Question

A small jar contained water, lime, and sugar in the ratio of 90:7:3. A glass contained only water and sugar in it. Contents of both (small jar and glass) were mixed in a bigger jar and the ratio of contents in the bigger jar was 85:5:10 (water, lime, and sugar respectively). Find the percentage of water in the bigger jar?

• A. 70
• B. 75
• C. 80
• D. 72.5
• E. 85

Answer 1

Answer: (E)

The problem involves mixing contents from two sources to determine the percentage of water in a final mixture. We are given information about the initial ratios and the final ratio after mixing. We need to solve for the percentage of water in the final mixture labeled as the "bigger jar".

First, let's consider the ratios. In the small jar, the ratio of water, lime, and sugar is 90:7:3. Let the common multiple be x. Therefore, the quantity of water in the small jar is 90x, lime is 7x, and sugar is 3x.

In the glass, we have only water and sugar. Since the contents are mixed such that the final ratio in the bigger jar becomes 85:5:10, no lime from the glass is needed. Hence, the entire lime part comes from the small jar, making it 7x.

Let the quantities in the glass be represented by y (water) and z (sugar). Thus, the equations based on the final ratio are as follows:

1. Water: 90x + y
2. Lime: 7x
3. Sugar: 3x + z

These need to add up to the total as per the final ratio 85:5:10.

The final ratio represents:
(90x + y) as 85 parts
7x as 5 parts
(3x + z) as 10 parts

We start with the lime component:

7x = 5 parts

Solve for x:

x = (5 / 7)

Now, substitute x in the ratios for water and sugar:

1. For water:

   90x + y = 85 parts

   
   

   90(5/7) + y = 85

   
   

   450/7 + y = 85

   
   

   y = 85 - 450/7

   
   

   y = (595/7) - (450/7)

   
   

   y = 145/7

2. For sugar:

   3x + z = 10 parts

   
   

   3(5/7) + z = 10

   
   

   15/7 + z = 10

   
   

   z = 10 - 15/7

   
   

   z = 70/7 - 15/7

   
   

   z = 55/7

Now, calculate the percentage of water:

Total parts = 85 + 5 + 10 = 100.

Percentage of water = (Water parts / Total parts) * 100% 
Percentage of water = (85 / 100) * 100% = 85%

Thus, the percentage of water in the bigger jar is 85%.