# 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?

A) Rs. 25 per kg

B) Rs. 28 per kg

C) Rs. 30 per kg

D) Rs. 32 per kg

Answer

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Hint: We need to have basic understanding on Percentages concepts, Cost price, selling price, profit and loss concept to solve this problem.

Given that Purchase cost of 200kg rice = $200 \times 25 = $Rs. 5000

Selling price of 80 kg rice at 10% gain is

$ \Rightarrow $110% of price

$ \Rightarrow \dfrac{{110}}{{100}} \times Rs.25$

So money earned by selling 80 kg rice.

$ = 80 \times \dfrac{{110}}{{100}} \times 25 = Rs.2,200$

Selling price of 40 kg rice at a loss of 4%$ \Rightarrow 96$% of price

$ \Rightarrow \dfrac{{96}}{{100}} \times Rs.25$

Money earned by selling 40 kg $\dfrac{{96}}{{100}} \times 25 = Rs.960$

Remaining quantity = 200 - 40 - 80 = 80kg

Total gain required = 8%

$ \Rightarrow $Overall money to be earned thru sales $ = \dfrac{{108}}{{100}} \times $cost = $\dfrac{{108}}{{100}} \times 5000 = Rs.5,400$

[Cost = total money he invested in buying 200 kg of rice at Rs.25/kg]

Money to be earned through sale of remaining 80 kg $ = Rs.5400 - Rs2200 - Rs.960 = Rs2240$

Selling price of the remainder rice $ = \dfrac{{2240}}{{80}} = Rs.28/kg$

Note: While solving these kinds of problems we need to clearly understand the given problem and we have to focus on what we have to find and think about how we can find that.

Selling price (S.P.) = Cost price (C.P.) + Profit (or) Cost price – Loss

Gain % $ = \dfrac{{Gain}}{{C.P.}}$ and Loss %$ = \dfrac{{Loss}}{{C.P.}}$

Given that Purchase cost of 200kg rice = $200 \times 25 = $Rs. 5000

Selling price of 80 kg rice at 10% gain is

$ \Rightarrow $110% of price

$ \Rightarrow \dfrac{{110}}{{100}} \times Rs.25$

So money earned by selling 80 kg rice.

$ = 80 \times \dfrac{{110}}{{100}} \times 25 = Rs.2,200$

Selling price of 40 kg rice at a loss of 4%$ \Rightarrow 96$% of price

$ \Rightarrow \dfrac{{96}}{{100}} \times Rs.25$

Money earned by selling 40 kg $\dfrac{{96}}{{100}} \times 25 = Rs.960$

Remaining quantity = 200 - 40 - 80 = 80kg

Total gain required = 8%

$ \Rightarrow $Overall money to be earned thru sales $ = \dfrac{{108}}{{100}} \times $cost = $\dfrac{{108}}{{100}} \times 5000 = Rs.5,400$

[Cost = total money he invested in buying 200 kg of rice at Rs.25/kg]

Money to be earned through sale of remaining 80 kg $ = Rs.5400 - Rs2200 - Rs.960 = Rs2240$

Selling price of the remainder rice $ = \dfrac{{2240}}{{80}} = Rs.28/kg$

Note: While solving these kinds of problems we need to clearly understand the given problem and we have to focus on what we have to find and think about how we can find that.

Selling price (S.P.) = Cost price (C.P.) + Profit (or) Cost price – Loss

Gain % $ = \dfrac{{Gain}}{{C.P.}}$ and Loss %$ = \dfrac{{Loss}}{{C.P.}}$

Last updated date: 23rd Sep 2023

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