From a container of wine, a thief has stolen 15 litres of wine and replaced it w

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Question
From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:
Options
A. 75 litres
B. 100 litres
C. 150 litres
D. 120 litres

Correct Answer

120 litres

Explanation

$\frac{w i n e (l e f t)}{w i n e (a d d e d)} = \frac{343}{169}$

It means $\frac{w i n e (l e f t)}{w i n e (i n i t i a l a m o u n t)} = \frac{343}{512}$ (since 343 + 169 = 512)

Thus, $343 x = 512 x {(1 - \frac{15}{k})}^{3}$

$\frac{343}{512} = {(\frac{7}{8})}^{3} = {(1 - \frac{15}{k})}^{3}$

$(1 - \frac{15}{k}) = \frac{7}{8} = (1 - \frac{1}{8})$

Thus the initial amount of wine was 120 liters.

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More questions

1. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options
A. 2 : 3
B. 1 : 1
C. 3 : 4
D. 4 : 3

Discuss

2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options
A. 65 sec
B. 89 sec
C. 100 sec
D. 150 sec

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3. What was the day of the week on 17^th June, 1998?
Options
A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Discuss

Correct Answer: Wednesday

Explanation:

17 ^th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3) ≡ 1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan.  Feb.   March    April    May      June 
(31 +  28  +  31   +   30   +   31   +   17) = 168 days

∴ 168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.

4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Options
A. 279
B. 283
C. 308
D. 318

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6.
For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?
Options
A. 15 : 14
B. 16 :15
C. 12 :11
D. 10 : 9

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7.
A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?
Options
A. 34%
B. 46%
C. 54%
D. 66%

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9.
An accurate clock shows the time as 3:00 after hour hand has moved 135�, the time would be?
Options
A. 7:30
B. 6:30
C. 8:00
D. 9:30

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10.
P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?
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A. Tuesday
B. Friday
C. Wednesday
D. Sunday

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Comments

⟹	5	A +	4	B	=	2	❨	6	A +	8	B	❩
	100		100			3		100		100

⟹	1	A +	1	B	=	1	A +	4	B
	20		25			25		75

⟹	❨	1	-	1	❩ A =	❨	4	-	1	❩ B
		20		25			75		25

Speed =	❨	240	❩m/sec = 10 m/sec.
		24

∴ Required time =	❨	240 + 650	❩sec = 89 sec.
		10

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Discussion

From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:

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5% of A + 4% of B =	2	(6% of A + 8% of B)
	3

Other number =	❨	11 x 7700	❩	= 308.
		275

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Discussion

From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:

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More in Aptitude:

Aptitude

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