3
Q:

# From the 50 liters of milk, 5 liters of milk is taken out and after it 5 liters of water is added to the rest amount of milk. Again 5 liters of milk and water is drawn out and it was replaced by 5 liters of water. If this process is continued  similarly for the third time, the amount of milk left after the third replacement:

 A) 45L B) 36.45L C) 40.5L D) 42.5L

Explanation:

General Formula:

Final or reduced concentration = initial concentration $\inline \dpi{100} \fn_cm \left ( 1-\frac{amount\: being\: replaced \: in \: each\: operation}{total\: amount} \right )^{n}$

where n is the number of times the same operation is being repeated. The "amount being replaced" could be pure or mixture as per the case. similarly ,"total amount" could also be either pure or mixture. Here amount being replaced denotes the quantity which is to be withdrawn in each time.

Therefore,    $\inline \dpi{100} \fn_cm 50\times \left ( 1-\frac{5}{50} \right )\times \left ( 1-\frac{5}{50} \right )\times \left ( 1-\frac{5}{50} \right )$

$\inline \dpi{100} \fn_cm 50\times \frac{45}{50}\times \frac{45}{50}\times \frac{45}{50}=50\times \left ( \frac{45}{50} \right )^{3}=50\times \left ( \frac{9}{10} \right )^{3}$

= 36.45 L

Q:

640 ml of a mixture contains milk and water in ratio 6:2. How much of the water is to be added to get a new mixture containing half milk and half water ?

 A) 360 ml B) 320 ml C) 310 ml D) 330 ml

Explanation:

Here total parts of milk and water in the solution is 6+2 = 8 parts
1part = 640/8 = 80
old mixture contains 6parts of milk and 2 parts of water(6:2).
To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.
i.e, 4 x 80 = 320 ml.

4 102
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

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

2 121
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%

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%.

5 90
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

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,
$\inline \fn_jvn \small \frac{4.5}{4.5+x}=\frac{3}{7}$
=> x=6
Hence 6ml of water is added.

3 121
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%