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:

Correct Answer: 80 lit

Explanation:

From the given data,

let the initial quantity of the mixture = 5x

Then,

$$\begin{gathered} 2 x - 16 3 x - 24 + 40 = 1 4 \\ 8 x - 64 = 3 x + 16 \\ 5 x = 80 \\ x = 16 lit \end{gathered}$$

 

Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.

Correct Answer: 91 liters

Explanation:

         Milk             Water 

         74%             26%        (initially) 

         76%             24%        ( after replacement) 

 

  Left amount = Initial amount  1 - r e p l a c e d a m o u n t t o t a l a m o u n t 

   24  = 26 1 - 7 k

=> k = 91 

Correct Answer: 22 lit

Explanation:

Let the capacity of the pot be 'P' litres.
Quantity of milk in the mixture before adding milk = 4/9 (P - 8)
After adding milk, quantity of milk in the mixture = 6/11 P.
6P/11 - 8 = 4/9(P - 8)
10P = 792 - 352 => P = 44.

The capacity of the pot is 44 liters.

Correct Answer: 15

Explanation:

Let quantity of mixture be x liters.

 

Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid =  x 1 - y x n units, Where n = no of operations . 

 

So, Quantity of Milk =  x 1 - 6 x 2  

 

Given that, Milk : Water = 9 : 16 

 

=> Milk : (Milk + Water) = 9 : (9+16)

 

=> Milk : Mixture = 9 : 25 

 

 Therefore,  x 1 - 6 x 2 x = 9 25

 

=> x = 15 liters

Correct Answer: 5 litres

Correct Answer: 9:1

Explanation:

Milk = 3/5 x 20 = 12 liters, water = 8 liters

 

If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.

 

Remaining milk = 12 - 6 = 6 liters

Remaining water = 8 - 4 = 4 liters

 

10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.

 

The ratio of milk and water in the new mixture = 16:4 = 4:1

 

If the process is repeated one more time and 10 liters of the mixture are removed,
then amount of milk removed = 4/5 x 10 = 8 liters.

 

Amount of water removed = 2 liters.

 

Remaining milk = (16 - 8) = 8 liters.

Remaining water = (4 -2) = 2 liters.

 

Now 10 lts milk is added => total milk = 18 lts

 

The required ratio of milk and water in the final mixture obtained

 

= (8 + 10):2 = 18:2 = 9:1.

Correct Answer: 120 litres

Explanation:

w i n e ( l e f t ) w i n e ( a d d e d ) = 343 169

 

It means  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 ) = 343 512    (since 343 + 169 = 512)

  

Thus,   343 x = 512 x 1 - 15 k 3

 

  343 512 = 7 8 3 = 1 - 15 k 3

 

  1 - 15 k = 7 8 = 1 - 1 8

  

Thus the initial amount of wine was 120 liters.

Correct Answer: 50 l

Explanation:

Let the tin contain 5x litres of liquids

5 x - 45 x 4 5 5 x - 45 x 1 5 + 45 = 2 5

=> 5(4x - 36) = 2(x + 36)

=> 20x - 180 = 2x + 72

=> x = 14 litres

Hence, the initial quantity of mixture = 70l

Quantity of liquid B

=  70 - 45 x 1 5 + 45

= 50 litres.

Correct Answer: 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%.

Correct Answer: 32 lit

Explanation:

Given mixture = 48 lit

Milk in it = 48 x 5/8 = 30 lit

=> Water in it = 48 - 30 = 18 lit

Let 'L' lit of water is added to make the ratio as 3:5

=> 30/(18+L) = 3/5

=> 150 = 54 + 3L

=> L = 32 lit.