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ChandlerBong
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 13 May 2023, 06:40
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

53% (02:30) correct 47% (02:42) wrong based on 329 sessions

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A shopkeeper buys rice at $B per kg and sells it for $S per kg. He cheats while selling rice and gives 20% less than the actual weight. If he makes a profit of 30% in a transaction, then find the ratio of B to S.

A. 8:13

B. 10:13

C. 25:26

D. 26:25

E. 13:8
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C
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 13 May 2023, 07:43
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ChandlerBong
A shopkeeper buys rice at $B per kg and sells it for $S per kg. He cheats while selling rice and gives 20% less than the actual weight. If he makes a profit of 30% in a transaction, then find the ratio of B to S.

A. 8:13

B. 10:13

C. 25:26

D. 26:25

E. 13:8
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The shopkeeper buys 1kg of rice at $\(B\)

The shopkeeper sells 0.8kg of rice at $\(S\)

Selling price of 1kg of rice = $\(\frac{S *5}{4}\)

Profit on one kg of rice = \(\frac{5S}{4} - B = \frac{5S - 4B }{ 4}\)

Percentage Profit = \(\frac{5S - 4B }{ 4B} * 100\)

Given:

\(\frac{5S - 4B }{ 4B} * 100 = 30\)

\(50S - 40B = 12B\)

\(50S = 52B\)

\(\frac{\text{B}}{\text{S}} = \frac{50}{52} = \frac{25}{26}\)

Option C
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 22 May 2023, 08:58
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gmatophobia
ChandlerBong
A shopkeeper buys rice at $B per kg and sells it for $S per kg. He cheats while selling rice and gives 20% less than the actual weight. If he makes a profit of 30% in a transaction, then find the ratio of B to S.

A. 8:13

B. 10:13

C. 25:26

D. 26:25

E. 13:8

The shopkeeper buys 1kg of rice at $\(B\)

The shopkeeper sells 0.8kg of rice at $\(S\)

Selling price of 1kg of rice = $\(\frac{S *5}{4}\)

Profit on one kg of rice = \(\frac{5S}{4} - B = \frac{5S - 4B }{ 4}\)

Percentage Profit = \(\frac{5S - 4B }{ 4B} * 100\)

Given:

\(\frac{5S - 4B }{ 4B} * 100 = 30\)

\(50S - 40B = 12B\)

\(50S = 52B\)

\(\frac{\text{B}}{\text{S}} = \frac{50}{52} = \frac{25}{26}\)

Option C
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Please how do you come by the 5/4?? Thanks
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 22 May 2023, 12:50
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DelademAnku

Please how do you come by the 5/4?? Thanks
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DelademAnku The question stem states that the shopkeeper sells 20% less than the actual weight.

Assume that a buyer buys 1 pound of rice for $ S from the shopkeeper. In reality, the buyer ends up with only 0.8 pound of rice for $ S (and not 1 pound).

Therefore the price that the shopkeeper makes by selling 1 pound of rice = $ \(\frac{1}{0.8} * S\)

= $ \(\frac{10}{8} * S\)

= $ \(\frac{5}{4} * S\)

Hope this clarifies how the multiplication factor was obtained.
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 23 May 2023, 16:33
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gmatophobia
DelademAnku

Please how do you come by the 5/4?? Thanks

DelademAnku The question stem states that the shopkeeper sells 20% less than the actual weight.

Assume that a buyer buys 1 pound of rice for $ S from the shopkeeper. In reality, the buyer ends up with only 0.8 pound of rice for $ S (and not 1 pound).

Therefore the price that the shopkeeper makes by selling 1 pound of rice = $ \(\frac{1}{0.8} * S\)

= $ \(\frac{10}{8} * S\)

= $ \(\frac{5}{4} * S\)

Hope this clarifies how the multiplication factor was obtained.
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yess,i get it now. But why at all do you have to divide?
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 23 May 2023, 17:48
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ChandlerBong
A shopkeeper buys rice at $B per kg and sells it for $S per kg. He cheats while selling rice and gives 20% less than the actual weight. If he makes a profit of 30% in a transaction, then find the ratio of B to S.

A. 8:13

B. 10:13

C. 25:26

D. 26:25

E. 13:8
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The cost price of 1 kg is B
The selling price of 0.8kg(he cheats on 20%) is S, making selling price per kg = \(\frac{S}{0.8}\)

Now 30% profit means the selling price is 1.3B

Thus \(1.3B=\frac{S}{0.8}……..\frac{B}{S}=\frac{1}{1.04}=\frac{100}{104}=\frac{25}{26}\)

C
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 21 Sep 2024, 03:18
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CP=0.8 kg×₹B/kg=₹0.8B
SP=1 kg×₹S/kg=₹S

Profit=SP−CP=₹S−₹0.8B which is = 30%

Profit=30%×CP=0.3×₹0.8B=₹0.24B
₹S−₹0.8B=₹0.24B

now solve for B/S

₹S=₹0.8B+₹0.24B=₹1.04B

B/S = 1/1.04
B/S = 100/104
B/S = 25/26


OPTION B
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 23 Sep 2024, 16:29
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I am getting
Cost $b, let B equal 10. So cost is $10 per KG
SP is $S for 1kg
and the profit per transaction is 30% (i.e. $3), which means he sold 800 grams for 13$

to calculate price per 1KG:
$13 * 5/4 = 65/4 = 16.25 (price per KG is 16.25)

B : S
10:16.25 which is 8:13

How did you assume a transaction means selling the full KG?
Why would I not assume a transaction means he sold 800grams and then my answer is A
Unfortunatley
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A shopkeeper buys rice at $B per kg and sells it for $S per kg. 01 Oct 2025, 06:12
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