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02 Mar 2020, 02:29
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C
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Difficulty:
65%
(hard)
Question Stats:
61% (02:35) correct
39%
(03:07)
wrong
based on 309
sessions
History
Date
Time
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A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. What is the value of x?
A. 5
B. 6
C. 7
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
A. 5
B. 6
C. 7
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
02 Mar 2020, 03:29
Kudos
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There are x kg of rice in the store:
1st customer: \(\frac{x}{2} +\frac{1}{2}= \frac{(x+1)}{2}\\
\)
2nd customer \((x- \frac{(x+1)}{2})/2 +\frac{1}{2}= \frac{(x- 1)}{4 }+\frac{1}{2}= \frac{(x+1)}{4}\)
3rd customer: Half the remaining amount plus \(\frac{1}{2} \) kg of rice --then, no rice is left.
--> that means remaining amount must be 1 kg after first 2 customers bought it.
---> \(\frac{(x+1)}{2}+ \frac{(x+1)}{4}+1 =x\)
\(\frac{(3x+7 )}{4} =x\) --> \(x= 7 \)
The answer is C.
1st customer: \(\frac{x}{2} +\frac{1}{2}= \frac{(x+1)}{2}\\
\)
2nd customer \((x- \frac{(x+1)}{2})/2 +\frac{1}{2}= \frac{(x- 1)}{4 }+\frac{1}{2}= \frac{(x+1)}{4}\)
3rd customer: Half the remaining amount plus \(\frac{1}{2} \) kg of rice --then, no rice is left.
--> that means remaining amount must be 1 kg after first 2 customers bought it.
---> \(\frac{(x+1)}{2}+ \frac{(x+1)}{4}+1 =x\)
\(\frac{(3x+7 )}{4} =x\) --> \(x= 7 \)
The answer is C.
02 Mar 2020, 03:36
Kudos
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Third customer is getting 'k' amount.
k/2=1/2
k= 1Kg
Second customer will get = 1+1= 2kg
First customer will get = (1+2) + 1= 4Kg
x= 1+2+4=7Kg
k/2=1/2
k= 1Kg
Second customer will get = 1+1= 2kg
First customer will get = (1+2) + 1= 4Kg
x= 1+2+4=7Kg
Bunuel
