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Q:

From  a container of wine, a thief has stolen 15 liters 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:

A) 75 liters B) 100 liters
C) 150 liters D) 120 liters

Answer:   D) 120 liters

Explanation:

\frac{wine(left)}{water(added)}=\frac{343}{169}

It means    \frac{wine(left)}{wine(initial\: amount)}=\frac{343}{512}       \left ( \because \: \: 343+169=512 \right )

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

\Rightarrow \: \: \frac{343}{512}=\left ( \frac{7}{8} \right )^{3}=\left ( 1-\frac{15}{k} \right )^{3}

\Rightarrow\: \: \left ( 1-\frac{15}{k} \right )=\frac{7}{8}=\left ( 1-\frac{1}{8} \right )

\Rightarrow \: \: K=120

Thus the initial amount of wine was 120 liters.

Q:

Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?

A) 193 : 122 B) 97 : 102
C) 115 : 201 D) 147 : 185
 
Answer & Explanation Answer: A) 193 : 122

Explanation:

Given the three mixtures ratio as (1:2),(2:3),(3:4)

(1+2),(2+3),(3+4)

Total content = 3,5,7

Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105

105/3 = 35 , 105/5 = 21 , 105/7 = 15

Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)

(35,70), (42,63), (45,60)

So overall mixture ratio of milk and water is

35+42+45 : 70+63+60

122:193

But in the question asked the ratio of water to milk = 193 : 122

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2 37
Q:

In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)

A) 80% B) 70%
C) 75% D) 62%
 
Answer & Explanation Answer: A) 80%

Explanation:

Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.

After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and

weight of a mixture = 60 + 15 = 75 gm.

So % of water = 100 x 60/75 = 80%.

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5 34
Q:

The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is ?

A) 6 ml B) 11 ml
C) 15 ml D) 9 ml
 
Answer & Explanation Answer: A) 6 ml

Explanation:

Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7
Let x ml of water be added
We get,

=> x=6
Hence 6ml of water is added.

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3 31
Q:

If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain ?

A) 25% B) 30%
C) 17% D) 19%
 
Answer & Explanation Answer: A) 25%

Explanation:

He has gain = 15 - 12 = 3,
Gain% = (3/12) x 100 = (100/4) = 25.
He has 25% gain.

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4 51
Q:

One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

A) 27 % B) 26 %
C) 29 % D) 21 %
 
Answer & Explanation Answer: A) 27 %

Explanation:

Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135  
X = 27

So, required percentage of benzene = 27 %

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5 97