A grocer purchased 200 kg of rice at ₹25 per kg. He sold 80 kg of it at gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total investment.
Answers
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
A grocer purchased 200 kg of rice at Rs. 25 per kg. He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total investment ?
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Purchase cost =200×25=Rs5,000
Selling price of 80 kg rice - at 10% gain ⇒ 110% of price
⇒
100
110
×Rs25.
So money earned by selling 80 kg rice =80×
100
110
× 25=Rs2,200
Selling price of 40 kg rice at a loss of 4% ⇒ 96% of price
⇒
100
96
×Rs25
Money earned by selling 40 kg =40×
100
96
×25=Rs 960
Remaining quantity =200−40−80=80kg
Total gain required = 8% ⇒
Overall money to be earned thru sales =
100
108
× cost =
100
108
×5,000=Rs5,400
Money to be earned through sale of remaining 80 kg
=Rs5,400−Rs2,200−Rs960=Rs2,240
Selling price of the remainder rice =
80kg
Rs2,240
=Rs28/kg
CP of 1 kg rice = Rs25
CP of 200 kg = Rs(25×200)
= Rs5000
CP of 80 kg rice = Rs(25×80)
= Rs 2000
SP of 80 kg of rice= Rs( 110×2000/100)
= Rs 2200. [ 10% gain]
CP of 40 kg rice =Rs(25×40)
= Rs1000
SP of 40 kg rice = Rs(96×1000/100)
= Rs960. [10% loss]
To get total 8% gain,
Total SP should be 108% of 5000
= Rs(108×5000/100)
= Rs5400
SP of the remaining rice (i.e. of 80 kg)
= Rs(5400-(2200-960))
= Rs2240
Therefore,
Required rate...
=Rs 2240/80
=Rs28 ...per kg ( ans)