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06 Aug 2024, 13:45
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D
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Difficulty:
85%
(hard)
Question Stats:
59% (03:02) correct
41%
(03:04)
wrong
based on 105
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A shop keeper buys rice at some price. Then, he packs the rice into packets of 1 kg, 2 kg and 3 kg. He sells the 3 kg packets at a profit of 20% and sells the 2 kg packets at a profit of 25%. The shopkeeper offers one 1 kg packet free with every packet of 3 kg. 1 kg packets are not sold separately. If the shopkeeper sells all the packets and ends up making no profit or loss, then the ratio of the number of 2 kg packets sold to the number of 3 kg packets sold is
A. 5:3
B. 8:5
C. 3:8
D. 4:5
E. 7:4
A. 5:3
B. 8:5
C. 3:8
D. 4:5
E. 7:4
05 Sep 2024, 10:32
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If the shopkeeper is selling the 2kg and 3kg both are profits, how does he end up making no profit or loss? Well, he's giving away 1kg packets for free, one for each 3kg packet he gives away. For him to end up making no profit, he needs to make an equivalent loss by giving away the 1kg packets. At this point, we can do the following:
The cost price of rice is proportional to the quantity (this is a reasonable assumption to make here, even though it isn't directly stated).
Let's say a kg of rice costs $1. (Safe to take these values here since we're only interested in ratios and not actual values)
Cost of 1kg packet = $1
Cost of 2kg packet = $2
Cost of 3kg packet = $3
Profit on 3 kg packet is 20%, so the selling price of a 3 kg packet is: $3.6
Profit on 2 kg packet is 25%, so the selling price of a 2 kg packet is: $2.5
In addition, a free 1 kg packet is given with each 3 kg packet. The cost of this 1 kg packet is $1.
(At this point, you can also start plugging in values to see where the cost price = the selling price. )
The total cost for 4 kg of rice (3 kg sold and 1 kg free) is $4
And the selling price for this 4kg of rice (3 kg sold and 1 kg free) is $3.6
So now we're making a loss of $0.4 for every 3kg of rice sold, which should be equal to the profit made from selling 2kg of rice.
Let x: number of 2kg packets sold and y: number of 3kg packets sold
0.5x = 0.4y => 5x = 4y => x:y = 4:5 (D)
.
The cost price of rice is proportional to the quantity (this is a reasonable assumption to make here, even though it isn't directly stated).
Let's say a kg of rice costs $1. (Safe to take these values here since we're only interested in ratios and not actual values)
Cost of 1kg packet = $1
Cost of 2kg packet = $2
Cost of 3kg packet = $3
Profit on 3 kg packet is 20%, so the selling price of a 3 kg packet is: $3.6
Profit on 2 kg packet is 25%, so the selling price of a 2 kg packet is: $2.5
In addition, a free 1 kg packet is given with each 3 kg packet. The cost of this 1 kg packet is $1.
(At this point, you can also start plugging in values to see where the cost price = the selling price. )
The total cost for 4 kg of rice (3 kg sold and 1 kg free) is $4
And the selling price for this 4kg of rice (3 kg sold and 1 kg free) is $3.6
So now we're making a loss of $0.4 for every 3kg of rice sold, which should be equal to the profit made from selling 2kg of rice.
Let x: number of 2kg packets sold and y: number of 3kg packets sold
0.5x = 0.4y => 5x = 4y => x:y = 4:5 (D)
.
General Discussion
11 Sep 2024, 08:44
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Let price per kg be P
Assume shopkeeper sold x 2 kg packs and y 3kg packs -
For the shopkeeper to make no profit or loss -
2P (1/4) x + 3P (1/5) y = P y (profit is on selling the 2 and 3 kg packs and the loss is due to giving the 1 kg packs for free; for no profit or loss these need to be equal)[2P -> cost of 2 kg, 1/4 -> profit of 25%, x -> number of 2kgs packs sold, 3P -> Cost of 3 KG, 1/5 -> profit of 20 %, y -> number of 3kgs packs sold, P -> cost of 1 kg rice, y -> number of 1 kg packs given away for free]
We need to find x/y
On solving the above equation,
x/y = 4/5
Assume shopkeeper sold x 2 kg packs and y 3kg packs -
For the shopkeeper to make no profit or loss -
2P (1/4) x + 3P (1/5) y = P y (profit is on selling the 2 and 3 kg packs and the loss is due to giving the 1 kg packs for free; for no profit or loss these need to be equal)[2P -> cost of 2 kg, 1/4 -> profit of 25%, x -> number of 2kgs packs sold, 3P -> Cost of 3 KG, 1/5 -> profit of 20 %, y -> number of 3kgs packs sold, P -> cost of 1 kg rice, y -> number of 1 kg packs given away for free]
We need to find x/y
On solving the above equation,
x/y = 4/5
