Question

a grocer purchased 200 kg of rice at 25 rs per kg his sold 80 kg of it at a gain of 10% and 40 kg at the loss of 4% at what rate per kg should he sell the remainder to gain 8% on his total investment


Step by step

Answer 1

200 kg of rice=₹25 per kg
TOTAL cost=200×25=₹5000
80 kg cp=80×25=₹2400
Gain=10%
Its sp=2400+(2400×10%)
=₹2640

40 kg cp=40×25=₹1000
Its loss=4%
Sp=1000-(1000×4/100)
=₹960
Remain rice in kg =200-(80+40)
=80kg
80 kg Cp=₹2400
TOTAL CP=₹5000
He have to gain 8% on total
5000+(5000×8/100)
=₹5900
Remain 80 kg Sp =5900-(960+2640)
=5900-3600
=₹2300
Remain rice kg=80kg
per kg cost=2300/80
=₹28.75 per/kg

Answer 2

hi ,Vedgya here is your solution

A grocer purchased 200 kg of rice at 25 rs per kg

∴1 kg rice cost Rs 200/25

∴CP of 80 kg rice =25 *80=Rs 2000

⇒gain of 10% on 80 kg rice

SP of 80 kg rice =[1+10/100]*2000 ........... {SP=(1+rate/100)*CP} for gain

⇒ Rs[ 110 * 20 ]= Rs 2200..............................[1]

CP of 40 kg rice=25 *40=Rs 1000

there is  loss of 4% on 40 kg rice

∴SP of 40 kg =[1-4/100]*1000 ........... {SP=(1-rate/100)*CP} for loss

⇒SP=Rs [96*10]=Rs 960..................................................[2]

∴ HIs total CP iof 200kg rice = [200*25] =Rs 5000

Now he wants a gained of 8% on 200 kg

His total SP will be [1+8/100]*5000 =108*50 =Rs 5400

∴rice left to be sold =[200-120]kg =80kg

SP of remaining 80 kg rice must be =Rs 5400-(Rs  2200+Rs 960) from{1}and {2}

⇒Rs 2240

∴Required rate of SP=  Rs 2240/80 =Rs28

Rs28 per kg  ans

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