ×8×3 × x / 76x
= 31.57 %
and same x oranges purchased at rate 5 for 60
oranges 3 for 40 costs 40/3 rs for one orange
so x oranges costs 40x/3 rs
oranges 5 for 60 costs 12 rs for one orange
so x oranges costs 12x rs
now total cost = 40x/3 + 12x
= 76x/3
total oranges purchased = 2x rs
now selling price is 3 for 50
so one orange price is 50/3
price of 2x oranges = 50/3 × 2x
= 100x/3
so gain is 100x/3 - 76x/3
= 24x/3
= 8x
now 76x/3 ---------- 8x
then 100 ----------- ???
solving , gain percentage = 100 ×8×3 × x / 76x
= 31.57 %
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